Student Feedback Journal

I want to try something new. I'm not sure what the outcome will be or what it should look like, so I will attempt to flesh it out here.

First I am in love with this easy-to-manage idea for warm ups and exit slips from @approx_normal. So I plan on trying that.

But I'm thinking of incorporating a student feedback journal into that warm-up time once a week.

I'm imagining a journal where students self-reflect on their learning behaviors throughout the week and then I comment back with feedback- strategies to try, habits I notice, things to avoid, common mistakes, etc. At this point, I'm leaning strictly toward self-reflection, not mathematical work. The index cards will give me the feedback I need. I'd like this journal to give them the feedback they need.

I'm thinking I would do that on Mondays and that would give me the rest of the week and the weekend to respond to each student.

So on our first Monday back, I'm thinking about asking them to reflect on the final exam. I like the questions from crstn85's Test Correction's post:

How did you study for this test?
Did you feel prepared before you took the test?
Did you feel you were doing well while you were taking the test?
Are you happy with the grade you earned?

I'm imagining I will get responses like:
"You can't study for a math test."
"Why study when you let us use index cards?"
"My grade sucks."
"I thought I would do good until I got to #1."
"This test was nothing like what we do in class."

I'm imagining I will respond like this:
"I need to teach you how to study for a math test."
"Index cards are a reminder, but they can't remind you if you never learned in the first place. How could we use index cards better?"
"What could you do next time to improve your grade?"
"What made you feel confident before the test? What made you lose confidence?"
"If this doesn't look like what we did in class, what do we need to change?"

And so will begin a lovely give and take of communication. Right? Yeah, right.

I think the first time I will let them write freely. The second time, I hope to help them clean up their writing a bit. I plan to do this by answering the same questions they are answering, at the same time, from a teacher's perspective. Then the next week, I will put mine on the doc camera and have them compare their responses to mine. Hopefully, they will point out things like writing complete sentences, using capital letters and appropriate grammar, restating the question, not using text speak, etc. Then I can give feedback on their responses as well as to how their responses are written.

I really want the purpose of these journals to be twofold: 1. For them to self-reflect on their habits so that I can hold them accountable and eventually they can hold themselves accountable. 2. To give myself an easy opportunity to give attention and feedback to EVERY student.

Obviously, self-reflection is a big part of why we tweet and blog. Obviously, I don't need to lecture you on the merits of self-reflection, study habits, and writing. Eventually, I'd like this to lead to math portfolios. But first, I need to spend more time researching that idea, deciding what I want those to be, and ultimately, creating one myself. My fairy godteachers @druinok and @approx_normal helped me to realize that I need to go through the experience myself before putting my students through that experience. It needs to be meaningful and have purpose. I also have a tendency to rush in to things, give up too quickly, and try to take on the world all at once. See, self-reflection + teacher feedback = better behavior.

If you noticed, I did a lot of 'imagining' and 'thinking' in this post. And now here's your chance to bring me back to reality.

Comment below.


10 Ways to Compare and Contrast

So I am totally copying and pasting this entire article from another site. I really like it and want to remember it and so this is the easiest way to find it. Who's blog am I more obsessed about that my own? Exactly.

Comparing and contrasting is a higher level thinking skill important across the curriculum. We compare and contrast characters in a story, word choice in writing, equations in math (think < > =, not to mention word problems ), different hypothesis in science, how holidays are celebrated in different cultures, etc. That is probably why comparing and contrasting shows up multiple times in the Common Core Standards. Here are some ideas for comparing and contrasting in your class.

  1. Venn Diagrams. In addition to using them on paper, you can make big ones on the floor with hula hoops and have kids use labeled index cards or Post Its to fill in the variables. 
  2. Analogies are great because you can use different criteria and then talk about which criteria was used. For example the analogy:  Mountain: Hill : : River : Stream is defined by size while:  December : Christmas : : February : Valentine's Day is defined by time. Here is a free Analogy Worksheet.
  3. Similes and Metaphors Like Analogies, students can identify what the criteria is for the comparison. Similes may be easier for younger students because the words "like" and "as" pretty much tell you what the criteria is, while you often have to work a little harder with a metaphor. 
  4. Would You Rather Questions present a forced choice between two more or less equal options, which can lead to some terrific discussions. Read more about using Would You Rather Questions with your students here.
  5. Class Polls, Bar Graphs, and Glyphs  Good way compare and contrast student's experiences, opinions, traits etc.
  6. Foldables can be used in so many ways for comparing and contrasting! Here are instructions on how to make some of the most common foldables.
  7. Rating and Ranking There are so many ways to use this. Students can use numbers to rank brainstormed ideas. They can use a rating scale to evaluate their own work, peer presentations, the usefulness of a particular lesson etc. 
  8. Comparisons over Time Everyone loves to see improvement. Having students complete a variety of tasks at the start of the year and then doing the same ones at the end is a wonderful way to compare then and now. Do this on a smaller scale with a pretest and post test for any unit of study.
  9. T Charts Simple, basic, effective and applicable to so many things. You can put a variable on each side of the chart (eg "Conductor" and "Insulator") or you could put the words "Same" and "Different" on each side and put a the things to be compared at the top (eg: "Mammals" and "Reptiles").
  10. Written Essay No one should leave school without being able to write a solid, well-organized compare and contrast essay, complete with examples from life or literature. They will need these skills for the essay portion of the SAT. 
Do you have a tool that has been particularly valuable? Please share!

Ch 3 Literacy Strategies for Improving Mathematics Instruction

I do these more for myself than anyone else, but here, I am quoting the most useful parts of this ASCD book (click links to read online for free). Basically, I'm editing out the boring. You're welcome.

I'm also just doing a couple of chapters at a time because it's kind of dry and I never know how much time I will have to read. So consider it a series if you like.

Joan M. Kenney
So the question becomes: If students have been taught the material and haven't learned or retained it, what can we as professionals do to change the scenario?
Writing [in this way] slows down and focuses my thinking; I am able to hear each word in my head and see it on paper. It is like a mindful meditation during which I shut out the rest of the world and am totally engaged in the process. 

Another benefit of writing is that it allow the page to become a holding place for our thoughts until we can build upon them. We can revisit our written thoughts as often as needed and thus revise our thinking. Although I start with an overall plan when I write, I do not know where the ideas and words will take me until the process of writing drags them out of me- much as many artists do not know where a picture is going until the paint touches the canvas.

Mathematics is beginning to be viewed less as a series of arithmetic calculations than as "the science of order, patterns, structure, and logical relationships" (Devlin, 2000).

As Zinsser stresses in his book Writing to Learn (1989), it is important that all students be involved in the mathematics classroom. Twenty-five students cannot all speak at the same 
time, but they can all write at the same time, and writing encourages them to become engaged in their learning.

Written explanations in mathematics are about what is being done and why it works. The type of thinking involved in justifying a strategy or explaining an answer is quite different from that needed to merely solve an equation. The process of writing about a mathematics problems will itself often lead to a solution.

