Classroom Instruction from A to Z

Classroom Instruction from A to Z
Barbara Blackburn

It isn't the strategy- it's how you use the strategy that makes a difference.

My goal is to give them information and let them internalize and give it back; not just force-fed info and make them regurgitate it. I want to give them an opportunity to internalize and express [their learning].

If they are allowed to choose how they will show that they understand the content, many students will invest more time and effort in the task.

Start with one idea and build on your success.

"Learning and teaching is messy stuff. It doesn't fit into bubbles." -Michele Forman

Think of data analysis like a triangle: classroom performance and standardized test scores should be evaluated together with a third data point, your teacher judgment.

Data shouldn't replace your judgment; it should help you make decisions.

Our students are not in their final state when we are teaching them.

The word but can serve as a red light or a stop sign for progress, The word and is like a green light.

Your language reflects your beliefs, and your students follow your model. If they hear you using words as an excuse, so will they.

Give students your BEST: belief, encouragement, support, time

Many students do not have a vision of anything more than where they are right now. You can help them create a vision for themselves through your words, actions, and activities so they they support each other.

"Students learn over half of what they know from visual images." -Mary Alice White

If your form of delivery isn't working, then find a different way to deliver it.

Rigor is not just about difficulty. Rigor is also about helping out students learn to critically think about their learning.

Complexity isn't about doing more work, it's about doing less drill and practice and more higher-level thinking activities.

Allowing students to take a zero reflects lowered expectations. It permits a student to get by without actually doing the work and says to the student, "You don't have to learn this."

Less is more. Give students small amounts of focused work that requires them to apply knowledge and evaluate information.

Our mode of instruction says, "Trust me. I know where we are going, so you don't need to." But students don't always respond positively to that approach.

Effective homework can be completed independently with minimal and appropriate support. If the assignment is too difficult, students are more likely to ask someone else to complete it for them.

"The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask him which he finds it hard to answer." -Alice Wellington Rollins

As you create questions for your students, remember to build in questions that are open ended, those that have more than one answer.

There are three types of reflection for students: reflecting on what they have learned, reflecting on how they learn, and reflecting on their progress.

Checking Prior Knowledge- First, she gives students three minutes to answer a short true/false questionnaire. Next, in pairs, students compare responses and use the textbook to check their answers. Each set of partners must rewrite any false statements so that they are true. She ends with a whole class discussion to ensure understanding.

During "Three Alike", she writes three words on the board or overhead projector. Students then have to explain what the words have in common.

I shuffle playing cards and each student takes one. While they are taking their cards, I make up the rules. Find your group by matching either the suit, the number, or picture. I prepare the deck ahead of time so that I will have the correct number of cards that will create the desired number of groups.

Just because we do something a lot doesn't mean it works.

Mathematical Mindsets: The Highlights {Part 5}

This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!

It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.

Enjoy!

Part 1 {here}
Part 2 {here}
Part 3{here}
Part 4 {here}

Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Jo Boaler

Chapter 9: Teaching Mathematics for a Growth Mindset

I believe in every one of them, that there is no such thing as a math brain or a math gene, and that I expect all of them to achieve at the highest levels. I love mistakes. Every time they make a mistake their brain grows. Failure and struggle do not mean that they cannot do math—these are the most important parts of math and learning. I don't value students' working quickly; I value their working in depth, creating interesting pathways and representations. I love student questions and will put these onto posters that I hang on the walls for the whole class to think about.

Math is a very creative subject that is, at its core, about visualizing patterns and creating solution paths that others can see, discuss, and critique.

To run a participation quiz, choose a task for students to work on in groups, then show them the ways of working that you value.

Once you have shown these to students, you can start them working. As they work together in groups, walk around the room watching group behavior, writing down comments.

As you circulate and take notes, quote students' actual words when they are noteworthy.

But it is even more important to communicate positive beliefs and expectations to students who are slow, appear unmotivated, or struggle. It is also important to realize that the speed at which students appear to grasp concepts is not indicative of their mathematics potential (Schwartz, 2001).

The most productive classrooms are those in which students work on complex problems, are encouraged to take risks, and can struggle and fail and still feel good about working on hard problems.

We must also resist valuing “effortless achievement”—praising students who are fast with math. Instead, we should value persistence and hard thinking.

When students fail and struggle it does not mean anything about their math potential; it means that their brains are growing, synapses are firing, and new pathways are being developed that will make them stronger in the future.

Instead of saying “You are so smart,” it is fine to say to students something like “It's great that you have learned that,” or “I love how you are thinking about the problem.”

My undergraduates have really worked on this and now praise people for having good thinking and for being accomplished, learned, hard working, and persistent.

There is always some logic in students' thinking, and it is good to find it, not so that we avoid the “failure” idea, but so that we honor students' thinking.

I recently read about a second-grade teacher, Nadia Boria, who offers this response to students when they ask for help: “Let's think about this for a minute. Do you want my brain to grow or do you want to grow your brain today?” (Frazier, 2015).

Mathematics tasks should offer plenty of space for learning. Instead of requiring that students simply give an answer, they should give students the opportunity to explore, create, and grow.

Open up math tasks:

• Instead of asking students to answer the question 1/2 divided by 1/4, ask them to make a conjecture about the answer to 1/2 divided by 1/4 and make sense of their answer, including a visual representation of the solution. As I described in Chapter Five , when Cathy Humphreys asked students to solve 1 ÷ 2/3 she started by saying, “You may know a rule for solving this question, but the rule doesn't matter today, I want you to make sense of your answer, to explain why your solution makes sense.” 
• Instead of asking students to simplify 1/3(2x + 15) + 8, a common problem given in algebra class, ask students to find all the ways they can represent that are equivalent.
• Instead of asking students how many squares are in the 100th case, ask them how they see the pattern growing, and to use that understanding to generalize to the 100th case

Ask students to discuss:

• Ways of seeing the mathematics 
• Ways of representing ideas 
• The different pathways through the problem and strategies 
• The different methods used: “Why did you choose those methods? How do they work?”

Encourage students to propose different methods to solve problems and then ask them to draw connections between methods, discussing for example, how they are similar and different or why one method may be used and not another. This could be done with methods used to solve number problems, such as those shown in Figure 5.1 , in Chapter Five .

Ask students to draw connections between concepts in mathematics when working on problems.

In my own teaching of mathematics, I encourage student creativity by posing interesting challenges and valuing students' thinking. I tell students I am not concerned about their finishing math problems quickly; what I really like to see is an interesting representation of ideas, or a creative method or solution. When I introduce mathematics to students in this way, they always surprise me with their creative thinking.

Teachers can encourage students to use intuition with any math problem simply by asking them what they think would work, before they are taught a method.

The teacher provocatively took the students' ideas and made incorrect statements for the students to challenge, and the class considered together all of the possible relationships of angles that preserve the definitions.

In the lesson in China, the teacher did not ask complete-this-sentence questions; she listened to students' ideas and made provocative statements in relation to their ideas that pushed forward their understanding. Her statements caused the students to respond with conjectures and reasons, thinking about the relationships between different angles.

If you give students the opportunity to extend problems, they will almost always come up with creative and rich opportunities to explore mathematics in depth, and that is a very worthwhile thing for them to do.

He points out that students currently spend 80% of the time they spend in math classrooms performing calculations, when they should instead be working on the other three parts of mathematics—setting up models, refining them, and using them to solve real problems.

In my own teaching experience, when I have asked students in classrooms to consider a situation and pose their own question, they have become instantly engaged, excited to draw on their own thinking and ideas. This is an idea for math classrooms that is very easy to implement and needs to be used only some of the time. Students should be able to experience this in school so that they are prepared to use it later in their mathematical lives.

It is so important that employees describe their mathematical pathways to others, in teams, because others can then use those pathways in their own work and investigations and can also see if there are errors in thinking or logic. This is the core of mathematical work; it is called reasoning.

When students act as a skeptic, they get an opportunity to question other students without having to take on the role of someone who doesn't understand.

Mathematical Mindsets: The Highlights {Part 4}

This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!

It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.

Enjoy!

Part 1 {here}
Part 2 {here}
Part 3{here}

Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Jo Boaler

Chapter 7: From Tracking to Growth Mindset Grouping

The strong messages associated with tracking are harmful to students whether they go into the lowest or highest groups (Boaler, 1997; Boaler, 2013a; Boaler & Wiliam, 2001; Boaler, Wiliam, & Brown, 2001).

