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.


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.


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.


How To...Teacher Moves

In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the tag to the right for more posts!

This is a collection of ideas and resources that I've read and wanted to use or have already used.

Get presenter’s to the front. One can only speak and the other can only point. They explain their thinking for one pair. Keep this light, safe and fun. If a student does not explain clearly enough or missing key elements, just let it go, they will most likely come out in later explanations.

Ask a student in the class to re-explain the presenter’s thinking.

"Get low" in the classroom so students don't look to you as the answer keeper.

Students write two truths and a lie about a function or math problem; see here for variations; include these type of questions on assessments.

Grade or give feedback with two or more highlighters.

When students say:

  • "What do I do next?" reply with "What do you think?"
  • "What do I do next?" reply with "How did you start?"
  • "Is this right?" reply with "What did you do?"
  • "Can you help me?" reply with "What should you do first?"
  • "I got the wrong answer." reply with "Can you find a mistake in your work?"
When asking students to share their responses with the class, say "Thank you" to acknowledge their answers without confirming if it's right or wrong. Practice that poker face!

Put self-assessment questions on quizzes and tests for students to reflect on what they think they know.

Include quadratic equations when teaching solving systems by substitution. {Great idea Meg!}

Help address gaps, spiral content, self-test, study, or review by giving students index card problems as they enter the room. You can make an answer key or have students line up or sit down based on the answers they get. {Thanks Nora!}

You can jump a few DOK levels by reversing the question....give students math problems and ask them what they solve instead of asking them to do the calculation. {Learn more from Fawn}

Here are three quick games to play when you have extra time in class that involve some strategy and logic. Always be prepared; this is a great back up. {Thanks to Julie!}

Sarah Carter shares four of her favorite review games. I know I always have my default games so it's great to mix it up with some new ideas. Here's another collection from Kim that I really loved and have gotten away from.

I am a huge fan of card sorts but this post really inspired me to kick mine up a notch. These ideas work great for INBs, individual studying, and pair practice. {Love these Brigid!}


Bell Ringers 3.0

One disadvantage of teaching in a tiny school is that you can't just reuse everything because you have the same students for three years in a row. So every year I have to find new first day of school activities and change things like my daily bell ringers.

Every year I find a new obsession so I would probably just change it anyway.

Updates from last year:
  • Changed the colors to match better
  • Took off the week labels {how is it that we got to school for 180 days but it's more than 36 weeks....so confusing}
  • Changed "Weigh It Wednesday" balance bender puzzles to "Work It Wednesday" brain teasers {thanks to weekly KenKen pdfs for educators!}
  • Changed "Thoughtful Q's Thursday" to "Number Talks Thursday" {excited but completely unprepared for these}
  • Updated estimation180 and WODB photos with new ones {thanks everyone who submits those!}

Here is THE powerpoint!

Now I have some questions. Last year I printed out front and back handouts every week for students. I know some people use Google Classroom for warm ups but I just don't think I can rely on our Internet on a daily basis. 

I know for sure I want students to write on Mental Math Mondays. 

I'm thinking I could use Google Forms for Tough Guess Tuesday estimation180 photos. Most people did not or could not calculate the error and error percentage. Do I need them to do that? Do I need them to write a description and a reason? How would I display the information in a useful way? 

Work It Wednesday are brain teasers that don't necessarily require writing...students could use dry erase markers on their desk. Do I need them to write anything?

For Number Talk Thursday, it's supposed to be mental so students could use marker again. But I also used some dot images so I could print those on paper for students to write on. I kind of like the idea of printing more than one of the same image so they can practice seeing different strategies. 

I know for sure I want students to use Plickers for Freaky Friday WODB. They love Plickers and I only use them a couple times of year. But do I want them to write their reasons? Or just call on random people to share their answers? I obviously don't grade these so do I NEED them to write?

I guess what I'm truly struggling with is....will they do it if I don't make them write it down and turn it in?

It would be great if I could use less paper...maybe fit one week per side, cutting the amount of copies I need in half. But my favorite part of last year's handouts was the questions I asked every week. They were random and let me get to know the students so much better. I guess I could use Google Classroom for those too...how would you do that? Every Friday post a question?