Once students have done some initial writing about a problem, they can share their strategies in small groups. In attempting to solve the problem, the students will have additional opportunities for writing.

If students begin the problem on their own, they are starting from their own mathematical way of thinking. Bringing their written solutions to the small group helps students investigate mathematics  more deeply.

Students need to untangle what is in their own minds first, get it on paper, and then share their thinking with others. (Love this statement with all my heart!) This ensures that there will be a range of responses to each question.

To quote Stigler and Hiebert (1999):
When this type of learning experience is used, the range of individual differences will be revealed. Individual differences are beneficial for the class because they produce a wide range of ideas and solution methods that provide the material for students' discussion and reflection. The variety of alternative methods allows students to compare them and construct connections among them. It is believed that all students benefit from the variety of ideas generated by their peers. (p. 94)
In order for mathematics writing to be effective, the following guidelines must be observed:
  • The problem must be appropriate for the students who are going to be writing about it.
  • The students must know how to use blocks, diagrams, pictures, or grids to work out their solutions before writing about them.
  • The students must have confidence in their ability to respond to the problem as individuals. They must think of themselves as successful mathematics learners.
  • The students must feel comfortable sharing their answers without fear of being ridiculed. This means that the teacher and other students have to accept all responses as worthy of discussion.
  • The problem must be discussed with the whole class, and all strategies must be reported. 
Other writing-to-learn strategies include journal keeping, creating problems similar to the one being solved, and directed expository writing.

In other words, teachers should use writing to engage students in mathematics thinking at the outset of a lesson and continue asking them to put their thinking in writing throughout the lesson to refine their thinking.

As the NCTM (2000) notes,
...Allowing students to grapple with their ideas and develop their own informal means of expressing them can be an effective way to foster engagement and ownership. (p. 63)

By recording their thinking about mathematics problems, students help explain the solutions- and the process of arriving at a solutions helps to develop the solution. Writing clarifies what it is the problems are asking. In order to justify their solutions, student writers are forced to think through, and find the meaning in, their responses.

Student writing helps teachers determine the type of learning that is occurring, informs them as to whether or not the students understand the lesson objectives, and reveals the level of understanding behind the students' algorithmic computations.


When Will We Ever Use This?

If you read my post IDK How to Learn This, you probably realized that I'm behind in the game as always. If you didn't read it, here's a summary: I don't know how math relates to real life.

After catching up on seven months of unread blogs, I find that Dan Meyer has already blogged about this. In depth. Multiple times.

In a way better visual of what I'm feeling, he posts about the popular infographic poster and why it never works.

In his Public Relations post, I loved this featured comment from Kathy Sierra:
"But another approach — since you used the word “enjoy” — is to simply consider math as an opportunity for puzzle-solving in interesting ways. After all, there is virtually NOTHING “personally relevant” in many of the games and pursuits people find so compelling, like, for example, Sudoku. Even chess. Or Angry Birds. Whether math is useful/relevant RIGHT NOW is a worthy and challenging goal."
 And to quote an article he linked to by Samuel Otten:
"I too believe in the value of building on students’ experiences, but rather than look for experience in the form of mathematical content appearing in their everyday lives, I look for experience in the form of mathematical thought processes—such as classifying, identifying patterns, and generalizing—and, most important, a desire to solve problems and make sense of the world."
I then took to Twitter with my complaints and lonely fit of rage. No one's responses were satisfying my need for a 'real-life' answer and so I sullenly accepted their responses with a doubtful 'I guess'. And then...IN SWOOPS...the calming voice of reason, aka @jackieb. She questioned me on why I first chose to teach math.

The short answer is that everything else seemed boring. The long answer is that my best subject was English but I couldn't bear the idea of teaching grammar and listening to students stuttering through reading aloud for the remainder of my days. I suck at science and history. Art was fun but I didn't have much skill to back it up. So that left me with math. The more I thought about it, the more it made sense. I like organizing and ordering things, figuring out puzzles, observing patterns, solving problems, and in general, making things work better. Plus, math is interactive; I would always be doing something.

When I said this to Jackie (in <140 characters) she calmly responded with:
Those sound like great "likes" for your students to like too. They may never "use" Alg2, but they'll use problem solving. Can you try to develop that sense of wanting to try to figure things out in your students?
Oh, Jackie. You make it all sound so simple.

Something else she said struck a chord with me after my post on raising expectations:
I can't always relate things to real life. In precalc I tell them that I don't know if they'll ever use this, but that I don't know what they'll be doing in 10 years. I then tell them I don't want them to not have choices open to them because they can't do math. Then we talk about the value of learning just for the sake of learning, the challenge of being able to solve tough problems,task perseverance, ... , then they get tired of me talking so much, so we get back to solving problems. 
How can I expect my students to be better if I don't give them the tools to do it with? I am subconsciously (or consciously I suppose) saying, "You won't ever need these skills because I don't believe you can ever become an engineer, mathematician, programmer, etc."  I'm doing the exact opposite of what I intend. Not that that's ever happened to you of course.

So now I am thinking...how can I lead my content, my class, my lessons around the fact that everyone loves a puzzle/pattern/mystery? How can I lead with what I enjoy so that my joy spills over into my students and their thinking and their actions?

Is there a pattern (very punny!) I can create so that our daily math experiences revolve around figuring out a pattern, solving a problem, mastering a puzzle?

Can I train students to think of life in terms of:

  • What do I know?
  • What pattern do I see?
  • What do I predict happens next?
  • How will changing the pattern affect the ending?
  • Can I change the pattern to create a different ending?
  • What patterns can I create to achieve the ending I want?

Hey, that kind of sounds like we're reading a story. Or avoiding bad relationships. Or being a better friend. Or breaking a bad habit.

And that sounds a lot more like real life than using systems of equations to decide which cell phone plan is better.

That's a puzzle I can solve.

Here is a start.

Ch 1-2 Literacy Strategies for Improving Mathematics Instruction

I do these more for myself than anyone else, but here, I am quoting the most useful parts of this ASCD book (click links to read online for free). Basically, I'm editing out the boring. You're welcome.

I'm also just doing a couple of chapters at a time because it's kind of dry and I never know how much time I will have to read. So consider it a series if you like.

Joan M. Kenney

*An ESL student thought of 'whole' numbers as 'hole' numbers, as in how many holes a number add. He thought 6 and 10 were odd numbers because they each only have one hole. He didn't know if 3 was even or odd because it could be considered as having two holes or two half holes which would make one whole hole. He knew the definition of even or odd but misunderstood 'whole'.

Younger students can be quit mystified by the fact that changing the orientation of a symbol- for example, an equal sign (=) from horizontal to vertical- can completely change its meaning.

Vocabulary can be confusing because the words mean different things in mathematics and nonmathematics contexts, because two diferent words sound the same, or because more than one word is used to describe the same concept.

Symbols may be confusing either because they look alike (e.g., the division ad square root symbols) or because different representations may be used to describe the same process.

Graphic representations may be confusing because of formatting variations or because the graphics are not consistently read in the same decision.