In the Third International Mathematics and Science Study, for example, the United States was found to have the greatest variability in student achievement—that is, the most tracking. The country with the highest achievement was Korea, which was also the country with the least tracking and the most equal achievement. The United States also had the strongest links between achievement and socioeconomic status, a result that has been attributed to tracking (Beaton & O'Dwyer, 2002). Countries as different as Finland and China top the world in mathematics performance, and both countries reject ability grouping, teaching all students high-level content.

They found that the students who worked without advanced classes took more advanced math, enjoyed math more, and passed the state test in New York a year earlier than students in tracks. Further, researchers showed that the advantages came across the achievement spectrum for low-and high-achieving students (Burris, Heubert, & Levin, 2006). These findings have been repeated in study after study (see, for example, Boaler, 2013b). A substantial body of research points to the harmful effects of tracking, yet the practice is used in most schools across the country.

Most of the unmotivated and bad behavior that happens in classrooms comes from students who do not believe that they can achieve.

In all of my experience teaching heterogeneous groups of students, I have found that when students start to believe they can achieve, and they understand that I believe in them, bad behavior and lack of motivation disappear.

They discovered that when they gave open tasks, all students were interested, challenged, and supported. Over time the students they thought of as low-achieving started working at higher levels, and the classroom was not divided into students who could and students who could not; it was a place full of excited students learning together and helping each other.

The choice or the challenge must always be available to all students.

A one-dimensional math class, of which there are many in the United States, is one in which one practice valued above all others—usually that of executing procedures correctly.

In a multidimensional math class, teachers think of all the ways to be mathematical. No one is good at all of these ways of working, but everyone is good at some of them.

A stunning 97% of students from the traditional approach said the same thing: “Pay careful attention.” This is a passive learning act that is associated with low achievement (Bransford, Brown, & Cocking, 1999).

In the Railside classes, when we asked students the same question, they came up with a range of ways of working, such as:

• Asking good questions 
• Rephrasing problems 
• Explaining 
• Using logic 
• Justifying methods 
• Using manipulatives 
• Connecting ideas 
• Helping others

A student named Rico said in an interview, “Back in middle school the only thing you worked on was your math skills. But here you work socially and you also try to learn to help people and get help. Like you improve on your social skills, math skills, and logic skills” (Railside student, year 1).

Another student, Jasmine, added, “With math you have to interact with everybody and talk to them and answer their questions. You can't be just like ‘Oh here's the book, look at the numbers and figure it out.’” When we asked, “Why is that different for math?” she said, “It's not just one way to do it. It's more interpretive. It's not just one answer. There's more than one way to get it. And then it's like: ‘Why does it work?’” (Railside student, year 1).

A theme of the algebra course, and then later all the courses in the school, was multiple representations—students were frequently asked to represent their ideas in different ways, such as through words, graphs, tables, symbols, and diagrams. Students were also encouraged to color code, representing ideas in the same color—for example, using the same color for the x in an expression, diagram, graph, table, and paragraph (see Exhibit 7.4 ).

Many more students were successful because there were many more ways to be successful.

Although the standardized state tests the students had to take under the State of California requirements did not value multidimensional mathematics, the students achieved at high levels because they had learned to be successful in class and to feel good about mathematics. They also approached the state tests as confident problem solvers willing to try any question.

Students were able to get started through encouraging each other, rereading questions, and asking each other questions.

What is the question asking us?
How could we rephrase this question?
What are the key parts of the problem?

But teachers frequently need to inject a new piece of information or a new direction into the group work. In complex instruction, teachers do not try to do this by quieting the whole class. Instead, they call the recorder/reporters out to join the teacher for a huddle. The recorder/reporters meet as a group with the teacher, who can give information that each recorder/reporter takes back to the groups. This not only helps the teacher but also gives the students responsibility that is intrinsically valuable in helping them feel empowered mathematically.

An interesting and subtle approach recommended in the complex instruction pedagogy is that of assigning competence . This practice involves teachers' raising the status of students who they think may be lower status in a group—by, for example, praising something they have said or done that has intellectual value, and bringing it to the group's or the whole class's attention. For example, teachers may ask a student to present an idea or publicly praise a student's work in a whole class setting.

An activity I always like groups to work on before introducing any math work is to ask them to discuss together the things they do and don't like other group members to do and say when they are working in a group on math.

I find that when students think for themselves about positive and negative group discussions and come up with their own lists, they are more thoughtful about the ways they interact in groups.

I also start classes by explaining to students what is important to me. I say that I do not value speed or people racing through math; I value people showing how they think about the math, and I like creative representations of ideas.

Yet another way the Railside teachers encouraged group responsibility is a method that is shocking to some, but that really communicates the idea that group members are responsible for each other. Occasionally the teachers gave what they called “group tests.” Students would take the test individually, but the teachers would take in only one test paper per group (randomly chosen) and grade it. That grade would then be the grade for all the students in the group. This was a very clear communication to students that they needed to make sure all of their group members understood the mathematics.

As the approach they experienced became more multidimensional, they came to regard each other in more multidimensional ways, valuing the different ways of seeing and understanding mathematics that different students brought to problems.

Many parents worry about high achievers in heterogeneous classes, thinking that low achievers will bring down their achievement, but this does not usually happen. High achievers are often high achievers in the U.S. system because they are procedurally fast. Often these students have not learned to think deeply about ideas, explain their work, or see mathematics from different perspectives because they have never been asked to do so. When they work in groups with different thinkers they are helped, both by going deeper and by having the opportunity to explain work, which deepens their understanding. Rather than groups being lowered by the presence of low achievers, group conversations rise to the level of the highest-thinking students. Neither the high nor the low achievers would be as helped if they were grouped only with similar achieving students.

Two practices I have come to regard as particularly important in promoting equity, and that were central to the responsibility students showed for each other, are justification and reasoning.

Always give help when needed, always ask for help when you need it.

Chapter 8: Assessment for a Growth Mindset

Students with no experience of examinations and tests can score at high levels because the most important preparation we can give students is a growth mindset, positive beliefs about their own ability, and problem-solving mathematical tools that they are prepared to use in any mathematical situation.

Study after study shows that grading reduces the achievement of students.

The students receiving comments learned twice as fast as the control group, the achievement gap between male and female students disappeared, and student attitudes improved.

When we give assessments to students, we create an important opportunity. Well-crafted tasks and questions accompanied by clear feedback offer students a growth mindset pathway that helps them to know that they can learn to high levels and, critically, how they can get there.

I have seen this shift happen with many teachers with whom I have worked. It comes about when teachers are treated as the professionals they are and are invited to use their own judgment, helped by research ideas, to create positive learning and assessment experiences for their students.

He went on to describe how the valuing of different mathematics strategies allowed him to feel he could work with mathematics in any way he wanted, to explore ideas and learn about numbers.

When students are given scores that tell them they rank below other students, they often give up on school, deciding that they will never be able to learn, and they take on the identity of an underperforming student.

The grades and scores given to students who are high achieving are just as damaging. Students develop the idea that they are an “A student” and start on a precarious fixed mindset learning path that makes them avoid harder work or challenges for fear that they will lose their A label. Such students often are devastated if they get a B or lower, for any of their work.

When students develop interest in the ideas they are learning, their motivation and their achievements increase.

They found something amazing: a form of assessment so powerful that if teachers shifted their practices and used it, it would raise the achievement of a country, as measured in international studies, from the middle of the pack to a place in the top five.

In A4L, students become knowledgeable about what they know, what they need to know, and ways to close the gap between the two. Students are given information about their flexible and growing learning pathways that contributes to their development of a growth mathematics mindset.

One important principle of A4L is that it teaches students responsibility for their own learning.

Assessment for learning can be thought of as having three parts: (1) clearly communicating to students what they have learned, (2) helping students become aware of where they are in their learning journey and where they need to reach, and (3) giving students information on ways to close the gap between where they are now and where they need to be (see Figure 8.3 ).

The researchers concluded that a large part of the students' previous low achievement came not from their purported lack of ability but from the fact that previously they had not known what they should really be focusing upon.

The two main strategies for helping students become aware of the math they are learning and their broader learning pathways are self-and peer assessment.

If students start each unit of work with clear statements about the mathematics they are going to learn, they start to focus on the bigger landscape of their learning journeys—they learn what is important, as well as what they need to work on to improve.

Studies have found that when students are asked to rate their understanding of their work through self-assessment, they are incredibly accurate at assessing their own understanding, and they do not over-or underestimate it (Black et al., 2002).