How do you guys handle your warm ups in a way that makes your heart smile? :-)


How To...Ask Better Questions

In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the tag to the right for more posts!

Learning is not a process of absorbing others' ideas, thoughts, or practices but involves uncovering one's own ideas, connecting new ideas to one's own thinking.

Questions that drive learning don't come from a list, they arise in response to student contributions.

But listing is my jam and I have to start somewhere!

Uncover Student Thinking

  • What do you notice?
  • What do you wonder?
  • What do you see?
  • What evidence do you have?
  • What is common?
  • What relationship do they have?
  • Can you convince me that...?
  • Can you clarify...?
  • What is the best way to graph this?
  • Which number would you change to change the graph the most?
  • 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?
  • What does _____ have to do with ____?
  • How are ____ and ____  alike? Different?
  • What makes you say that?
  • How did you get your answer to number,,,?
  • What should you be doing right now?
  • What should you be working on?

Student Voice/Reflection

  • 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?

Student Conferences

  • 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?

Teacher Reflection

  • What can I do to make this lesson more powerful?
  • How am I going to engage my students?
  • What am I missing?
  • How can I make this better?


How To...Build Relationship

In my own personal effort to #ExpandMTBoS, I'm starting a new category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the tag to the right for more posts!

"The kids have to be your greatest source of enjoyment as an educator." -Angela Watson 

If nothing else, I can say this is true for me. I really enjoy my students. I love getting to know them, asking them questions, hanging out with them all day, making them laugh, listening to their stories, having inside jokes, and just watching them grow into good humans. I think building relationship with students is one of my strong points.

Just don't judge me by my facial expressions, especially before 10:00 AM.

I have kind of a unique situation I guess. I went to the same school my entire life and then came back to teach here. My dad went here, my aunts, uncles, and cousins, and my grandpa even helped build the school. When I started my first year of teaching, my sisters were still in high school. Our numbers have dropped from around 250 when I graduated to about half that now. We are a small school in a small community. I am the only math teacher. So I have every student for three years in a row and some four. I pretty much know them before I meet them and have probably taught someone related to them or I went to school with someone related to them. I also have an excellent memory so I have no problem learning and remembering names.

But I still think I'm pretty good at getting students to like me.

I may not be good at building morale with my colleagues but I think I have some great routines with students {Thanks to Christie for inspiring me back with her latest post}:

  • I have names memorized on day one and I go out of my way to pronounce/spell them correctly and never call them the name of a relative.
  • I let my personality shine through in my powerpoint slides and worksheets and directions. I say please and thank you in my directions, I use smiley faces, sarcasm, and I anticipate their thinking..."Press Enter 3 times. Yes, you have to actually do it three times." "Read the directions below. This is all based on reading so you do have to actually read this time."
  • I have a school Instagram account for all students and I post pictures of classroom activities, group photos, photos from dance and spirit week and prom, announcements, etc.
  • My classroom is clean, colorful, organized, decorated, and always smells good. I know that most teachers don't go to my extreme with decorating but the students really appreciate seeing your personality and likes come out in classroom decorations. I'm looking at you, dude teachers. I have three air fresheners going at all times and I eliminate clutter as much as possible. I have whiteboards all around the room which also helps brighten the room. Students appreciate that I'm one of the few who care what my classroom looks and feels like.
  • My favorite thing to do is buy students their favorite candy for their birthday. I have 85 students but it works out to only be a couple dollars a week or so. I've also used a "Happy Birthday" chair cover from Dollar Tree and written a dry erase birthday message on their desk. I'm going to try to remember to do all three this year.
  • I also have a 'two nice things' rule. Anytime a students says something rude/mean about someone, they have to immediately say two nice things. This applies anytime I hear the rudeness (hallway, ball game, class) and regardless of who the person is or if they are in the room.
  • I dress cute. This may seem random but when the majority of the teachers wear khakis, tennis shoes, and t-shirts every single day, the teacher who wears an actual outfit stands out to students. Dress for the job you want, not the job you have,
  • I keep up with current trends, sort of. Language is one of my gifts so I pick up pretty easily on slang, abbreviations, etc. I'm not a big music person but I try to know popular stuff so that I can relate when students bring it up. Or even better, if they say a song lyric or movie quote and I can finish it. They are always impressed by that. Find students that have the same favorite TV shows so you can talk about them through the year. Have answers ready to go for your favorite everything because it will come up at some point. Also be prepared to discuss tattoos, drinking, piercings, parties, drugs, etc They want to know ALL THE THINGS.
  • Go to their stuff. I'm the cheer coach so obviously I go to every basketball game but even before I coached I did that too. Also I like basketball and we were really good. But I also try to hit up volleyball games and stuff too. The more kids that ask you about an event, the more likely you should go.
  • Ask them questions and then actually remember the answers. I love to talk to students about what they want to be when they grow up and come back to that throughout the year. Also, most kids are known for something...a hobby, talent, music obsession, book nerd, athlete, etc. It's really easy to find something to connect with them about. But remembering and building on that are what sets you apart. Which, if they matter to you, is pretty easy to do.
  • Have a sense of humor. I've really got to pull back on my sarcasm but making people laugh is the easiest way to connect. You do you!
  • Show excellence in your job. I never miss a day of school. {I have an amazing immune system, no husband, and and no kids} I plan out every period, all period long. I try to learn new technology. I try to find cool things on Pinterest. Students know that I'm actively working to be better at my job and they know I really want them to learn.
  • Listen to their stories. Our gut reaction is to give adulty advice, and I do that too, but really listen and try to ask questions before giving answers.
  • I always have a small amount of seniors 5-9 in class, on my Student Council, or on my cheer squad. I make little goody bags for each one. They are almost always girls so they usually consist of ponytails, bobby pins, safety pins, hand sanitizer, mints, flossers, travel toothbrushes, tissues, etc. This year I even made a little real life meaning to go along with each item. Now do not be overwhelmed by this because gift giving is my love language, Dollar Tree is my love language, and like I said, I have very small class sizes.
  • Every Monday I ask students about their weekend. Sometimes I ask every person in class or sometimes a few students monopolize the whole conversation. I don't mind and I think it's a nice way to start the week. Now students often ask me about my weekend and they know my usual routine is groceries, clean, church, tv, and naps. If I actually do anything interesting, I make sure to tell them.
  • I used the Remind app as often as possible: quizzes, tests, any sort of deadline, dress up days, assemblies, early dismissals, money due, things for sale, scholarship deadlines, school events, picture day, when I am out for PD, to tell them good luck on ACT day, to tell them to drive safely home from prom, to wish them happy holidays throughout the year etc.
  • I started high fiving every student at the door last year but it fell to the wayside. I still always greet them at the door in some way though.
  • Give students compliments but only when you mean them. This is just something personal for me but I try to give students compliments as often as I can. But not if I don't mean it. If someone gets a drastic haircut that I don't like, I make sure to notice it without complimenting. "I see you got a haircut. Do you like it?" I want them to feel noticed but I'm not going to lie. I get a lot of compliments from students and I sure wouldn't want to feel like they were lying to me either.
  • Dress up for those silly spirit week days. I am the Student Council advisor so it would be pretty bad if I didn't participate. But I am 1 of 2 teachers who actually do. Two. How do we expect students to have school spirit and pride when we don't? Students love to see you look silly- it makes you human. So let them teach you that new dance move or try to rap that song. Let them know you can let your guard down and have a good time.
  • And my number one tip.....don't be a teacher if you don't like teaching, if you don't like students, or if you don't think students will ever amount to anything. I don't know why this has to be said but just don't. You're making everything worse and you should just go find yourself a cubicle somewhere and sit down.
New Ideas
  • I'm wanting to send out good news postcards this year! I've thought about it for a couple years, maybe I will actually do it.
  • Use Remind to wish students Happy Birthday!

Basically it comes down to this...I try. I make an effort to care and show that I care.

And that's pretty cool.


INB Goodies

Every year I change my table of contents for my INB so you'll be glad to know this year is no different. See past versions here.