One strategy we arrived at is for teachers to model their thinking out loud as they read and figure out what a problem is asking them to do. Other strategies include dialoguing with students about any difficulties they may have in understanding a problem and asking different students to share their understanding. 

James Bullock (1994) defines mathematics as a form of language invented by humans to discuss abstract concepts of numbers and space.

The meaning that readers draw will depend largely on their prior knowledge of the information and on the kinds of thinking they do after they read the text (Draper, 2002): Can they synthesize the information? Can they decide what information is important? Can they draw inferences from what they've read?

In English there are many small words, such as pronouns, prepositions, and conjunctions, that make a big difference in student understanding of mathematics problems. For example:
  • The words of and off cause a lot of confusion in solving percentage problems, as the percent of something is quite distinct from the percent off something.
  • The word a can mean “any” in mathematics. When asking students to “show that a number divisible by 6 is even,” we aren't asking for a specific example, but for the students to show that all numbers divisible by 6 have to be even.
  • When we take the area “of” a triangle, we mean what the students think of as “inside” the triangle.
  • The square (second power) “of” the hypotenuse gives the same numerical value as the area of the square that can be constructed “on” the hypotenuse.
In her book Yellow Brick Roads (2003), Janet Allen suggests that teachers need to ask themselves the following critical questions about a text:
  • What is the major concept?
  • How can I help students connect this concept to their lives?
  • Are there key concepts or specialized vocabulary that needs to be introduced because students could not get meaning from the context?
  • How could we use the pictures, charts, and graphs to predict or anticipate content?
  • What supplemental materials do I need to provide to support reading?
If we are really trying to help students read and understand for themselves, we must ask them questions instead of explicitly telling them what the text means: “What information do you have that might help you answer this question?” “Does the fact that this is a ‘follow-up’ help us to decipher the question?”

As the reading progresses, the teacher should ask process questions that she wants the students to ask themselves in the future. They may be asked to predict what the reading will be about simply by reading the title of the piece (if there is one, such as a graph or story problem). Next the students should make two columns on a piece of paper, one headed “What I Predict” and the other headed “What I Know.” Once the students have silently read each section of the piece, they should fill out each column accordingly. At this point, the teacher should ask students questions such as the following:
  • What would you be doing in that situation?
  • Does this make sense?
  • What does the picture/graph/chart tell you?
  • How does the title connect to what we're reading?
  • Why are these words in capital letters?
  • Why is there extra white space here?
  • What does that word mean in this context?
Figure 2.4 shows a simple example of a possible guided reading for a lesson from an algebra text. The text would be unveiled one paragraph (or equation) at a time rather than given to the students as one continuous passage.

Figure 2.4. Guided Reading Example

Solving Systems Using Substitution 
1. What does the title tell you? 
From a car wash, a service club made $109 that was divided between the Girl Scouts and the Boy Scouts. There were twice as many girls as boys, so the decision was made to give the girls twice as much money. How much did each group receive? 
2. Before you read further, how would you translate this story problem into equations? 
Translate each condition into an equation. 
Suppose the Boy Scouts receive B dollars and the Girl Scouts receive G dollars. We number the equations in the system for reference. 
3. What do they mean here by “condition”? 
The sum of the amounts is $109. 
(1) B + G = 109 
Girls get twice as much as boys. 
(2) G = 2B 
4. Did you come up with two equations in answer to question 2 above? Are the equations here the same as yours? If not, how are they different? Can you see a way to substitute? 
Since G = 2B in equation (2), you can substitute 2B for G in equation (1). 
B + 2B = 109 
3B = 109 
B = 36 1/3 
5. How did they arrive at this equation? 
6. Do you see how it follows? 
7. Does it make sense? How did they get this? 
To find G, substitute 36 1/3 for B in either equation. We use equation (2). 
8. Do this, then we'll read the next part. 
G = 2B 
= 2 × 36 1/3 
= 72 2/3 
So the solution is (B, G) = (36 1/3, 72 2/3). 
The Boy Scouts will receive $36.33, and the Girl Scouts will get $72.67. 
9. Did you get the same result? 
Are both conditions satisfied? 
10. What conditions do they mean here? 
Will the groups receive a total of $109? 
Yes, $36.33 + $72.67 = $109. Will the boys get twice as much as the girls? Yes, it is as close as possible. 
11. How would you show this? 
Where did they get this equation? 
Note: Text in the left column above is adapted from University of Chicago School Mathematics Project: Algebra (p. 536), by J. McConnell et al., 1990, Glenview, IL: Scott Foresman. 

Students are helped not by having their reading and interpreting done for them, but rather by being asked questions when they don't understand the text. The goal is for students to internalize these questions and use them on their own.



Factoring ax^2 + bx + c

After reading Amy's post about airplane factoring, I decided to share the way I teach factoring.

I start out by teaching how to pull out the GCF, how to factor by grouping, then how to factor x^2 + bx + c using the diamond or the x-factor method. Those kind of have to be taught before this method. But it works.

I used the same problems she did so that you can compare the different methods.

The original problem

Multiply the first and last numbers. This answer, -12, is the top of the x. 
The bottom of the x is the coefficient of x, in this case -1.
The sides of the x are two numbers that multiply to equal -12 and add to equal -1.

The students have a LOT of practice with the x-factor so they find that its -4 and 3.
Now they rewrite the problem, replacing the -x with a -4x + 3x.

Draw in our parentheses and now we have factoring by grouping, which students are also very familiar with.

Pull the GCF of each binomial out in front (in green).
Write what's left in parentheses (in pink).
Final answer: Write the common binomial first (in pink).
Write what's left behind. (in green).


You've just been x-factored!

 Another example for comparison.