In addition to receiving the criteria, students need to be given time to reflect upon their learning, which they can do during a lesson, at the end of a lesson, or even at home.

Peer assessment is a similar strategy to self-assessment, as it also involves giving students clear criteria for assessment, but they use it to assess each other's work rather than their own. When students assess each other's work they gain additional opportunities to become aware of the mathematics they are learning and need to learn.

Peer assessment has been shown to be highly effective, in part because students are often much more open to hearing criticism or a suggestion for change from another student, and peers usually communicate in ways that are easily understood by each other.

When students are given information that communicates clearly what they are learning, and they are asked, at frequent intervals, to reflect on their learning, they develop responsibility for their own learning.

An effective way for students to become knowledgeable about the ideas they are learning is to provide some class time for reflection. Ask students at the end of a lesson to reflect using questions such as those in Exhibit 8.4.

As I noted in Chapter Four, brain science tells us that the most powerful learning occurs when we use different pathways in the brain.

They tell us that mathematics learning, particularly the formal abstract mathematics that takes up a lot of the school curriculum, is enhanced when students are using visual and intuitive mathematical thinking, connected with numerical thinking.

In this realm there is one method that stands above all others in its effectiveness: the process of teachers giving students diagnostic comments on their work. One of the greatest gifts you can give to your students is your knowledge, ideas, and feedback on their mathematical development, when phrased positively and with growth messages.

Always allow students to resubmit any work or test for a higher grade

Share grades with school administrators but not with the students.

Use multidimensional grading.

Do not use a 100-point scale.

Do not include early assignments {review?} from math class in the end-of-class grade .

Do not include homework, if given, as any part of grading.

Mathematical Mindsets: The Highlights {Part 3}

This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!

It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.

Enjoy!
See Part 1{here}and Part 2 {here}

Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Jo Boaler

Chapter 5: Rich Mathematical Tasks

Teachers are the most important resource for students. They are the ones who can create exciting mathematics environments, give students the positive messages they need, and take any math task and make it one that piques students' curiosity and interest. Studies have shown that the teacher has a greater impact on student learning than any other variable (Darling-Hammond, 2000).

This is intrinsically interesting, but it's also true that most people I meet, even high-level mathematics users, have never realized numbers can be so open and number problems can be solved in so many ways. When this realization is combined with visual insights into the mathematical ways of working, engagement is intensified.

I have learned through this that people are fascinated by flexibility and openness in mathematics. Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people.

Teachers can create such mathematical excitement in classrooms, with any task, by asking students for the different ways they see and can solve tasks and by encouraging discussion of different ways of seeing problems.

They tried out ideas with each other, many of which were incorrect but helpful in ultimately forming a pathway to the solution.

Important observations that reveal opportunities to improve the engagement of all students:

• The task is challenging but accessible .
• The boys saw the task as a puzzle
• The visual thinking about the growth of the task gave the boys understanding of the way the pattern grew
• They had all developed their own way of seeing the pattern growth
• The classroom had been set up to encourage students to propose ideas without being afraid of making mistakes
• We had taught the students to respect each other's thinking
• The students were using their own ideas,
• The boys were working together
• The boys were working heterogeneously.

When we don't ask students to think visually, we miss an incredible opportunity to increase their understanding.

Additionally, students did not think they were finding a standard answer for us; they thought they were exploring methods and using their own ideas and thoughts, which included their own ways of seeing mathematical growth.

The researchers found that when students were given problems to solve, and they did not know methods to solve them, but they were given opportunity to explore the problems, they became curious, and their brains were primed to learn new methods, so that when teachers taught the methods, students paid greater attention to them and were more motivated to learn them.

The teacher taught them the methods when they were needed, rather than the usual approach of teaching a method that students then practiced.

When students are asked to think intuitively, many good things happen. First, they stop thinking narrowly about single methods and consider mathematics more broadly. Second, they realize they have to use their own minds—thinking, sense making, and reasoning. They stop thinking their task is just to repeat methods, and they realize their task is to think about the appropriateness of different methods. And third, as the Schwartz and Bransford research study showed, their brains become primed to learn new methods (Schwartz & Bransford, 1998).

When teachers are designers, creating and adapting tasks, they are the most powerful teachers they can be.

Making math tasks richer:
1. Can You Open the Task to Encourage Multiple Methods, Pathways, and Representations?
2. Can You Make It an Inquiry Task?
When students think their role is not to reproduce a method but to come up with an idea, everything changes (Duckworth, 1991).
The mathematics is more complex and exciting because students are using their ideas and thoughts.
3. Can You Ask the Problem Before Teaching the Method?
4. Can You Add a Visual Component?
5. Can You Make It Low Floor and High Ceiling?
When students are invited to ask a harder question, they often light up, totally engaged by the opportunity to use their own thinking and creativity.
6. Can You Add the Requirement to Convince and Reason?

In every math conversation, students were asked to reason, explaining why they had chosen particular methods and why they made sense. This opened up mathematical pathways and allowed students who had not understood to both gain understanding and ask questions, adding to the understanding of the original student.

She explains that there are three levels of being convincing (Boaler & Humphreys, 2005):

• Convince yourself 
• Convince a friend 
• Convince a skeptic 

It is fairly easy to convince yourself or a friend, but you need high levels of reasoning to convince a skeptic. Cathy tells her students that they need to be skeptics, pushing other students to always give full and convincing reasons.

When I ask students to play the role of being the skeptic, I explain that they need to demand to be fully convinced. Students really enjoy challenging each other for convincing reasons, and this helps them learn mathematical reasoning and proof.

Open up the task so that there are multiple methods, pathways, and representations. Include inquiry opportunities. Ask the problem before teaching the method. Add a visual component and ask students how they see the mathematics. Extend the task to make it lower floor and higher ceiling. Ask students to convince and reason; be skeptical.

Chapter 6: Mathematics and the Path to Equity

When we have gifted programs in schools we tell students that some of the students are genetically different; this message is not only very damaging but also incorrect.

Some people who have excelled in math choose not to be proud of the hard work and struggle they went through; they prefer to think they were born with a gift. There are many problems with this idea, one being that students who are successful through hard work often think that they are imposters because their achievement was not effortless.

The researchers went on to study the factors in the students' environment that led to different feelings of belonging, and they found that two factors worked against feelings of belonging. One was the message that math ability is a fixed trait; the other was the idea that women have less ability than men. These ideas shaped women's, but not men's, sense of belonging in math. The women's lowered sense of belonging meant that they pursued fewer math courses and received lower grades. Women who received the message that math ability is learned were protected from negative stereotypes—they maintained a high sense of belonging in math and remained intent on pursuing mathematics in the future.

We need all teachers to believe in all students, to reject the idea of some students being suitable for higher-level math and others not, and to work to make higher-level math available to all students, whatever their prior achievement, skin color, or gender.

Some teachers believe that some students cannot achieve at high levels of high school because they live in poverty or because of their previous preparation. In Chapter One I gave an example of high school teachers who made this argument to their school board, but teachers such as those at Life Academy are proving this wrong every day, through teaching high-level mathematics and positive messages to all students.

This is unfortunate, as we know that students who are advanced in math from an early age are more likely to drop math when they get the opportunity and achieve at lower levels.

Making math more equitable:
1. Offer all students high-level content
2. Work to change ideas about who can achieve in mathematics
The studies also show, encouragingly, that students who have a growth mindset are able to shrug off stereotyped messages and continue to success; this speaks again to the huge need for students, and teachers, to develop growth mindset beliefs about their own subjects and transmit growth mindset messages to students.
3. Encourage students to think deeply about mathematics
Unfortunately, the procedural nature of mathematics teaching in many classes means that deep understanding is often not available, and when girls cannot gain deep understanding they underachieve, turn away from mathematics, and often develop anxiety. Girls have much higher levels of anxiety about mathematics than boys do (Organisation for Economic Co-operation and Development [OECD], 2015), and the unavailability of deep understanding is one main reason for this (Boaler, 2014a).
4. Teach students to work together
When the Chinese American students found mathematics difficult, they were supported—first by knowing that everyone was struggling and then by working together to solve problems.
5. Give girls and students of color additional encouragement to learn math and science
The researchers found that the levels of anxiety held by women elementary teachers predicted the achievement of the girls in their classes, but not the boys (Beilock et al., 2009).
Researchers found that when mothers told their daughters “I was no good at math in school” their daughter's achievement immediately went down (Eccles & Jacobs, 1986). Teachers need to replace sympathetic messages such as “Don't worry, math isn't your thing” with positive messages such as “You can do this, I believe in you, math is all about effort and hard work.” Subsequent experiments showed that women underachieved when they simply marked their gender in a box before taking the test, compared to those who did not have to do that. Role models are extremely important to students—and one of the reasons it is so important to diversify the teaching force.
6. Eliminate (or at least change the nature of) homework
PISA, the international assessment group, with a data set of 13 million students, recently made a major announcement. After studying the relationships among homework, achievement, and equity, they announced that homework perpetuates inequities in education (Program for International Student Assessment [PISA], 2015).