I really liked the box split in half for page numbers. I did not like the boxes underneath each concept title. I did not like that I called it a skill and a concept on the same page....like what?

I simplified it and added more rows. {Fonts are ChunkFive Roman and Running for a cause} Another change I made came from a great PD strategy. I put a circle in front of each skill. I'm going to ask students to shade in the circle based on how confident they feel about doing it. I figure I'll ask three times, using a different color each time: the day after they learn it, after they take a quiz over it, and on study guide day. It's powerful to watch the circles fill up.

I'm really trying to build in regular reflection so that's one small way.

Another larger way is to have a reflection page for the whole unit. We always start a new unit with a table of contents page on the RHP, leaving the LHP empty. Seems like a great place to summarize the previous unit.

I stole all of this from Sarah Carter {see here and here} but I would still love your feedback. I used her reflection post to make changes.

Next on my reflection agenda is to steal Kathryn Belmonte's idea of student nominations. Please check out her presentation here and my summary here.

Does this count as a close? {Two birds. One stone.} I want to end class with reflection time but also use the idea of nominations as positive peer pressure to take it home and make it better. I obviously gave up on homework again but I really did like the idea of a reflection question. Maybe I will switch it up between asking on Google Classroom or Remind and the INB reflection assignment.



31 Days of Reflection Calendar

I have to begin by explaining how this post proves Sara Vanderwerf wrong. She presented this to us on Monday afternoon and told us to make our list in the next 24 hours or we wouldn't do it.

It took me 24x4 hours to actually do it but I did so na na boo boo on you.

I had already favorited this tweet from earlier in the week, not really knowing what it pertained to, just literally liking it.

I ended TMC with Sara's session on reflection. She recommended at least 1-5 minutes of daily reflection. She also recommended reflecting with another teacher. She and a colleague take a walk around the building each day after school. One of Sara's methods was to make a customizable calendar of 31 pictures she likes that reminds her of things she wants to be intentional about in her classroom. {There's that pesky i-word again,} She printed hers out and hung them on a binder clip in her classroom to flip through each day.

Well I jumped ALL over that. I mean think about my trigger words here.... "customizable", "make", "calendar", "printed", "binder clip".

For me, even stronger than pictures are quotes. I have always loved them. I filled up floppy disks with Notepad files of quotes pasted from the Internet. I have journals full of them. I screenshot them. They're my fave.

Please don't even be surprised that they are this color or chevron or that I made it pretty. {Font is Covered By Your Grace}

You. Already. Know.

Odd numbers are quotes and even numbers are things to do.

I CANNOT wait to print and laminate these {I can wait for the cutting part} and hang them up in my room. Most of them came from the book Unshakeable and my own blog post about baby steps I will take in the classroom this year. What better way to remind myself of all my grand plans than to literally look at them every day?

Here's to year 8: 8 is the number of new beginnings and 7 was my 7 year slump. I declare the best year yet with a newly reflective and intentional teacher!



#TMC16 Underwhelming Myself

It's inevitable that you will be overwhelmed at some point at TMC.

Either you're overwhelmed by all the ideas and strategies and things you must change immediately, overstimulation, fan-girling, getting up early and going to bed late, wearing real clothes, going out to eat for every meal, and so on.

At some point in those four days, my perspective shifted. I love how God's timing makes everything converge. Before TMC I read Unshakeable by Angela Watson and Mathematical Mindsets by Jo Boaler. One encouraged me, one overwhelmed me and upended what I thought I knew about teaching math.

Then when I go to TMC, I hear two specific things that echoed those books more than once:
  1. Time is not your most valuable resource, your energy is
  2. So be intentional with your time and your craft
So in an effort to underwhelm myself and be intentional, I'm going to share the big ideas that I'm overwhelmed inspired by and the baby steps that I will take this year, without feeling the need to change everything or change nothing.

