Tuesday, August 30, 2016

#MTBoSBlaugust Day 19: Thoughts for Starting Geometry

Second to last post of #MTBoSBlaugust! This has been an incredibly rewarding experience, gotten me ready for back to school, and helped me see how much blogging increases my critical thinking about my teaching. 

I've done a lot of blogging about my plans for establishing a classroom that is more aligned with growth mindset and I intend on letting that inform a lot of my first day activities. I'm going to start both my preps with the Post It Activity I mentioned earlier to get conversation going. The questions have totally changed from my original post, but my goal is have 7 questions that align with the 7 class norms Jo Boaler talked about in Mathematical Mindsets and I outlined in my class norms videos.  I'll blog about them more on the first day of school! 

From there, my PLC typically goes straight into content. And while I want to make sure I'm keeping pace with a new prep, I also want to set the tone of critical thinking, collaboration, and discussion. I can't stand the idea of having kids copy definitions on day 1....it hurts my heart. Here's what I'm thinking and I'm definitely happy to take any feedback you have! 

1) Pair/Share on why precise language is important to the kids personally. I'm thinking:

  • curfew
  • school rules
  • other awesome things they might come up with?
And just generally things like these:
Side note: this is my FAVORITE teaching tool for the AP exam.
It's how I get my kids to finally stop using the work "it" in their answers. 
Then, we can get into a brief overview of who Euclid was and how this attention to detail was incredibly important to him. We are going to think like mathematicians in this class and in order to do that, we need to be sure we're being precise. 

2) Students work in pairs to complete this investigation from Discovering Geometry: An Inductive Approach (Key Curriculum Press) and wrap up with generating class definitions

3) Give students a list of geometric terms and have them work with their partner to generate the most precise definition they can given their prior knowledge. This will not only get them communicating, but hopefully help me pre-assess what they remember and give me time to walk around and talk to kids individually. 

4) Discuss their definitions as we generate our own class definitions. Culminate with filling in notes for the day that address notation. 

Thoughts? Favorite ways to address such a vocab-heavy course? Favorite Euclid videos? Feel free to comment! 

Monday, August 29, 2016

#MTBoSBlaugust Day 18: Good Signs

Today I finally got a chance to get into my classroom and start setting up. My mind has been spinning since orientation with questions and ideas, especially since my husband was able to get into his classroom weeks ago since it wasn't being used for summer school. We spent last week hearing a lot about admin's stance on education and I genuinely felt like this was a group of educators who, at least in intention, were there for the kids. There was encouragement to take risks, to try new things, to innovate, and to advocate for the students. It all sounds so good in theory, but you never know what things look like in day-to-day practice. I hoped I would be meeting other colleagues who wanted to challenge themselves, innovate, and bring a positive attitude to collaboration.

While I was puttering around in my room today trying to figure out where to start, a smiling face popped her head in my door to introduce herself. She was a veteran teacher, someone who had been there for a while and offered to help in any way she could. She assured me that I should ask for help and that it was a math department norm to be asking questions of each other to make our teaching better. We began to talk about sharing classrooms since she hadn't met the other new teacher yet with whom she'd be sharing and then she said something that obviously piqued my interest: that she wanted to talk to the other teacher since she was trying something "new and crazy" this year. Knowing that she wanted to better her strategies in classroom management, she had spent a large part of her summer researching ways to facilitate that through classroom design. She was going to start differentiating her seating options by creating zones: individual desks, groups and pairs, big comfy folding chairs, etc. This way students could work in the most appropriate situation for them, even if that wasn't what everyone else was doing. The craziest part? She doesn't even have her own classroom. She thought this was going to be good for kids, so she was willing to spend the time setting up and taking down the room before she floated to another room. She was working to negotiate the obviously unique scenario with the other teacher using the room.

I haven't been to a staff meeting yet and I haven't even met most of my PLC, but knowing that there are people who are pushing themselves every day to break out of their comfort zone to benefit a student is nothing but a good sign to me.

And obviously, I had to hang my first posters. 