Additionally, they questioned whether homework has any academic value at all, as it did not seem to raise achievement for students. This is not an isolated finding; academic research has consistently found homework to either negatively affect or not affect achievement. Baker and LeTendre (2005), for example, compared standardized math scores across different countries and found no positive link between frequency of math homework and students' math achievement. 

Mikki (2006) found that countries that gave more math homework had lower overall test scores than those that gave less math homework (Mikki, 2006). Kitsantas, Cheema, and Ware (2011) examined 5,000 15-and 16-year-olds across different income levels and ethnic backgrounds and also found that the more time students spent on math homework, the lower their math achievement across all ethnic groups.

When we assign homework to students, we provide barriers to the students who most need our support. This fact, alone, makes homework indefensible to me.

It is unfair and unwise to give students difficult problems to do when they are tired, sometimes even exhausted, at the end of the day. I wonder if teachers who set homework think that children have afternoon hours to complete it, with a doting parent who does not work on hand. If they do not think this, then I do not understand why they feel they can dictate how children should spend family time in the evenings.

The value of most math homework across the United States is low, and the harm is significant.


Homework should be given only if the homework task is worthwhile and draws upon the opportunity for reflection or active investigation around the home.

Mathematical Mindsets: The Highlights {Part 2}

This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!

It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.

Enjoy!

Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Jo Boaler

See Part 1 {here}

Chapter 3: The Creativity and Beauty in Mathematics

But mathematics, real mathematics, is a subject full of uncertainty; it is about explorations, conjectures, and interpretations, not definitive answers.

But Hersh points out that it is the questions that drive mathematics. Solving problems and making up new ones is the essence of mathematical life.

Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it—which is the essence of real mathematics—they become more deeply engaged and perform at higher levels.

What employers need, he argues, is people who can ask good questions, set up models, analyze results, and interpret mathematical answers. It used to be that employers needed people to calculate; they no longer need this. What they need is people to think and reason.

Parents often do not see the need for something that is at the heart of mathematics: the discipline. Many parents have asked me: What is the point of my child explaining their work if they can get the answer right? My answer is always the same: Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics.

Mathematics is a very social subject, as proof comes about when mathematicians can convince other mathematicians of logical connections.

Group and whole class discussions are really important. Not only are they the greatest aid to understanding—as students rarely understand ideas without talking through them—and not only do they enliven the subject and engage students, but they teach students to reason and to critique each other's reasoning, both of which are central in today's high-tech workplaces.

We also want students reasoning in mathematics classrooms because the act of reasoning through a problem and considering another person's reasoning is interesting for students. Students and adults are much more engaged when they are given open math problems and allowed to come up with methods and pathways than if they are working on problems that require a calculation and answer.

What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.

The powerful thinkers are those who make connections, think logically, and use space, data, and numbers creatively.

Chapter 4: Creating Mathematical Mindsets: The Importance of Flexibility with Numbers

The best and most important start we can give our students is to encourage them to play with numbers and shapes, thinking about what patterns and ideas they can see.

Successful math users have an approach to math, as well as mathematical understanding, that sets them apart from less successful users. They approach math with the desire to understand it and to think about it, and with the confidence that they can make sense of it. Successful math users search for patterns and relationships and think about connections. They approach math with a mathematical mindset , knowing that math is a subject of growth and their role is to learn and think about new ideas. We need to instill this mathematical mindset in students from their first experiences of math.

When students see math as a broad landscape of unexplored puzzles in which they can wander around, asking questions and thinking about relationships, they understand that their role is thinking, sense making, and growing.

Instead of approaching numbers with flexibility and number sense, they seemed to cling to formal procedures they had learned, using them very precisely, not abandoning them even when it made sense to do so. The low achievers did not know less , they just did not use numbers flexibly—probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts instead of interacting with numbers flexibly (Boaler, 2015a). The researchers pointed out something else important—the mathematics the low achievers were using was a harder mathematics. It is much easier to subtract 5 from 20 than to start at 21 and count down 16 numbers.

Notably, the brain can only compress concepts; it cannot compress rules and methods. Therefore students who do not engage in conceptual thinking and instead approach mathematics as a list of rules to remember are not engaging in the critical process of compression, so their brain is unable to organize and file away ideas; instead, it struggles to hold onto long lists of methods and rules. This is why it is so important to help students approach mathematics conceptually at all times.

The left side of the brain handles factual and technical information; the right side brain handles visual and spatial information. Researchers have found that mathematics learning and performance are optimized when the two sides of the brain are communicating (Park & Brannon, 2013).

The implications of this finding are extremely important for mathematics learning, as they tell us that learning the formal abstract mathematics that makes up a lot of the school curriculum is enhanced when students are using visual and intuitive mathematical thinking.

The antithesis of this approach is a focus on rote memorization and speed. The more we emphasize memorization to students, the less willing they become to think about numbers and their relations and to use and develop number sense.

The hippocampus, like other brain regions, is not fixed and can grow at any time, as illustrated by the London Black Cab studies (Woollett & Maguire, 2011), but it will always be the case that some students are faster or slower when memorizing, and this has nothing to do with mathematics potential. 

All subjects require the memorization of some facts, but mathematics is the only subject in which teachers believe they should be tested under timed conditions. Why do we treat mathematics in this way? We have the research evidence that shows students can learn math facts much more powerfully with engaging activities; now is the time to use this evidence and liberate students from mathematics fear.

It is important to revisit mathematical ideas, but the “practice” of methods over and over again is unhelpful. When you learn a new idea in mathematics, it is helpful to reinforce that idea, and the best way to do this is by using it in different ways. We do students a great disservice when we pull out the most simple version of an idea and give students 40 questions that repeat it. Worksheets that repeat the same idea over and over turn students away from math, are unnecessary, and do not prepare them to use the idea in different situations.

First, practicing isolating methods induces boredom in students; many students simply turn off when they think their role is to passively accept a method (Boaler & Greeno, 2000) and repeat it over and over again.

Second, most practice examples give the most simplified and disconnected version of the method to be practiced, giving students no sense of when or how they might use the method.

When textbooks introduce only the simplest version of an idea, students are denied the opportunity to learn what the idea really is.

When learning a definition, it is helpful to offer different examples—some of which barely meet the definition and some of which do not meet it at all—instead of perfect examples each time.

Students are given uncomplicated situations that require the simple use of a procedure (or often, no situation at all). They learn the method, but when they are given realistic mathematics problems or when they need to use math in the world, they are unable to use the methods (Organisation for Economic Co-operation and Development, 2013). Real problems often require the choice and adaptation of methods that students have often never learned to use or even think about.

One significant problem the students from the traditional school faced in the national examination—a set of procedural questions—was that they did not know which method to choose to answer questions. They had practiced methods over and over but had never been asked to consider a situation and choose a method.

It is also part of the reason that students do not develop mathematical mindsets; they do not see their role as thinking and sense making; rather, they see it as taking methods and repeating them. Students are led to think there is no place for thinking in math class.

In a second study, conducted in the United States, we asked students in a similar practice model of math teaching what their role was in the math classroom (Boaler & Staples, 2005). A stunning 97% of students said the same thing: their role was to “pay careful attention.” This passive act of watching—not thinking, reasoning, or sense making—does not lead to understanding or the development of a mathematical mindset.

Large research studies have shown that the presence or absence of homework has minimal or no effects on achievement (Challenge Success, 2012) and that homework leads to significant inequities.

Research also shows that the only time homework is effective is when students are given a worthwhile learning experience, not worksheets of practice problems, and when homework is seen not as a norm but as an occasional opportunity to offer a meaningful task.

Two innovative teachers I work with in Vista Unified School District, Yekaterina Milvidskaia and Tiana Tebelman, developed a set of homework reflection questions that they choose from each day to help their students process and understand the mathematics they have met that day at a deeper level. They typically assign one reflection question for students to respond to each night and one to five mathematical questions to work on (depending on the complexity of the problems).