  • When I read blog posts, I will actually comment on them
  • When I get on Twitter, I will answer a question or encourage someone
  • I will share resources on Twitter in addition to just asking questions
Collaborate with Elementary Teachers
  • Use our early release time to sit in on elementary meetings and see how they plan or RTI
  • Ask elementary teachers some favorite teaching strategies
  • Pick one course, probably Algebra I, and list pre-skills for each skill throughout the year
  • Use Kuta to create pre-assessments over the summer
  • Try to create intervention boards, if even just one board per unit
  • Number Talks
Explore Math
  • Try this on a small scale with my senior math class, especially great toward the end of the year
  • Also try The Mathematician Project!
Make It Stick
  • Actually read the book
  • Start the year by educating students on growth mindset and come back to it all year
  • Add self-assessment questions to quizzes and tests
  • Regularly incorporate reflection into our INBs or as homework through Google Classroom
  • Try an end of unit summary sheet for INB
  • Actually close the lesson
More Than Resources
  • Be more intentional with my blog posts...instead of just sharing resources, share how and why I created them 
  • Be deliberate in practicing my questioning skills and reflecting
  • Keep running Google Docs for each course to reflect on lessons, formative feedback for myself, and also share with the world
  • Make a 31 day calendar of pictures that remind you of things to intentionally focus on on a daily basis.
  • Follow people on Twitter that don't look like me
  • Create a place for students to talk and get out of the way
  • Read and engage in #educolor chats
Mathematical Mindsets
  • Repeat growth mindset
  • Continue not giving homework
  • Ask students to look for a visual first
Teacher Moves

For the first time, I didn't leave feeling star struck, so overwhelmed that I wanted to cry, afraid that I'm a terrible teacher, or guilty that I'm not doing enough.

I feel supported. These are my people. They've got my back. 

I've decided that I will no longer be overwhelmed by TMC but I will be inspired by the great amount of good work to do and I will get started!

And to quote one of my favorites, "I'm committing myself to this work for years, not months- and it's okay to have miles left to go."

Minneapolis was a lovely city! The weather was gorgeous, there were parks and grass and water everywhere. I did a lot of walking, shopping, and eating. I visited at least five different towns and enjoyed Augsburg College campus. I truly enjoyed myself so I hope you enjoy some pictures!

And I would NEVER forget our annual song:


#TMC16 Can't Turn Around

I've flown on a plane three times, TMC being two of those three. I'm still a little unfamiliar but mostly okay with how airports work.

Kind of like teaching.

I'm just walking around the airport following the crowd; I don't exactly know where I'm going but I'll read the signs and figure it out while I'm walking.

Kind of like teaching.

If I'm really lost, I could stand still and be upset. But that doesn't get me any closer to my destination. It's better for me to just stop and ask for help.

Kind of like teaching.

When the plane just sits on the ground for 30+ minutes, I can be upset that my time is being wasted, or I can do something productive with my time that is passing by anyway.

Kind of like teaching.

When I'm on the plane, I can do what I want to do like sleep or read a book and ignore everything around me. Or I can look out the window and enjoy and reflect on what's around me, what I see, and how I am part of an extraordinary, creative, very detailed, big picture.

Kind of like teaching.

When I'm driving on the Interstate, following the explicit GPS directions, and I miss a turn or make a wrong one, I could just pull over and give up. "Well. that's it guys, I'm just never going to get there." Or I just keep driving while the GPS gives me a new route to the same destination.

Kind of like teaching.

When I'm in a new city, I can go to all the same places like Wal-Mart, Target, Dollar Tree, and McDonalds. I'm comfortable with those. I know where everything is. I know how much things cost. Or I could go to new places like Lake Harriet, Lake Nokomis, Minnehaha Falls, Fat Lorenzo's, Noodle Company, Mesa Pizza, Davanni's, Broder's Pasta Bar, Mall of America, and Bubba Gump Shrimp and Co. I can see and enjoy things in moments that I can't get back, in moments that I'm not in my comfort zone.

You never know what you're going to get.

Kind of like teaching.

I can be overwhelmed by all the choices of streets, restaurants, and stores that I've never heard of, don't know how to get to, and don't know if I will like. Or I can pick one, plan a route, and try it. If I like it, I can go two nights in a row. If I don't like it, I can just not go there.

Kind of like teaching.