Semester Review

This is a review of my semester so far to help me focus on things I need to change and for me to evaluate our progress by the end of the year. So if you don't want to be bored to tears, go ahead and click around somewhere else.
  1. Achievement Period- The best thing we've started doing is going down to the elementary once a week and working with the students one-on-one during their guided reading time. The teachers adore it, the kids get individual attention, I don't have to do anything, and my students feel like rock stars. I think it unifies them and boosts their confidence in their own ability. We were doing Silent Reading on Tuesdays which fell to the wayside but I will definitely be bringing that back. I need to devote one day to Career Cruising, even if I do think it's useless. That takes up three days a week. I'm planning on doing that on Fridays and having students print out a current event off the Internet so we can discuss that on Monday. Plus we talk about our weekends on Mondays so that will pretty much take up the whole period. That leaves me with Wednesday. I need to find some good character ed activities. Otherwise it will end up being study hall which means chaos.
  2. ACT Test Prep- I started the year with the lowest of the lows and it was miserable. They desperately needed differentiated instruction that I just could not get. My management skills, as always, were terrible. The class is supposed to be a refresher but you can't refresh what they've never learned. Then we rotated and I got the high of the highs. It was lovely. I haven't taught top students in forever. They care about their scores, they try, they explain, they work together, they listen, they know things. They still don't bring pencils and they too roll their eyes and sigh heavily but hey, they're teenagers. It's like a natural reaction. Our routine is to practice problems, the next day take a short test, the third day go over test results and commonly missed problems, the next day is Silent Reading, and the last day is a study hall. My instructional coach had all the materials made from last year so I basically make copies and answer key and then let them loose. I have one more week with them and then we rotate to the middle or what we call bubble kids. The plan was that I would have them closest to the actual test date because math is our downfall and maybe we could push a few into the meets category. I will hate to lose these top students but anything is better than the lows. I felt terrible every day because I knew I was not doing them any justice whatsoever. Nobody needs a daily reminder of their failure.
  3. Algebra II- My favorite class of all! I've gotten some really good resources from another teacher but having only 5 students takes the cake, I love, love, love it. The class runs itself and they do all of the work. I make the bell ringer with five problems and each student is responsible for doing one on the board and explaining to the class. We do a lot of board work or just them working together and I roll around in my rolly chair and help. They have totally blown me away with their reasoning and critical thinking and plus, they are really entertaining. 
  4. Plan- The last few weeks of the semester I started getting to school about 30 minutes earlier and getting all of my copies made for the day and my classroom setup. It started me off in a much better mood and also freed up my plan period to accomplish other things. I'm super proud of that.
  5. Algebra I- I think Algebra II has stolen my love away from Algebra I. I think the class is just a weird mix and since they are freshman, I still think they haven't really got used to me. It's kind of a weird, stiff environment. My other students have had me now for two or three years in a row and so they are waaaay different around me. My pacing guide has really helped this year. Last year I got totally bogged down in linear equations for months and this year, I didn't. I'm proud of that. About half of the class stays with me, and the other half just...show up at random moments. lol I have an extra moody girl, a sneaky girl, a girl that works at a snail's pace, and a boy who thinks its cool to not try and fail. Those are the ones that I'm never sure what's going on in their minds. I have three who are really solid and basically keep the class going. It's a class of 10 which is a good number but...it's just not nearly as fun as it was. I don't even know what to say about it.
  6. Algebra II- My other Algebra II class of 4 students. They aren't academically where my third hour class is and I have some problems with attendance, but the class is run the same way. It's great because these four students easily slipped through the cracks in previous years and now they cannot escape my individual attention. Cackle, cackle. 
  7. Geometry- The bane of my existence. It's strange because any thing I read or hear about, when I think about implementing it, it's in this class. My instructional coach bet me that this would end up being my favorite class since it's my biggest, 25. She was wrong. It's definitely been the one that's made me grow and stretch the most but I still detest it. My management skills are to blame once again. The thing that's worked the best, which doesn't mean it has worked, is giving them another homework problem every time they get too loud. I don't like punishing the whole class like that but then the quiet students are more likely to shush everyone. I have the most success when I play our review pong game. They love it and they do work together. They get a little loud but nothing compared to how they act during regular class. I moved them into pairs and I think that has helped because it creates much more space in the class but students still have someone they can talk to. I've gotten to teacher-centered again and need to start doing more student-centered activities. I also need to quit being a baby and just write people up but I just doubt that's going to happen.
  8. Geometry Lab- This class is a waste of time. No one can tell me what I'm supposed to be doing and there is no curriculum. Basically, it is a class of sophomore Geometry students who did not meet on their Explore tests as Freshman. So we call it Geo Lab but students are supposed to be doing something to increase their test scores. Except nobody can tell me what that is. What I've started most recently is breaking them into groups of three. One group works with me on whiteboards learning a new skill. A second group works independently on their bids as part of their Real World Math projects. A third group works on the computers on ALEKS, which they absolutely hate. I'm thinking of using Khan Academy to replace ALEKS but I just detest those darn videos so much. I don't think he should stutter and I just don't think he explains it in the best way. But unless I decide to make my own (which I will eventually, just probably not this year) I guess I will have to suck it up and deal with it.
  • Extracurriculars- We did Homecoming in December this year so it will be really nice to not have to worry about that in January. Our boys basketball team is awesome this year so I am really enjoying going to their games. I've been presenting almost every month at our school improvement days about technology so I am loving that. It has opened the doors for me to talk to and work with other teachers and help send resources their way. I have spent the last couple years intimidated by others because so many teachers were my teachers. I never wanted to be the new teacher who acted better than everyone and like they knew everything so I really took a backseat. But now I am coming out of my shell! I just love more opportunities to teach! I've also been making our monthly agendas so now they are pretty and that makes my heart happy. We've done peer observations which have been really interesting and I love to have other teachers come and watch me. Our cohort is taking a teaching methods course right now in our graduate program. I have not been impressed with our classes so far. I suppose its because I read so much and blog and twitter but....I haven't learned anything yet. I've already known everything we've talked about and actually done most of it in my classroom. I also feel like there is major grade inflation here. Some teachers seemingly give A's to everyone which doesn't inspire me to try very hard. The only class that was new for me was on observation techniques, but I don't see getting to use them unless I actually become a coach or something. I still need to videotape myself and try the techniques. I officially am not in survival mode any longer. I am no longer panicked and feeling clueless. The amount of preps is tough but I haven't died yet. I'm feeling pretty solid. I'm done with my evaluations for the year and they went well so that's a relief. I noticed that I've migrated back to more teacher-centered and so that's a goal to work on this semester, along with my many ponderings. Also, I stood up for myself in a situation where I felt I was being treated unfairly. And that made me happy.
 And that's a wrap.

Gr8 Expectations

In a lot of things I've been reading recently, the topics of high expectations and self-fulfilling prophecy have shown up a lot. It's really had me thinking. What are my expectations for my students? Honestly...I don't think I've communicated any expectations at all. Except maybe to bring a pencil every day.

How do we express high expectations? How do we express expectations at all? What expectations have I expressed without knowing it? When I think about it, I imagine a grandiose speech at the beginning of the year where a teacher says what they expect. The end. How do you go about raising the bar and holding them accountable to higher standards? How do you hold them to it?

I had to write about this for my midterm in my graduate teaching methods class. First I had to tell of a personal account with a teacher and self-fulfilling prophecy. It was the hardest question on the entire test for me. I couldn't think of one single example, good or bad. I couldn't remember a teacher every saying anything that affected me that way. Then we had to write three action steps for raising expectations in our own classroom. I had to google it because I sure didn't know how! This is what I came up with:
One action step I could take to raise my expectations would be to implement the participation points contract mentioned in question number six. This would be a great way to clearly define my expectations for student behavior in my classroom. By having students read, check mark, and sign, they are agreeing to a higher level of behavior.

A second action step I could take would be modeling. I am thinking of implementing math portfolios in my classroom next year. What that means is that a student would be responsible for writing a skill description, creating an example and working it out, and explaining the problem solving process for the essential skills in any given unit. I would have to model for students an excellent, average, and unsatisfactory example so that students know my expectations are higher than just scribbling down a sentence. 