Questions that ask students to think about errors or confusions are particularly helpful in encouraging students' self-reflection, and they will often result in the students' understanding the mathematics for the first time.

Number talks are the best pedagogical method I know for developing number sense and helping students see the flexible and conceptual nature of math.

A growth mindset is important, but for this to inspire students to high levels of mathematics learning, they also need a mathematics mindset. We need students to have growth beliefs about themselves and accompany these with growth beliefs about the nature of mathematics and their role within it.

Mathematical Mindsets: The Highlights {Part 1}

This book I would say has changed my thoughts on math, teaching, and teaching math more than any other I've read in my seven year career. I will recommend it and link it forever. I will have to post my highlighted notes from it in several posts because no one would ever scroll through all of it otherwise! There is just so much to process and that I will need to read over and over again- so many opportunities for growth and change!

It's only $10.71 for the paperback and $7.99 for the Kindle version. You NEED this book. But until you get your own, this should be enough to make you want more.

Enjoy!

Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching
Jo Boaler

Introduction: The Power of Mindset
When students get the idea they cannot do math, they often maintain a negative relationship with mathematics throughout the rest of their lives.

Research studies have established that the more math classes students take, the higher their earnings ten years later.

Research has also found that students who take advanced math classes learn ways of working and thinking—especially learning to reason and be logical—that make them more productive in their jobs. Students taking advanced math learn how to approach mathematical situations so that once they are employed, they are promoted to more demanding and more highly paid positions than those who did not take mathematics to advanced levels (Rose & Betts, 2004).

That single belief—that math is a “gift” that some people have and others don't—is responsible for much of the widespread math failure in the world.

Math is conveyed as a really hard subject that is uninteresting, inaccessible, and only for “nerds”; it is not for cool, engaging people, and it is not for girls. It is no wonder that so many children in schools disengage from math and believe they cannot do well.

Part of the change we need to see in mathematics is acknowledgment of the creative and interpretive nature of mathematics. Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making, and interpretation of methods; it is a set of ideas that helps illuminate the world; and it is constantly changing. Math problems should encourage and acknowledge the different ways in which people see mathematics and the different pathways they take to solve problems. When these changes happen, students engage with math more deeply and well.

They believe that mathematics ability is a sign of intelligence and that math is a gift, and if they don't have that gift then they are not only bad at math but they are unintelligent and unlikely to ever do well in life.

Chapter 1: The Brain and Mathematics Learning

If you learn something deeply, the synaptic activity will create lasting connections in your brain, forming structural pathways, but if you visit an idea only once or in a superficial way, the synaptic connections can “wash away” like pathways made in the sand. Synapses fire when learning happens, but learning does not happen only in classrooms or when reading books; synapses fire when we have conversations, play games, or build with toys, and in the course of many, many other experiences.

If brains can change in three weeks, imagine what can happen in a year of math class if students are given the right math materials and they receive positive messages about their potential and ability.

The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math, and everyone can achieve at the highest levels in school.

What I am saying is that any brain differences children are born with are nowhere near as important as the brain growth experiences they have throughout life.

Every second of the day our brain synapses are firing, and students raised in stimulating environments with growth mindset messages are capable of anything.

A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn. The very best opportunities to learn come about when students believe in themselves.

In other studies, researchers have shown that students' (and adults') mindsets can change from fixed to growth, and when that happens their learning approach becomes significantly more positive and successful (Blackwell et al., 2007).

The highest-achieving students in the world are those with a growth mindset, and they outrank the other students by the equivalent of more than a year of mathematics (see Figure 1.6 ).

It turns out that even believing you are smart—one of the fixed mindset messages—is damaging, as students with this fixed mindset are less willing to try more challenging work or subjects because they are afraid of slipping up and no longer being seen as smart. Students with a growth mindset take on hard work, and they view mistakes as a challenge and motivation to do more.

When students are given fixed praise—for example, being told they are smart when they do something well—they may feel good at first, but when they fail later (and everyone does) they think that means they are not so smart after all.

Praise feels good, but when people are praised for who they are as a person (“You are so smart”) rather than what they did (“That is an amazing piece of work”), they get the idea that they have a fixed amount of ability.

Telling students they are smart sets them up for problems later. As students go through school and life, failing at many tasks—which, again, is perfectly natural—they evaluate themselves, deciding how smart or not smart this means they really are. Instead of praising students for being smart, or any other personal attribute, it's better to say things like: “It is great that you have learned that,” and “You have thought really deeply about this.”

Chapter 2: The Power of Mistakes and Struggle

“Every time a student makes a mistake in math, they grow a synapse.”

One reason it is so significant is that it speaks to the huge power and value of mistakes, although students everywhere think that when they make a mistake it means that they are not a “math person” or worse, that they are not smart.

When teachers ask me how this can be possible, I tell them that the best thinking we have on this now is that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged, and this is the time when the brain grows the most.

First, the researchers found that the students' brains reacted with greater ERN and Pe responses—electrical activity—when they made mistakes than when their answers were correct. Second, they found that the brain activity was greater following mistakes for individuals with a growth mindset than for individuals with a fixed mindset.

The study also found that individuals with a growth mindset had a greater awareness of errors than individuals with a fixed mindset, so they were more likely to go back and correct errors.

It tells us that the ideas we hold about ourselves—in particular, whether we believe in ourselves or not—change the workings of our brains. If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake.

He points out: “Imperfection is a part of any creative process and of life, yet for some reason we live in a culture that has a paralyzing fear of failure, which prevents action and hardens a rigid perfectionism. It's the single most disempowering state of mind you can have if you'd like to be more creative, inventive, or entrepreneurial.”

He also summarizes the habits of successful people in general, saying that successful people:

• Feel comfortable being wrong 
• Try seemingly wild ideas 
• Are open to different experiences 
• Play with ideas without judging them 
• Are willing to go against traditional ideas 
• Keep going through difficulties 

It's also a good time to reinforce important messages—that when the student made this mistake, it was good, because they were in a stage of cognitive struggle and their brain was sparking and growing.

I said “Do you know what just happened? When you got that answer wrong your brain grew, but when you got the answer right, nothing happened in your brain; there was no brain growth.”

If we want students to be making mistakes, we need to give them challenging work that will be difficult for them, that will prompt disequilibrium.

In workshops with Carol Dweck I often hear her tell parents to communicate to their children that it is not impressive to get work correct, as that shows they were not learning.

This is a radical message, but we need to give students strong messages to override an idea they often get in school—that it is most important to get everything correct, and that correctness is a sign of intelligence.

When mathematics is taught as an open and creative subject, all about connections, learning, and growth, and mistakes are encouraged, incredible things happen.

The Classroom Chef

Mad props to fellow #MTBoS-ers +Matt Vaudrey and +john stevens for publishing and promoting their book!

Had to support my fellow Twitterfam and here is a little taste:


 The Classroom Chef: Sharpen Your Lessons, Season Your Classes, Make Math Meaningful 

Standards, curricula, and educational trends come and go, but good teaching is timeless.

Chapter 1 Finding Meaning in Math (or any) Class

Risk-taking began our evolution from catastrophic failures to incremental successes, and something incredible began to happen. Students started taking risks of their own.

Chapter 2 Giving Up on Processed Food

What we hope you’ll understand is that the pain is worth it—valuable even—because it pushes you to make a change.

The easiest way to manage a classroom is to keep students engaged and curious.

Students will care if you ask an interesting question.  If our students walk away from this unit with only one thing, it must be meaningful. On a deeper level, the questions we ask must hook the students without compromising the content.

Putting our students first gives us a better start in developing a lesson centered on them.

Explain the learning goal in the simplest way possible.

Boredom is the enemy in math class. Entertainment is not the same as engagement, and students spend most of their time at home seeking an entertaining experience. You—the teacher—have to offer a meaningful experience.

If I’m scripting out my entire lesson without room for the natural flow of a class, what value am I adding to the material?  By contrast, when the class is focused on a story, a question, or a weird idea, discussion flows naturally with the content propelling it.

When we do reach out for input, it’s usually for affirmation, not for improvement.

Chapter 3 There’s No Substitute for Preparation

Success in teaching, however—unlike success in calculus and Spanish—wasn’t tied to effort or desire.

According to the Wongs, students feel safe when they know what to expect; with routine, humans are comfortable. “Students want to know who you are as a person and if you will treat them with respect. It is important that you allay any fears they may have about being in your class. The best way to do this is to smile, exude caring, and communicate positive expectations.” The routine matters more than any lesson you teach.