I can feel guilty about cost of traveling or I can be intentional about getting the most value out of the cost. I can feel guilty because I don't know how to fly a plane myself or I can be intentional about making the flight go as smoothly as possibly. I can worry about all the ways this plane could go down or I could focus on how amazing it is that this is my life and that traveling is so accessible and constantly improving. I can be afraid because I'm not in control of my own safety or the lives of everyone on the plane with me or I can choose to operate out of love instead of fear, to be the best passenger I can be, and to look on the bright side.

Kind of like teaching.

When I feel uncomfortable, afraid, guilty, upset, or lost, it kind of doesn't matter. I chose to drive to the airport. I chose to get on the plane. I chose to pick up a car and drive to a hotel.

All my choices led me here.

Why not choose the best? Why not choose to enjoy, to be grateful, to learn, to grow, to ask for help, to try something new, to take baby steps, to reflect, to plan new adventures year after year?

After all...

I can't turn around now.


#TMC16 My Favorites

My favorites is probably the best PD strategy I've ever seen: let teacher's sign up to share something short or medium that is their favorite. It's great for people who can't think of a whole session to present.

{Hedge} SnagIt: 1) Capture student thinking (parent buy in) 2) How to videos 3) Editing tool
Fuse App: transfer your mobile content to full TechSmith products over the same wifi connection, document camera http://bit.ly/HedgesStuff

{Debbie Boden} Ms. Pac Man Transformations by Robert Kaplinsky

{Sam Shah} Explore (or have your Ss explore it) at explore-math.weebly.com

{David Wees} It takes time to create good questions. We ask over 2.5 million questions throughout our career. You've already asked a lot but you still have a lot of time and thousands of questions to left ask.

{Connie Haugneland} Mission Trips to Rawanda to share teaching strategies from #mtbos with schools who have limited to no resources.

{Jonathon Schoolcraft} Use Plickers for checks for understanding at the end of class and for WODB

{Anna Blinstein} Flipped Classroom (Feedback Meetings) Creating Cultures of Thinking book bit.ly/29Lf9hm 20 minutes meetings every two weeks; singles, pairs, or triads; you or student takes notes; discuss assignments of past two weeks; later sessions incorporate overall progress in the course and how they've incorporated past feedback

{Dave Slabol} Maps and Math Splitting up cities into NFL zones with perpendicular bisectors; Geogebra or pencil/paper

{Joel Bezaire} The Math Game With The Lame Name variable analysis.info

{Greg Taylor} Turn popular songs into math songs. 1. Videos exist already. 2. Have students write lyrics. 3. Do it yourself.

{Jonathon Claydon} Varsity Math- t-shirts, stickers, lazer tag

{Heather Kohn} Engineering Design Process; Doing math in an engineering framework;

{Edmund Harris} Second math coloring book comes out November 29th with two lesson plans

{Sara Vaughn} Plug in your sharpener out in the hallway. Students come in pre-sharpened. Students in other classes stop by to sharpen. The noise is no longer a distraction. Kids who mess with it get caught on camera.

{Brian Miller} Blog past by karimkai "On Purpose" 'conversations that matter- use math to understand concepts that make them better citizens

{Denis Sheeran} I See Math gigs is.com Make Google presentation, white background, default text
Slide 1. Title Slide 2. Picture Slide 3. Vague Guiding Questions We're used to seeing math. Shared folder tinyurl.com/ISeeMath

Smarty Pins Game smartypins.withgoogle.com Mixes maps and trivia

{Tom Hall} We do a disservice to our students when we don't admit we could do better. We expect students to admit failure but how often do we?

{Amy Zimmer} Culture Setting Icebreaker
1. Groups of 3
2. One piece of paper and one writing utensil
3. Determine oldest to youngest
4. Youngest- scribe, next-time keeper, next- make everyone introduce themselves, eldest- reporter
5. Collectively determine a favorite book, movie, game
6. Popcorn the list and massage the answers
7. Have reporter introduce group and favorite book, movie, game

{Max Ray-Riek} Triangle Congruence using Transformations
Games to work through triangle congruence shortcuts.