My third action step would be to hold students accountable by consistently providing detailed feedback. Whether on homework, tests, classroom participation, or on portfolio assignments, by giving students detailed feedback on their progress, I am letting them know where they are and where I expect them to be. I’m also communicating to them that they cannot just slip by unnoticed and that they are expected to improve. Along with that, I am providing direct instruction to support and assist them with improving.
Am I totally off the mark here? The main thing I found during my googling followed along the themes of modeling. If I expect more out of them, then I have to clearly model what I expect. But clearly modeling expectations doesn't necessarily mean they are high expectations. I guess what I'm truly asking is, what are high expectations? What should I expect out of my students? And then, how do I express that? 

I suppose modeling behaviors, exemplar assignments, and using rubrics to grade are ways of clearly defining what is expected. But how do you hold them to it? What do you do if they are not performing according to your expectations? I imagine a stern face, arms crossed, deep voice: "I expect better out of you."  But that can't be it. It has to be more than just talk, right? Right?

How can I have great expectations when I don't know what great is or how to express it?

Things I Am Pondering

            • Student Feedback Notebook- A year-long dialogue between me and each student in a special notebook. Could: address academic, behavior, personal concerns, document  progress, suggestions for improvement, highlight misconceptions, maintain meaningful relationships between me and each student, or just be really cool.

            • Show them, don't tell them. Actions speak louder than words.


                    IDK How to Learn This

                    Over my break so far, I've read some great books: The End of Molasses Classes by Ron Clark, The Excellent 11 by Ron Clark, and Teach With Your Heart by Erin Gruwell.

                    Now I know that these are out of the ordinary teachers. The books made me laugh, cry, and get angry. Parts of them inspired me, parts of them made me want to quit. But what bothered me the most was...I couldn't relate.

                    I loved reading about how Erin Gruwell used pop culture to engage students in reading and writing. I loved how Ron Clark took his students on life changing field trips that related to what they were studying in history. But how does this apply to teaching math?

                    I can never think of ways to incorporate new ideas into what I teach. I can read something on the Internet, find a new iPad app, hear something at a conference, and immediately think of how it would work beautifully in English or Social Studies. I never know how to make things work for math.

                    I don't know how to relate math to real life. It doesn't relate. They will never use this stuff in real life. I sure don't. How will learning systems of equations help them deal with their problems at home? How will graphing parabolas help them avoid drama? How will using the distance formula help them face their fears and overcome obstacles and become amazing people? How can math be life changing?

                    I know I sound like one of my own whiny students, but I can't help it. These are emotions that I face time and again. I am not inspired by math, why should they be? Am I teaching the wrong subject?

                    How is it that I put in all this time and feel like I am killing myself and yet still only accomplishing a fraction of what other teachers are doing? We can't even use experience as an excuse. Erin Gruwell started doing crazy things even in her student teaching.

                    I'm not having a pity party or saying I suck. I'm saying that mentally, I cannot wrap my head around bringing math to life, relating it to the world, planning field trips around math, or making it inspiring.

                    I don't know how to be that person.

                    That frustrates me because I feel like I can't learn. And not being able to learn just upsets me to the very core of my being. I am a professional learner! I may suck at things but I can always learn how to be better. And now, I can't.

                    I don't know how to learn this.



                    I haven't blogged in so long I've almost forgotten how. I had all kinds of ideas I wanted to blog and no time to do it in- now the situation is reversed. I'm going to blog my most recent calamity in hopes that that will jog my memory...

                    I wrote really good final exams.

                    I worked really hard and am really proud of what I accomplished.

                    Then the students took them.


                    In the past two years, I wrote terrible finals. Things we never really talked about, missing graphs and diagrams, questions with no answers, etc. It was bad. I cried.

                    This year, they cried. Okay, only one actually cried.

                    I created the tests. Then I broke the material up into three different days of review in order to cover everything. We did worksheets, whole class reviews, group game reviews, working one problem at a time, and so on. After each concept we've learned, we stop and write an index card on how to do it and an example problem. The students were allowed to use these index cards on the final.

                    Each test was 35 questions. 30 multiple choice, 5 open-ended, and all of them required thinking. It took the majority of the students the entire hour and twenty minutes to finish. It was hard and they told me about it. But only one person said they felt like it was things we had never done before. That's a huge improvement for me personally. The grades were not very good. About half failed. Out of all of my classes I had one A. One. Wow. I think I surprised even myself. I felt compassion for them but not guilt like in previous years.

                    But in a lot of cases, I felt like the grade truly represented their knowledge And in some it clearly didn't.

                    I honestly feel like the content of the tests was within their reach. They're just not used to stretchig.

                    This single event has taught me the importance of backward design more than everything I have read, heard, and discussed with others. I'm all excited to plan my unit tests ahead of time during the next semester. I know I should have done this from the beginning so I don't need a lecture on that.

                    My dilemma is, what do I do with the students' grades? Do I let them stand in hopes that students will take things more seriously and try harder? Do I cushion them because my unit tests didn't line up with the final exam and that's my fault? Do I give them a chance to make corrections when it is supposed to be a summary of everything they've learned? Do I just get over feeling bad when it's only the first semester and I let them use index cards as well? Will I get in trouble when my principal sees such terrible grades?

                    I need help from all you final exam fairies.

                    P.S. I started teaching things in December that I was teaching last year in February. I beat myself by two months. That is the power of a pacing guide people!


                    Quiet Mouse Experiment

                    I've had a lot of problems with students constantly talking in my Geometry class. I have 25 students and it's just not a good combination. I've tried lecturing and guilt tripping them about respect. I've tried holding them late after class. My most recent strategy was to add a homework problem every time they get loud. For example, if I wanted them to do 8 problems, I'd make a worksheet of 16 and write an 8 on the board. If they get loud, I walk over to the board, cross out the 8, and write a 9. I like it because it's nonverbal and doesn't interrupt the class. Also, they can't argue with it. If I start walking near the board, they try to quiet everyone down. It's helped some but it hasn't changed the fact that they don't respect me and ignore what I say.

                    So I decided to experiment. I've wanted to do this since my first year of teaching but was never sure I could pull it off. I did not talk. I went through the entire class without speaking. It was so fun!

                    I stood at the door and talked to students as they came in. When class started, I started the timer for 4 minutes to signal students to work on the bell ringer. When students called me over to ask questions, I spoke to them individually. From then on, I didn't speak. When the timer went off, I worked out the problems on the board so students could check their work. Normally I would explain the problem and call on students to tell me what to write. This time I wrote in silence and they magically did the same.

                    Our lesson was on the midpoint formula. I had a worksheet and corresponding PowerPoint but in a tragic turn of events, the worksheet pictures were different from the PowerPoint. Oh no! So instead of the worksheet, I held up a blank piece of paper. They got the hint and got out paper. I showed a horizontal line on the coordinate plane and the PowerPoint asked, How could we find the midpoint? A couple students figured out that we could just count the squares and then take half of that. The next picture showed a slanted line so that their method no longer worked. I pointed at the endpoints of the line and they gave me the coordinates.  Then I showed them the formula and they told me what to write. We went through several problems that way. I pointed to students when they needed to write. When they asked questions, I redirected it back to the class and other students explained. I walked around to monitor their progress.

                    I was amazed at my own ability to communicate without speaking.