Giving students a choice in their social interactions, as well as their academics, is one powerful way to establish a culture of respect for the individuals in your classroom. Train your students to listen to your full instructions without moving. Then when you say, “Go,” they can spring into action.

Instead of cold-calling students—or asking the whole class and waiting for raised hands—play a one-minute song, prompting students to talk to their partners. While the song plays, tap five or six students and say, “I’m calling on you.” When the song ends, call on each student, but give no indication if they’re correct or not.

Chapter 4 False Starts and Better Beginnings 

A long appetizer is not a time-suck, but a genuine opportunity to build interest for a lesson. Try something anyway. Your attempt to breathe life into a dusty topic will, at worst, be a welcome distraction to break up the day, or, at best, forge a deeper relationship between the content and the students.

Chapter 5 Serving Up Appetizers in Your Classroom “

Reflecting on my own career, I spent too much time validating the interesting answers and not enough time validating the right ones. When we—the teachers—remove the disparity in how we validate responses, our students benefit. A negative response to incorrect answers cements the idea that going back to correct an error is more foolish than stepping up to admit a mistake. However, giving Diane the opportunity not only to correct the error but also to make it better validated that it was fine to make a mistake, as long as she fixed it.

Remember, teaching is hard. Creating great learners is even harder. We owe it to our students to constantly seek meaningful ways to engage them and pique their curiosity.

Pseudo-context like this shows students that math is like vegetables: gross stuff that adults dress up in an attempt to make it attractive to kids.If they’re bored, they’ll find something else to do—and you won’t like what they find.

This is where we might clash with some of the latest educational trends; we would much rather students have a meaningful experience in class than restate a standard. If the lesson was meaningful enough to students that they can recall the theme of the day, that’s a step in the right direction.

Chapter 6 Barbie Zipline

Two questions we don’t ask often enough: What is this missing? How can it be better?

Chapter 7 Mullet Ratio

When all of the students can access the material at their own comfort level, that’s an effective math class. Every student has equal access to argue something none of them know about. When students are frustrated for too long, they begin to lose interest.

Chapter 11 The Plating Presentation is Everything! 

Jamie noticed two things: her students retained the information better when they discovered it, and crafting an environment where students discover the information is really tough at first.

At once, all the students rise and circulate through the other pods of desks. Once all students are seated, Mrs. Duncan says, “Think silently to yourself about what your friend did.” After a minute of silent think time, they discuss the work in front of them with their new table group. After mooching work from someone else in the class, students speak louder and more confidently about the math at their table.

The difference between a great math lesson and a great math teacher is the questions. A great math teacher can ask questions that get students interested in any lesson, much like a chef can transform even a grilled cheese sandwich into a Mediterranean pesto panini. Student responses will be all over the map (at first). And they may take some coaxing to navigate toward mathematical thinking and reasoning.

One of our jobs is to teach students how to think critically, ask for more information, and identify what’s important. They need our patience and guidance as they practice their critical thinking skills, especially early in the year.

We have two pieces of good news about student questioning: you can start tomorrow honing those skills, and your class culture will naturally become more accommodating. The process of teacher growth can start right away. I just made a commitment to learn, to be better, and I’m following through.

My kids can solve problems, but what is problem-solving? Simply put, it is what you do when you don’t know what to do.

Some of the typical questions I ask kids when they are finishing up their work are, “Does it make sense? If someone else sits down and looks at your work, will they be able to understand it? Did you go back into the context? Where is the proof? Can you show your thinking another way? What equation could you write that would represent your work?” In the lesson above, my standard was “looking for students to use knowledge of base ten and the relationship between addition and subtraction,” but the students didn’t see that as the focus.

 Chapter 12 How to Make Your Own Entrée

The attitude of I’m not a math person is far worse than the attitude I struggle in math. The latter is an admission of a current challenge, one that can be beaten with hard work, while the former implies some are born with a math muscle and some are not. This attitude is corrosive to our students, our own work ethic, and our society as a whole.

We’re saying use your best when you know your students need it.

When improving a lesson, aim for relevant and settle for interesting.

In handing over the ownership of the mistake to someone else, you empower the students to find the faults and correct them.

Students will naturally buy into a classroom culture when they feel like their voices matter, and these questions can help involve student voice: Is this working? What can we do better tomorrow? What did we like about the lesson? If there was one component to keep from this lesson, what would it be? If we could change something in the lesson, what would it be? Where could we have done better? Notice that these aren’t “I” questions; they are “we” questions. The responsibility for the tone of the classroom falls on the teacher. When students see you value the process of teaching, they will begin to value—and take responsibility for—the process of learning. The class culture, then, is the responsibility of all , but it begins with you involving your students in the process of creating a better learning experience. We must listen to our students’ point of view and use our professional judgment to determine what will work best. Creating a class culture where it is acceptable to appropriately criticize work is difficult, but necessary, for the growth we seek in our classrooms.

The best thing I learned from working with Mandy is that if I ask for input only from teachers in my content area, my lessons will never be truly diverse and inclusive.

Chapter 13 The World Needs More Education Geeks

Being a geek is all about being honest about what you enjoy and not being afraid to demonstrate that affection. It means never having to play it cool about how much you like something. It’s basically a license to proudly emote on a somewhat childish level rather than behave like a supposed adult. Being a geek is extremely liberating.

Chapter 14 Make Your Lessons Pop

What can I do to make this lesson more powerful?

How am I going to engage my students?

“Curiosity is far more powerful than engagement.”

Be committed to reaching all students by any means necessary.

“If you’re bored, the kids are definitely bored.” The opposite of bored isn’t entertained; it’s curious.

Chapter 15 Rethinking Assessment

This is an opportunity to show students that four core subjects don’t dictate their overall intelligence. I want my kids to know they are smarter than me about something.

Teaching is truly an art, but asking Russell to prove what he knew in a way we chose stole his imagination’s ability and desire to create. I learned from doing this type of assessment students will work as hard as they can when given the freedom to do so.

Instead of giving students more time to produce a better product, defeating The Suck encourages teachers to give less time to get a better product.

How can you do something student-centered in your classroom to allow students the freedom to prove what they know? And what would they do if they got to choose what’s comfortable for them? 

Model risk by trying new lessons; show students that you’ll deviate from what’s comfortable.

Model risk by showing vulnerability.

Model risk by encouraging guesses.

Chapter 16 Risks and Rewards 

If you don’t know the answer, take a guess. Take a risk. While it is true that classrooms are unforgiving places to learn to teach, the stakes are really low if your students like you.

Here’s how it looks: You try a risky lesson. It goes okay. You give a regular lesson. Students are more interested in your style because you tried something risky. You try a riskier lesson. It goes okay. Students are more interested in your risky lessons. You try a still riskier lesson. It goes awfully terribly horrible and ends in a fireball engulfing the village . You give three days of regular, safe lessons in a row, and a student asks, “Can we do something fun today?” Your students prefer risky lessons, even if they fail spectacularly. A fantastic belly flop is still better than stepping down the ladder into the shallow end for 180 days in a row. You’ll be easily forgiven by students, because your risk usually pays off, even if a few lessons don’t.

 Sir Arthur C. Clarke, author of 2001: A Space Odyssey , once said, “A teacher who can be replaced by a machine should be.”

 Teachers love talking about teaching; bad teachers love talking about bad teaching.

Unshakeable

I've been asking others for ideas on boosting school morale and +Shelli Temple suggested the book Unshakeable by Angela Watson. I read it and highlighted a lot of stuff. I really feel like I learned a lot of this already in my last years, and especially the last year. During the middle of last school year I was really close to a point of wanting to quit and find a different job. Which turned into a lot of personal growth on my part.

Now I think my school would benefit greatly if every other high school teacher in my school actually read and applied these but there were still some good reminders.

If it's not on the Internet then it didn't actually happen! Bold are the chapter titles and yellow are my most favorite highlights.

Unshakeable: 20 Ways to Enjoy Teaching Every Day...No Matter What

Angela Watson

Preface: Can anyone really enjoy every day in the classroom?

When you continually make a series of small positive choices, they eventually become strong, unshakeable habits that are an essential part of who you are.

The goal we keep striving for is to become unshakeable: so resolute in our determination to enjoy our work that no outside circumstance can steal that joy away.

1 Share your authentic self to bring passion and energy to your teaching

The real you is memorable.