{Sue Van Huttum} book

{Jeremy Bloch} Learning about Coding in Math Class, Bootstrap algebraic video game programming, Bootstrap 1 builds on coding, Bootstrap 2 is coding from scratch

{Glenn Waddell} Make a decision to live outside your comfort zone and face your fears. You can't face your fears once and beat them; you have to keep facing them regularly. Fear is what keeps us separated.

{Kathryn Belmonte} Students use post-it's to write positive  notes in a gallery walk for INB assignments. Giving students a audience for their work increases the level of work they produce.

1. Ask students for nominations.
2. Display nominated work on the document camera.
3. The nomination must give a reason for the nomination.
*Any nominee can accept or decline.

{Megan Schmidt} we are all hard on ourselves and we need to be cognizant of that in people of all professions.

{Hannah Mesick} Write upcoming birthdays on a birthday board; give 5 bonus points for any assignment; use a Happy Birthday chair cover and write a dry erase message; use birthdays as an analogy for function mapping to determine the difference between functions and relations.

#TMC16 Getting Triggy With It: Interactive Trig {Kristen Fouss}

Getting Triggy With It: Interactive Trig
Kristen Fouss
Saturday 2:45-3:45

1) Smartie Arc

2) Measure the angles of a triangle in radians; triangles equal 180 should equal 3.14 radians

3) Build the unit circle by building three for degrees, radians, and ordered pairs with patty paper; manipulate the party paper to form triangles in all four quadrants

4) Trig Wheel-two different colors, one in radians, one in degrees; cut out, cut dotted radius, and label;

5) Finger Trick

6) Stations

7) Jay Cutler timeline- write equation for graph and test it in Desmos

8) Plot your biorhythms

9) Interactive Quiz goo.gl/ntq6S0

#TMC16 Journaling and Writing in Mathematics {Anna Blinstein}

Journaling and Writing in Mathematics
Anna Blinstein
Sunday 4:00-5:00

What do you value in your classroom? How will more writing help you achieve this? What concerns do you have about more writing with students?

Writing helps:
-mathematical practices
-closes gender gaps (especially deeply reflective writing}

-Start small
-Get buy in
-Make it regular
-Give feedback
-Ask students to reflect on their writing

-ask on the bottom of quizzes/tests what question they were most proud of and which one was most challenging
-one thing I learned today is...
-name another lesson this reminded you of
-what's one thing you're the best at
-weekly reflection about something they've learned

Progress from short response to learning logs and journals, to formal write-ups.

Carmel Schettino's blog and rubrics

#TMC16 Using the Box Method {Anna Hester}

Using the Box (Area) Method to Create Coherence and Connections
Anna Hester
Saturday 4:00-4:30

The box method builds on the area model and creates coherence between operations.

Check out @gfletchy's multiplication video for background

Move from one arbitrary method (FOIL) to methods that connect and build (area model, box method).

Factoring Progression
GCF --> Difference of 2 Squares -->; Trinomials

#TMC16 "Just Enough" Approach to Intervention {Michelle Naidu}

A "just enough" approach to intervention for students with gaps in their mathematical understandings
Michelle Naidu
Morning Session 9:30-11:30

Day 1
What we know about differentiation:

What we wonder:

We're operating under the definition that differentiation is not changing any outcomes or standards but bringing students to grade level expectations. How do we build readiness before new grade level instruction?

*Snowball strategy to safely share writing and knowledge where the room corrects misunderstanding;  at least three times for struggling students.


The Planning Process
Determine outcomes and plan backwards <--> Plan better together <--> Discuss and reflect on changes for improvement

Instructional Pillars
Mastery Learning <--> Learner Readiness <--> Formative Assessment 
<--><-->Day 1 

Curriculum sort: literally print out standards from each grade level. Resort into piles of "things you
would like to teach together" which then become units. There is something powerful about figuring
out your own patterns in teaching rather than relying on a linear pre-determined list. Do your expectations match what the documents and standards actually say?

If we're going to teach to mastery, we have to have a fine-tuned focus of exactly what students are expected to know. Enrichment is great but can't go into a students's grade.

Throw out the "nice to knows" and fine tune to the "need to knows".