                    Some students were really angry at me. Which I still haven't figured out. Some were very helpful interpreters. There were two students who I don't think have truly understood anything we've done all year that were completely engaged, did their homework, and actually enjoyed class.

                    I asked them three questions at the end of class as an exit slip.

                    1. Did you learn better or worse?
                    2. What was the point of this experiment?
                    3. Did you have any questions that were not answered?

                    The responses to number one were 8 better, 6 worse, 5 the same, 2 no answer.

                    The responses to number 3 were 13 no, 5 yes, 3 no answer.

                    The response to number 2 were incredibly valuable. Here are some of their comments:

                    -To make us do more work
                    -To see if we an learn without you talking
                    -Learn to be quiet
                    -To see if it would help us learn
                    -To have our friends try and teach us
                    -To see if we could learn without your help
                    -To show you can teach and we can learn without talking. It's about paying attention and reading directions. Making us think more.
                    -I learnt better today somewhat because it was us learning.
                    -To learn in a different way

                    The next day I showed them the results and put up the following quote:

                    "If students could learn math by just listening, teachers would have been replaced by tape recorders a long time ago."

                    I asked them what this meant. They commented that you need to do more than hear it, you need to see it and actually do it.

                    Then I asked them how I could talk less so that they could learn more. Some of their suggestions were that I talk 2 days a week and not talk 3 days a week, not talk until they asked me a question, and only talk 5 times a period.

                    I haven't really decided what I'm going to do but I have been really noticing how much unnecessary talking I do and I hope I'm doing a good job of cutting it out.

                    My biggest takeaway from this experiment is that my students do not listen to what I say. As soon as I start talking, they tune out. They know I will repeat it or that it does not matter. This is a part of my issue with respect but I haven't  figured out how to master that yet.

                    By not talking, I forced them to watch me and pay attention. I forced them to listen to each other, not talk over each other, and try to understand on their own.

                    I forced myself to communicate only what matters.

                    I think I made them think.

                    Shh. Don't say a word.


                    Todd Whitaker- What Great Teachers Do Differently

                    Today was our regional teacher's institute and our speaker was Todd Whitaker, author of What Great Teachers Do Differently.  I read the book a couple years ago and posted the main points.

                    He was a great speaker: funny, interacted with the audience, easy to understand.

                    Here are my main takeaways:

                    1. Negative people have no power. We give power to them. Pouters pout and whiners whine because it works. Who is not on any committee, doesn't do any extra curricular activities, has the easiest load, and the smallest classes? The people who complain. It is easier to avoid, ignore, or give in then to face them head on and deal with it. But pouters will pout and whiners will whine until it doesn't work anymore.

                    2. Treat everyone as if they're good. Good people deserve it and crummy people can't stand it. The example he gave is when you are in a grocery store and see a parent freaking out and yelling at their kid. The parent is not uncomfortable. We are. We have a problem with the behavior but the child has the bigger problem. Our normal reaction would be to ignore or go down a different aisle. He said, what if we went up to the parent and (treating them as if they are good) asked them a normal question, like where is the coffee? For a moment, it shifts the situation. Will the parent yell at you? Maybe. But you already knew they were an idiot the moment you walked down the aisle. Don't let troublemakers, whiners, and pouters be invisible.

                    3. What's great about teaching is that it matters. What's hard about teaching is that it matters every day. Ten days out of ten we should never yell, never argue, and never use sarcasm. Ten days out of ten we should treat students with respect and dignity because we never know which day it's going to make a difference for them.

                    4. What great teachers do differently is know how they come across.


                    Literacy in the Math Classroom: Journal Prompts

                    Our big push for the year is literacy across the curriculum.

                    I'm excited about two new ideas I'm trying.

                    First of all, I have a first hour achievement period which is comparable to a homeroom or advisory. We've done a lot of different things. We watch Channel One news and have discussions, we have a silent reading day each week, we have regular study halls, etc etc. This year we got a bunch of new posters that line the hallway entrance. They are the ones with black borders that focus on a character trait like honesty, integrity and so on. Each student had to pick a quote. Then they had to find a picture on the Internet that went along with the quote. They had to write a one page reflection on why they chose this quote, how it relates to their life, and how their picture describes the quote. I didn't give them a due date, they just worked until they were done and then took turns presenting to the class. Then I had students vote on the best paper, best presentation, and funniest presentation. This sparked the idea to have students write and present more and more until we get to a point where students can self-assess and asses each other using a rubric. I'll be interested to see how the quality of what they create changes during the process.

                    I found these super amazeball notebooks at Wal-Mart. They are black and white and covered with designs and you can doodle on them and design them however you want. Slightly reminiscent of comic books. They come in a pack of 3 and cost $1. My students love them!

                    The part they don't know is that they only have 56 pages of paper. Ok, well they can read, so they do know that. But what they don't suspect is that once we run out of paper, I want to transition them to blogging. :) But how can I do that when I don't have enough computers. Enter Project iPad. I've decided that right now while we have the grant is the prime time to start a 1:1 iPad program at our school. So I've neatly tied that into our literacy project by having the students research and write papers in support of the idea, complete with main evidence, supporting arguments, and so on. The students are greatly intrigued. We started by doing a bubble/web/concept map graphic organizer on benefits of an iPad. Monday we are going to list the potential downfalls. Our literacy coach came in and talked to them about public speaking and gave them a graphic organizer that outlines a speech. We are going to use our webs to prioritize what should go in our outline and build our paper around that. I'm trying to get other teachers and classes involved so that every student has a say in it. How powerful will that be? And I'm hoping that the administration won't be able to deny every single student who has researched, written, and presented a well-thought out argument.

                    I also planned to do a lot of creative writing prompts to hopefully hook them into writing, thinking outside the box, and better expressing themselves. I found two great sites for prompts: creativewritingprompts.com and http://writingprompts.tumblr.com/ I went through the first site and picked the ones I liked best and made a pretty PowerPoint to use in my classroom. I like the second website too because it adds the visual piece. I will definitely be adding to this but it is a fantastic way to start.

                    My second idea takes place in my eighth hour class. The class is a supplemental Geometry class for students who did not meet or exceed in their standardized test scores. There is no real curriculum and no one can tell me what I should be doing. So far, I've been doing a mixture of extra help with geometry, reviewing stuff from the end of algebra, and teaching new stuff that I didn't quite get to in algebra. I bought the same amazeball notebooks for them too but their writing prompts will be focused on math instead of creative writing. Earlier I had posted a list of algebra writing prompts and now I am slowly transitioning that into another pretty Powerpoint. My thinking is to start class with journal time because my next door neighbor English teacher does that with them already. In all my other classes, I start off with a bell ringer. But by eighth hour, I'm usually tired and winging it. This is definitely a better solution. I think it is also a healthy break for the students who have me two hours in a row. It gives them a chance to be quiet, think, write, and discuss. My thinking is that the writing prompt will drive the material we learn/practice/review that day. Eventually, I want to have stations that students rotate through (that's another post entirely) so I'm wondering if it would work to have a writing station, board work station, and online (ALEKS) station. It would give students about 15 minutes per station. More on that later.