Don’t try to turn off your “teacher brain” when you leave the school building. Be on the perpetual lookout for new stories to tell your students and consider how you can use your daily life experiences to make instruction more relatable and meaningful. Allow yourself to draw inspiration from your outside interests, and take those experiences back to the classroom to enhance your lessons.

Though you may be required to implement some lessons you dislike, always look out for opportunities to integrate activities that you do enjoy.

Variety is not the most important factor here—your enthusiasm is.

With unshakeable enthusiasm, you have to develop that trait in your whole self, not just the one compartment of your life that is devoted to work. You have to consciously make the choice to surround yourself with people and influences that inspire you to be a passionate person.

Energy is one of our most important resources, but most of us give very little thought as to how we manage it and produce more of it.

Firstly, passionate and accomplished people make time for things that replenish their energy levels.

Secondly, accomplished people tend to be extremely driven by a greater purpose.

2 Allocate your time and energy wisely through productive routines

Go to school each day with the mindset that you’re there to work.

Don’t start off your day by doing anything that puts you in a bad mood.

The other thing you should never do in the morning is any task that’s absolutely essential to the rest of your day.

Use your time before the first bell to do things that get you excited about your day and make you feel prepared for your lessons.

Lesson learned: planning time is not guaranteed, and if there’s a task that must be done in order for me to teach a lesson after my planning time, I’d better handle it the day prior!

It’s very important to decompress if you’re in a bad mood during the school day, because if you don’t, you’ll take your bad mood out on the kids and be too exhausted to teach the way you need to.

Alternatively, choose two specific times during the school day to look at work email, such as 10 minutes before school starts and 10 minutes before your planning period ends. That should be ample time to read and respond to anything that’s urgent and you’ll have no choice but to logout after a few minutes because students will start arriving.

3 Establish healthy habits for bringing work home and decompressing

Decide before the week starts what your game plan will be so when Friday comes, you don’t end up completely overwhelmed by all the things you didn’t accomplish.

Frame the task so that it gives you a meaningful payoff, whatever that might be.

4 Determine how to do what matters most and let go of the rest

You can do anything, but you can’t do everything.

There are many things you need to get done, but chances are, there’s one thing that’s more important than everything else.

Build faith in yourself that you can do hard and unpleasant things.

Whenever you are unsure of your priorities or unable to make a decision about how to use your time, ask yourself, Which of these tasks will benefit students the most? and dedicate more energy to those tasks. You can always feel good about time you spend helping kids and meeting their needs.

5 Go the extra mile for families (but don’t take forever to get there)

Remember, the objective here is to enjoy teaching every day. It is not to teach parents a lesson or make people behave the way they “ought to.” You can fight a battle without letting it consume you mentally, and you can also let things go for the sake of having peace. Sometimes the choice is to be right or to have a right relationship with someone else, and it’s worth considering which one is the case for you.

7 Do your part to create a positive school culture

It’s impossible to be happy during a moment in which you’re complaining. Impossible.

Complainers get irritated by people who continually find the good in things, so they tend to avoid optimistic personality types at all costs.

Refusing to listen to complaints means that those negative words will have no effect on you. Other teachers will be drawn to you as they witness how you manage to shut down complainers. Although it can be somewhat therapeutic for them to have someone to vent with, it is also a relief to be around a positive person who lifts them up.

Always keep moving the conversation forward.

You are too busy to waste time complaining, and there’s no need to hide that in order to appear friendly!

Remind yourself that rude and negative comments are usually not personal. Criticism is more of a reflection of the person who is saying it than the recipient. So if a colleague criticizes something about your teaching or tries to make you feel inferior, let it slide off your back. Tell yourself, This is his/ her problem, and it’s not about me. I refuse to allow people who dislike their job to make me dislike mine, too. I’m not permitting those rude comments to take up any more space in my mind. I’m dismissing them, and I’m replacing them now with thoughts about something that worked well in my classroom today.

You can suggest starting every staff and/ or team meeting with a couple of positive anecdotes so teachers can share classroom successes.

Another idea is to coordinate with your colleagues and send a weekly or monthly accomplishments email. Create a shared Google Doc or form where any staff member can quickly type in something that worked well in his or her classroom, and the person in charge just copies and pastes the text into an email or other newsletter which gets sent to the whole staff. bulletin board or dry erase board in the staff lounge and write notes about your accomplishments on it: Sam learned 10 new sight words today! We finally finished our holiday project! I figured out a system for handling make-up work!

You can also try a Teacher of the Week trophy with your entire faculty or just your grade level team. This should be done on a scheduled, rotating basis so that no one is left out. Announce at the beginning of the meeting who that week’s honored teacher will be, and make small pieces of stationery or notepads available for other staff members to write encouraging messages on. Collect the notes, place them in the trophy, and at the end of the meeting, award it to the teacher.

9 Let your vision define your value and measure of success 

Define your value as a teacher. Your worth does not come from someone else’s approval, and it does not come from how many kids you can get to pass a standardized test.

Each challenge you face—no matter how frustrating or mundane or impossible—is a chance to work toward a greater purpose that matters deeply to you.

Your vision must compel you to expend your most precious resource, energy. It must compel you to put your heart and soul into your work so that you get intrinsic satisfaction from completing it.

My personal vision for teaching (and for life) is to create things that are valuable for as many other people as possible.

I choose to view every aspect of my life as an opportunity to create.

Creating things of value is how I serve others and serve God. No matter how tired I am, if I view the task at hand as an opportunity to create, I can summon the energy to keep going.

You cannot allow other people’s actions to determine whether you feel good about your work, and recognition cannot be your primary motivation for working hard.

You must learn to reflect on and recognize your own work. Practice setting goals and rewarding yourself when you meet them. Build your personal learning network so that you have a group of educators to celebrate your accomplishments with. Don’t be shy about sharing your successes with your educator friends, and help them celebrate their small wins, too.

There is very little immediate gratification in our work, and we have to learn to live with that. Teaching is very much like the sowing of seeds… it takes months or even years to see the fruit of our labor at times. Often the payoff from our efforts won’t be evident until long after a student has left our classrooms.

Trust that your hard work will manifest in positive ways for a very long time to come. Stay focused on your vision. When you teach, you don’t always get a short term reward, but you do leave a legacy. You have a choice about what that legacy will be.

10 Uncover the compelling reason for every lesson you teach

Placing a problem in an artificial context for kids doesn’t necessarily mean the kids are going to think the work is relevant and important.

We make the mistake of believing that learning must be fun when in fact real learning is often hard work.

Figure out what students will gain from completing the task and stay focused on that as you plan and teach. Then share with students the benefit you’ve uncovered. When we truly believe in the purpose of an activity, we enjoy teaching more and do it with greater effectiveness.

I absolutely love this quote from Krissy Venosdale: “Posting a lesson target before teaching a lesson is like announcing what a gift is before it’s opened. Post a question. Bring curiosity and thinking back to the classroom!”

11 Create curriculum “bright spots” you can’t wait to teach

Don’t wait for something enjoyable to happen: plan for it! Be intentional. Create bright spots not only for your students, but also for yourself.

12 Incorporate playfulness and have fun with learning

No highlights here. :|

13 Build in periods of rest and downtime throughout your day

Sustainability is key, so always view your choices within the framework of what you can maintain over the long haul. How are your instructional practices right now going to affect your energy level later in the day? The week? The year? 5 years from now?

Remember: energy, not time, is your most precious resource.

Put simply, the person doing the most talking is the person doing the most learning. So if you’re spending almost your entire day at the front of the classroom leading a discussion or activity, you are the primary beneficiary of all that effort, because you’re the one doing all the work.

If you’re feeling overstimulated and overwhelmed, many of your students probably are, too!

Take time to think about your own limitations and plan around them. Experiment with different class time structures so that you can allow for low energy periods without sacrificing instructional quality.

Don’t put pressure on yourself to be constantly stimulating kids’ minds and pushing them to work harder. Often they, like us, will perform better when allowed to have a few moments to decompress, unwind, and regroup.

14 Construct a self-running classroom that frees you to teach

When students understand and follow predictable routines, you are free to become creative with your instruction.

Teach students to have confidence in themselves and be independent thinkers—if they’re not sure what to do, they should try to think of the solution first.

When giving feedback to kids, try turning your statements into questions and prompts. Instead of saying to a group, Nice work over there, I like the strategy you used for ___, ask the kids to reflect on their own work: Tell me how your group has chosen to solve ___. Instead of telling a child, Take a look at #3—that answer is incorrect, say, Would you tell me how you got the answer for #3? Not only will these questions get students talking instead of you, kids will also have the chance to reflect on and articulate their learning.