Back pedal to decide the pre-skills. What specific pre-skills do students need for new instruction? Narrow it down to the size and type of numbers...when can you stop caring?

Example: For a 6th grade fractions unit, students learn the area model. So they need to know how to find the area of rectangles but not triangles or circles. They need to know how to multiply and divide
two digit numbers but not three.

Map new instruction in one color and pre-skills into a different color. Then chunk pre-skills into
different colors.

Day 2

Everything about this is professional judgment and that's where the power of collaboration shines. This is where vertical alignment becomes important- to find and fill in holes and eliminate disconnects between teachers and grades.

-map grade level
-map pre-skills
-cluster pre-skills

How much can/will you intervene? What is enough for them to understand the new instruction? What do you really care about?

Website Resource achievethecore.org coherency map

Pick a few problems and work them to list the skills needed in each step. Also make note of vocabulary words.

In the past pre-assessments normally look like grade level instruction being given to students and teachers being 'surprised' when they didn't know what they hadn't learned.

Suggested Structure:
-one skill per question
-short (one page)
-as little language as possible

No longer than one page front and back with plenty of white writing space.

We want to quickly know the exact problem.

It's low stakes for students because there is no penalty and quick turnaround.

Grade interventions with stickers to show patterns.

When units build on skills that you've taught earlier in the year, use your own information to decide
what/if to pre-assess.

If you're not going to do anything with it, then don't pre-assess.

Learning Opportunities if they don't know

Learning Opportunities if they do know
-NOT previewing new material
-meaningful interaction with current topic

All students should experience enrichment at some point, some students will need enriched enrichment.

Different units have different levels of pre-skills.

Cut out beginning of school review to insert review right before the skill that requires it.

Your intervention is proportionate to what you need students to know.

Each color is a different station. A station is a tri-fold board with the five categories. Students only go to the station(s) they need and then hang out in enrichment until the whole class is ready. Each station has an exit quiz before moving on.

Day 3

Interventions should be prepared for 1-3 units and no less.

Intervention Boards have same pockets where only contents and titles change.

Set up two classroom sets of boards on each side of the room to minimize traffic.

Mark exit quizzes in front of students to promote discussion.

Color code quizzes to each station.

Make two versions of exit quizzes for students who fail the first one. It was so rare to need a third quiz that you can cycle back to the first one.

Go slow to go fast. Building students up with success on pre-skills makes new instruction go faster and better.

Deep professional learning comes from arguing over what standards mean and what matters.

Designate quiz days so that other days can be spent working one-on-one with students. Have a quiz table where students have to wait for an open spot so that you can grade in real time.

This process can't fix students' learning disabilities but it can support. It is not a cure all but more students will be successful and more students will reach grade level.

Student attendance improves because students feel successful.

There is nothing superhuman about this work. It just takes time.

How will I start?


A great strategy for PD {and for students} is to first have people list barriers to the work or topic you present with empty circles in front of them. Throughout the session/lesson, have students color in the circles when they feel like it is no longer a barrier or when they feel like that barrier has been addressed.

It was really powerful to discuss when and why we could fill in these circles and literally watch the barriers fall.

Thank you Michelle for being a calm, steady, reassuring voice through our panic and fear that turned into confident plans.


#TMC16 31 Days of Inspiration Via Pictures on Twitter {Sara VanDerWerf}

31 Days of Inspiration Via Pictures on Twitter
Sara VanDerWerf
Monday Flex

Pictures speak louder and faster than anything else.

Use photos of group work to list good characteristics of group work. Let the photos do the work.

Photos elicit emotion.

We focus more on how to make students better but rarely focus on how to make me better.

Visuals help develop strategies.

What do you most want to remember to do well this next year?

1. Be intentional with my time on school work outside of school.

2. Never skip the close!

Commit to 1-5 minutes of daily reflection.

Make a list of what you are passionate about in your classroom. How can you regularly reflect on your personal list of things you want to remember to do more of.

Make a 31 day calendar of pictures that remind you of things to intentionally focus on.

"Get low" in the classroom so students don't look to you as the answer keeper.