                    Some students have me for first and eighth hour and have my next door neighbor for English so that is at least 3 times a day that they will be writing and ultimately engaging in critical thinking. I'm excited about the prospects!

                    Oh, you probably want to know how I'm going to grade. For now, I think I will just be giving participation points. Friday I had everyone read their answers out loud. I may glance at them weekly to make sure they are actually writing and not just spouting off at the mouth. In the future, I hope to have students self-assess or assess each other. Our literacy team came up with a fantastic rubric but in my opinion, it is too much for my students' short journal writings. Seems way more appropriate for papers, not necessarily a paragraph or so. But then that just means me and my students will have to create our own. More team work and collaboration.



                    Naming Basic Geometry Terms Pt II

                    I previously posted about my students coming up with the idea to do a hands-on geometry activity with pipe cleaners, fuzzy balls, construction paper, and letters to review points, lines planes, and such. Each student had their own packet. They used a piece of construction paper for their plane.

                    This Powerpoint was posted up front, which gave them directions on something to create. This relied heavily on their ability to read and understand the terms and labels posted. See example.

                    PowerPoint slide:


                    As they arranged, I walked around and checked students' work but I did choose to create a mock example on the following Powerpoint slide. This way, if I did overlook some students, they were still able to self-assess and gauge their own understanding. This also created good opportunities for students to tell how they did it differently and discuss different ways of getting the right answer.

                    I thought this was a worthwhile activity and I would like to do more things like this, I'm not sure how much I believe in learning styles, but I do believe in connecting ideas with students in as many ways as possible.

                    As I mentioned before, what I am most proud of is that my students came up with the idea, put the supplies together, participated, and then as a class we reflected and discussed the results. This has been the best and most realistic example of team work and collaboration that we have accomplished yet.



                    Highlighters for Dummies

                    Our big push this year is literacy across the curriculum. We've put together a literacy team, of course, with the hope that it will be teacher led. Our plan is to devote some of our SIP monthly meeting time to teaching a new strategy and giving teachers time to discuss and reflect. I don't know if this is as common in your school but in our school, we never sit back and talk about if things work or how to improve them. Basically, if it didn't work the first time, we give up and think of another idea. Also, when individual teachers go to conferences, we never give them the opportunity to share what they learned with the rest of the faculty. We are missing out. So I am really hoping that self-reflection is a big part of this.

                    I am not on the literacy team but my graduate practicum is based on re-designing professional development so it makes sense that I am working hand in hand with the literacy team. So the team developed a definition and I created a poster.

                    We previously had a short meeting where all teachers brainstormed ways to integrate literacy into their content areas. And thus, another poster.

                    We have also started doing peer observations which has been fun. I noticed that a lot of middle school teachers model highlighting in their classrooms which is something we don't do in the high school. So I started thinking, how could I use highlighting in my classroom? I think it would be a great literacy strategy that would be easy to integrate into every content area. We do a lot of examples and some definitions. I make everything so it is very possible for my students to highlight since I don't use textbooks. But how could we do it so that it is beneficial?

                    I brainstormed with my students and they said I could tell them the important things that will be on the test. So I turned that around and thought that it could be a good summary of the lesson. Students tell me what is important and then highlight. But that brought up the question of, how do you study for a math test? I don't really know because I never studied either. I review with students in class so I don't know how they would go about studying on their own. We are currently using index concept cards to summarize a concept. Students suggested a way to review would be for me to give them problems and using their cards, tell me which concept it goes with. Another teacher suggested that I give them a list of terms/examples at the beginning of the unit and we could highlight in different colors. Then as we go along, we could highlight with different colors in our notes so that students know what each term/example refers to. But to me, we could do that without highlighting. For example, I could just say 'Refer to Example 1". I don't want to highlight for the sake of highlighting, but I do think it could be a valuable skill for students to learn and carry with them.

                    How do you teach students to study for math? How do you summarize your lessons? How could highlighting be effectively used in a math classroom?


                    Class Reflection

                    My instructional coach is a lover of the jigsaw cooperative learning structure. I've used it a few times but I have not yet reached the stage of lover. I tried it for the first time in my class of 25 anddddddd.....it didn't go so well. I had them line up from smallest shoe size to largest without talking. Then I counted them into groups of four. I ended up with six different groups which totally threw me off. I only had four problems prepared. What I did was create a worksheet of eight problems, four different types. One was worked out as a reference example. Their task was to complete one problem and teach it to their group. I just totally messed up the logistics.

                    I don't want to explain all that, I want to focus on the reflection I had with my class after that. I asked them what they thought about the activity and they did a GREAT job of raising their hands and listening to each other speak. Their comments were that the activity took too much time due to all the moving back and forth between groups. They also said there were too many people trying to talk and explain at the same time. It ended up being loud, noisy, and crazy. Also some of them said they like to get right to work instead of wasting time moving around and explaining. They preferred working in pairs to groups. I told them we could compromise on working in pairs if we worked in some way where students are explaining to each other since that is the most beneficial part. They came up with the idea to have pairs pair up and explain to each other. I'm okay with that idea.

                    I later talked to my instructional coach and we figured out how I screwed everything up. So I will try jigsaw again at some point. But I really liked the fact that my last two blog posts have been positive, real-life example of problem-solving and collaboration. I hope that I am improving their ability to reflect and self-assess. I hope. I feel like we are working together as a team for the good of all. Aww, fuzzy butterflies and bear hugs. Now, how can I do a better job and do it in every class?

                    Something I need to reflect on I suppose.


                    Naming Basic Geometry Terms

                    My first unit in Geometry was about basic definitions: plane, line, segment, point, ray, coplanar, collinear, noncollinear, parallel, perpendicular, etc. From there we classified angles and did the Angle Addition Postulate, complete with algebra and variables on both sides. Next we discussed angle pair relationships: vertical, linear pair, adjacent, complementary, and supplementary. Again with the algebra, solving equations, and variables on both sides. So now we are reviewing and ready to test over Unit 1. I gave my students a review packet to work on with a partner. They are really struggling with the naming and labeling piece. They actually asked me if they could have a test of only solving for angle measurements with lots of algebra.

                    When we first went over basic terms, we wrote definitions, drew a picture, and wrote how to label. We did practice problems, homework, and bell ringers. They are still struggling. From what I can see, the confusing thing is when you can name the same thing in two different ways. For example, a line can be named with one lowercase letter or two capital letters. A plane can be named with one floating letter that isn't a point or with three points that lie on the plane.

                    Ooh, an idea just hit me! What if I compare it to names? The lowercase letter is like a nickname and the two capital letters are a first and last name representing the first and last point of the line. Is this something that makes sense and is likely to help?

                    We were scheduled to test on Monday but I could tell my students were not feeling good about that. I was truly frustrated with myself because I couldn't think of any other way to teach them what seems to be so simple in my head. I sat down and brainstormed with my 8th hour Geo lab students about what we could do.