Always be on the lookout for moments when you summarize or review for students, and make a conscious decision to get their input instead.

Perhaps most importantly, don’t steal the struggle. It can be uncomfortable to watch passively as kids figure out an answer, but they often need time and silence so they can think. Resist the urge to talk students through every step of a problem, and instead just observe.

When our goal is constructing a self-running classroom, we must resist the urge to lecture students every time someone forgets their materials, interrupts, or makes an inappropriate noise.

My absolute favorite question, which works in just about any situation, is: What should you be doing right now?

Why are you sitting there doing nothing? becomes What should you be working on?

15 Motivate students to take charge of their learning

Any topic instantly becomes more fun and meaningful for everyone involved when the kids are given some ownership of how they learn.

I remember being incredibly anxious about one particular conference because we were going to have to tell a parent that her child was in danger of being retained because he wasn’t putting forth any effort in his work. My co-teacher said to me, “What are you nervous about? We’re not telling the parent that, the kid is!” And she sat that child right down at the conference table with us and proceeded to ask him questions like these: 

• How do you think you’ve been doing in class? 
• What areas do you think need improvement? 
• Why do you think that? 
• How has your homework been going? 
• Can you explain why you haven’t been doing it? 
• What about class time—can you show your mom your notes? 
• I see very few notes—would you tell us what’s happening with that? 
• How is all of this affecting your grades? 
• What do you think will happen if your grades don’t improve? 
• What needs to change in order for you to do better? 
• How can your teachers help you be more successful? 
• How can mom and dad help? 
• What is our plan moving forward, starting today, to help you improve? 

Those are pretty deep questions for an eight-year-old, but the child did a remarkable job responding. I remember sitting at that table absolutely astounded that neither I nor my co-teacher had to say anything negative about the child to his mother. We did not criticize, shame, tell on, or scold him. The whole conversation revolved around the child reflecting on his choices and then determining what he would do to improve… in front of three witnesses who were going to hold him accountable! 

We made no accusations and said nothing that the parent could throw in our faces later or complain to the principal about. Instead, we’d learned a lot about how the student viewed his school performance and the things that were distracting him and holding him back. We were able to end the conference with a firm plan for improvement that everyone present was fully invested in.

One way to tell who owns the learning is to observe who is asking the questions. If the teacher is doing all the questioning and the students are just answering, it’s possible the kids are being busy or compliant but are not truly taking ownership of what’s happening in the classroom.

16 Connect with kids and gain energy instead of letting them drain you

*******The kids have to be your greatest source of enjoyment as an educator.******* {I cannot stress this enoughhhhhh....why are you teaching when you don't like kids?}

Here’s what you do: download my free Daily Connections form from unshakeablebook.com, or just divide your class list into fifths. Each group of students will be assigned a day of the week. If you have 25 kids in your class, that means you’ll have 5 targeted kids for Monday, 5 for Tuesday, and so on. Each day, look at your list and see which kids you need to pay extra attention to that day. You could even pray for those students or think positive thoughts for them, if you choose.

17 Choose to love kids most when they act most unlovable

Here’s the conclusion that I finally learned the hard way: the teacher is always the most influential person in the room. It’s true! The teacher is the deciding element.

We as teachers have the power to balance out kids’ negative energy with our own positive energy

For the sake of the kids as well as your own sanity, students’ moods cannot be allowed to control your day.

If you help someone feel better, they will behave better.

As I relinquished control, I found that it was much easier to keep my peace and not take offense when dealing with defiant student behaviors.

I needed to spend more time identifying and addressing the reasons why children were acting out in the first place. Identifying kids’ triggers often tells me a lot about why they are misbehaving, which means I can then put supports in place to prevent problems from occurring.

So we need to understand that we are creating our own stress and unhappiness by comparing reality to our ideal.

Sometimes there is nothing inherently wrong with the child’s actions; it’s only their timing that’s inappropriate. 

You can avoid losing your cool every time the kids act out by reminding yourself, This is normal behavior for them, and needing more practice is normal! I can handle this!

Students often learn a lot more from practicing the right behavior than they do from being punished for the wrong behavior. Give them many, many opportunities to internalize your expectations.

Tell yourself, I will not let the out-of-control emotions of a child create out-of-control emotions in me. I will act and not react. I will not carry this incident with me all day long. Once it’s over, I’m letting it go.

A student might be acting out because she or he is: not clear about the expectations, wanting attention, bored, expelling excess energy, meeting a need for power or control, or trying desperately to avoid failure.

Always make it your goal to respond in love.

When you correct or respond to a child from love, your intention is completely different than if you respond from anger, annoyance, or disapproval.

Kids do not control your behaviors and emotions. You can choose to react to difficult students out of anger and spend most of your workweek in a rage, or you can choose to act from a place of love.

Never lose faith in your students and assume they are incapable of change. They must sense that you believe in them and their potential to improve.

These students are yours: take them as they are, and love them through the unlovable parts. Your patience and compassion has the potential to influence them for a lifetime.

18 Be truly present and look for the light bulb moments

Each time you’re pulled away from the physical or mental task you’ve decided is your most important focus right now, you're going to get more frustrated. You’re then going to take that frustration out on your students and anyone else in your path, creating more negativity as well as guilt.

When you’re fully present with kids, you process interruptions and unwanted behaviors differently in your mind and attend to them rather than your own agenda. Choosing to be present will create a level of patience that softens your mood as well as your words, body language, and tone.

Practice thinking only about the thing you’re supposed to be doing right now.

So, I’ve had to retrain myself to think of every plan I make as a simple guideline or outline that will be adjusted. In other words, I now plan to be flexible with my plan.

When you are focused on being tuned into kids, listening to kids, and responding to kids, they will learn naturally. Students will sense that they have your full attention and that you’re enjoying interacting with them, and their engagement (and achievement) will increase as a result.

Having someone’s time and energy, their full presence in both body and mind—is one of the most precious things you can offer to your students and other people you care about.

******A person with a blank or neutral expression could be hiding any emotion or be a million miles away mentally. But it’s nearly impossible to smile genuinely at someone if you are concentrating on something other than them. So if you want to try being more present with your students, just smile at them, and presence will naturally follow.**** {I soooo have to work on this. I suffer majorly from RBF. I did better last year but I still have so far to go.}

Project the energy to your class that you believe they are going to say something highly intelligent or thoughtful in response. I think you’ll notice immediately that some of your hesitant students feel more comfortable participating when they see a warm, welcoming smile that communicates, You have something important to say and I want to hear it.

You show up, day after day, and work these little miracles all day long without even realizing you’re doing it. You’re probably so focused on everything you didn’t do that you don’t realize how much you’ve actually accomplished. I am urging you—stop for a moment. Be present. See what you are doing. Really, truly, see it. Your work is important.

19 Re-write the story you tell yourself about teaching

If the story is not producing the results you want—peace, fulfillment, enthusiasm, and happiness—you cannot keep telling it.

I can’t keep a good attitude because I’m surrounded by negativity. New story: I choose to seek out people who inspire and uplift me.
New habit: Join a Facebook group for positive teachers who enjoy sharing ideas. 

I can never achieve a work-life balance.
New story: I manage my time and energy well, and create effective schedules.
New habit: Schedule time in the evening for family first, and use the leftover time for work.

I don't have time for getting the sleep I need.
New story: I make time for sleep because I know it creates more energy the next day.
New habit: Go to bed at 11 pm every night, regardless of what’s done or not done.

20 Innovate and adapt to make teaching an adventure

Most of us are too busy to regularly—or ever—step back from our daily routines and reflect on what is and isn’t working.

See if you can create a habit of reflecting on your work for just a few minutes each day. Ask yourself,

• What was the best part of this day? 
• What did I do to create or contribute to that success? 
• What was something I’d like to see go better next time? 
• How did I contribute to that obstacle or setback? 
• What can I do to improve? 
• What is the biggest lesson I learned today? 
• What am I most looking forward to tomorrow?

And when faced with systemic changes that are clearly bad for kids and teachers, your ultimate goal must be to maintain your enthusiasm for teaching. Complaining all day and obsessing all night does nothing to help you or the kids. It only creates burnout, and a burned out, jaded teacher is of no value to anyone.

You cannot make instructional decisions based on fear. You must be motivated by what is best practice and most effective for kids.