                    They came up with the idea that we needed to do something hands-on where students could see, touch, feel, and actually move things around to get a better understanding. I sent three students to the computers to look for any helpful ideas. The rest of us scoured my room for supplies and the students then created packets of the following supplies for each student:

                    We will use a sheet of construction paper for a plane. The arrows are to form a line. I bought fuzzy balls to use as points and to create line segments or rays. We gave letters so that we could label.

                    Now my problem is, I don't know what to do with this. Should I give them a list of things to create? Should I post it on the SMART board so I can check each student's progress as we go? What kind of things do I need to tell them to create in order to practice naming and labeling?

                    My students on the computer found this 5 minute tutorial video that they thought did a good job of going step-by-step through each term. They also found this video of a geometry rap.

                    So my plan is to do a bell ringer with maybe a diagram and the answers scrambled so that they have to do matching, maybe? That might help them connect the right way to label. Then discuss the nickname idea I mentioned earlier. Next show the two videos. After that comes the putting things together...but what am I going to tell them to do? 
                    I need some suggestions please!


                    The Textbook Debacle

                    On my last post about being overworked and needing to use the textbook, Kate Nowak linked me to a PCMI presentation on using a scaffold to make textbooks more usable. I contacted the presenter, Marcelle Good and with her permission, wanted to share her perspective (emphasis mine).

                    Me: My students don't use textbooks at all because I basically create my own. I make daily worksheets using problems, scenarios, and diagrams from the book but I *try* to scaffold or ask questions in a way that starts with what they know how to do and leads into the new material.

                    Marcelle: My students don't use textbooks, either, but this year I was introduced to a really good textbook from which I based many of my lessons. It saved me a lot of time and I'm looking forward to doing more of it this year.

                    I had an aha moment in working with Leslie Hamburger, who is a consultant with WestEd and is their "Quality Teaching of English Learners" math expert. Their philosophy on scaffolding is the idea that a scaffold is something you use repeatedly, students internalize, and then they are able to do the work without the scaffold.

                    So, for example, the best scaffold in my classroom are my "Sentence Starters for Accountable Talk." At the beginning of the year, I'll have students in small groups with a list of sentence starters (I agree with...I also think.../ I respectfully disagree with..../I had a different idea.../I'm not sure what this means, but I think it might be about.../etc.) that they are required to use. At first, this is awkward and weird, but my students are learning English and I find that even native speakers tend to struggle with academic conversation. The next step is those Sentence Starters are on the table. By December, they're in poster form on the wall. When students say something in a really great way, I highlight it and often add what they say to the poster ("I'm not sure what this means, but..." came from a great student moment in trying to figure stuff out). By the end of the year, in classroom discussions (in my room and also in their other classes), students had internalized the language and were able to have an academic conversation. Students don't sound scripted anymore, and they'll take this manner of speaking with them to future classes. So, that's a scaffold - model, apprenticeship, independence.

                    Thinking about that as my basis for a scaffold, I moved to thinking about how to get students to read a text. As you pointed out, guiding questions are really important ways to get at a text, so this may be splitting hairs, but I started to think about chunking the text and finding a prompt that could work for everything. So, in the powerpoint you saw, I think I included, the "Summarize, draw a picture, or ask a question about the text" prompt. That's something that I used every time I took something from a textbook. What was nice about it, is that by May, students had internalized how to do that (I didn't start using the textbook until February, and I was still experimenting with how to use it, so I wasn't ever able to move away from the prompt). But the idea would be that that would be the prompt starting in the beginning of the year, then we'd move to boxes with no prompt, then I'd ideally be able to give them a text with a wide enough margin at the side that they could read a text and make notes about it.

                    None of this is super innovative, but there was something really powerful that happened for me when I separated the idea of a worksheet that I create from scratch with good guiding questions to move students forward (which students obviously need) from the idea of scaffolding a lesson.

                    The text/worksheet/activity is one thing, and the scaffolding is something else. It's the repeatable protocol or prompt or idea that students are familiar with that will help guide them through a challenging lesson. When I go back to thinking about Vygotsky, the purpose of scaffolding thinking was to move a student to a place where they would be a more independent problem solver, or an apprenticeship. I want to think about what students can internalize and use without me and make sure I'm building that into my lessons, with the hope that at some point, when they're in a new class or setting and they see a challenging mathematical text or hear a challenging idea, they'll have a whole bunch of tools to figure it out. The stuff that relies on my asking them really good questions to help them move forward is important, but thinking about how to move them to a place where they internalize a way that they can generate their own questions, or find some way to look at the math and start to activate prior knowledge on their own is where they become more independent.

                    So, in math, accessing prior knowledge is super important and is something you do in your lessons. Good math students and mathematicians somehow get really good at it, and find a way to do this on their own. They look at an unfamiliar problem or topic, and immediately start going through their mental database of math that they know and make connections that can help them understand the new topic. It's amazing. So, the question is, how do you get students to go from accessing prior knowledge because you prompt them, to looking at something and being able to access the appropriate prior knowledge on their own? And I think the idea is what is the next step? How can math teachers be explicit: I am asking you about this stuff because you already know it and it's going to help you! To, a more, "What is it that you know that will help you with this?" to students automatically doing that. And the scaffold is the repeatable, internalizable thing that gets them there, and the first step of that scaffold is just asking them the question that will make them think about it, but maybe with something that makes clear to them that what you're doing is trying to activate their prior knowledge so that the teaching part that you're doing and the reasoning behind it is clear to the students so they can get there on their own someday. So, a rudimentary example would be on every worksheet with a new topic, there's a heading that says, "Activate Prior Knowledge" and there's a box where you ask general questions to guide students to what they already know that can help them, and in the beginning, you answer those questions as a class or as a small group. Then you take away pieces of it, so at the end of the year, you just have a heading and some empty space that students start brainstorming in. They'll still get stuck, they'll still need your good questions, but it means you have to spend less time making worksheets (this was my main goal), and the students are taking over a little bit more of the cognitive load.

                    Again, this could be splitting hairs, but I really struggle with trying to make teaching sustainable, and to get back to the textbook idea, it was great to find a good book that asked those good guiding questions for me, so that I could spend my time thinking more about the habits of mind and the practices I wanted my students to have. I still write a lot of my own stuff, but my goal in the next few years is to have a textbook take care of the What so that I can just think about the How.


                    I loved hearing her perspective and I had never thought of creating a general, scaffold box. I always recreate the way the textbook presents the information because I think it sucks. So I don't think that I could use the scaffold box and still just used the textbook. But, Marcelle is using the CME Project textbook which is apparently amazing compared to anything I've ever seen.

                    What was really a highlight for me is that no matter how good I am at questioning, that is not helping them to be independent thinkers and problem solvers. They might be thinking better while they're with me but they aren't learning how to think on their own.

                    I still hate my textbooks. They are confusing. But is it a valuable skill that I'm causing my students to miss out on? I'm still not totally sure but I still know I won't be using the textbook. I guess next step would be to check out the CME Project and try to integrate more parts of the book along with the scaffold box.

                    Anyone else familiar with the CME Project?