Friday, August 26, 2016

#MTBoSBlaugust Day 17: The Power of Yet Poster

A while ago, I saved this poster on Pinterest because I loved the sentiment! I knew I wanted something like this to go into my classroom this year, but when I found out I'd be floating I figured it would be a nice idea for the future. (The pin was a dead link, so not sure where this originated. I'm happy to give credit if it was yours- let me know!!)

Since I just found out that I do in fact have a classroom and was reminded of the poster by this tweet tonight:
I decided it was time for me to make one of my own! 

I am playing around with how I like it laid out best and if I want to back them with another color or not, but here is what they're looking like right now (shoutout to my toes in picture #1 and 3):

I will post pictures once I get into my classroom and get decorating....naturally it's the last hallway to be waxed! 

Thursday, August 25, 2016

#MTBoSBlaugust Day 16: Designing for Growth Mindset

I just finished a few days of New Teacher Orientation and it was invigorating, albeit a little overwhelming. We talked about so much that it's hard to keep track, but one of things that stuck with me is a word that came up over and over today in our discussion of the district vision: intentionality. 

This has been a huge focus for me over the past year and one that I never quite had a word to describe. I like to think that I always try to do what's best for kids with the knowledge I have at that moment and that takes a lot of intentional design. This was a huge factor in piloting my blended learning course, my STEM courses, and will remain a huge factor as I move forward. 

I've done a lot of work on mindset this summer and I'm trying to question my own practices as much as possible, always with "What is best for kids?" at the center. I feel like I have wrapped my head around how I want to present my belief in my students and in growth mindset in the opening days and I'm regularly stealing things from around the MTBoS to hang in my room (SINCE I JUST FOUND OUT I'M NOT FLOATING ANYMORE! #yassss). I have spent the last 3 years designing problem-based experiences for my students through STEM and my pedagogical approach tends towards these open-ended tasks and encouraging student collaboration. Of course I have room for improvement, but it's an area I'm more comfortable. 

But with growth mindset, I am starting to feel like the devil is in the details. We convey messages to kids through the instructional choices we make every day and these messages are often stronger than anything we say out loud.  These are my next 2 devils to tackle right now:

1) Homework

I am particularly not proud of my homework setup. Sure, I give considerably less homework than a lot of teachers and try to select meaningful problems that are worth my students' time. But in general, my students check their answers against a key that is projected and I check for effort. It's plain and it is beneficial to students who choose to use it appropriately, but not to everyone. And I'm going to be totally honest....I'm haven't worked with my whole PLC yet, but I am highly doubting they would be jumping on board to eliminating or drastically changing the nature of homework as defined by Jo Boaler in Mathematical Mindsets. I know the issues that would occur if 1 teacher decided to totally eliminate homework if others didn't also get on board. And I am still working my way towards being 100% comfortable with it. I want to make some changes that will benefit my kids and create more equity, but I need to take some baby steps to do this. 

I also want to build metacognitive skills in my class and I know that self-reflection about homework can be a vital place to infuse that.

This NCTM blog got me thinking more about my homework practice:

I totally agree that neither system promotes analysis of mistakes and I like the author's proposal to use those mistakes as teaching tools. I like the idea of student ownership over their own work and assessment, but I know there are loopholes here for students who want to take any easy way out. 

I am sooooooo open to suggestions on this. Please share your homework grading practices and why you love them. I want to be inspired, #MTBoS! 

2) Assessment

Let's be real....kids dread assessments. Any assessment. Ask them to take out a piece of blank paper and write their name and you'll see the anxiety on their faces. We need to build a different relationship for our kids, so they can start to use assessments as a tool for growth instead of a judgement of their character. 

I have high hopes that someday I can find a beautiful standards-based assessment routine where my kids will see assessment as a tool for learning instead of a judgement. This is a new road for me, as I've started to focus more and more on my assessment practices as I have gone further in my career. But SBG seems daunting to take on, especially in a public school setting where many other people are teaching the same course as you. I'm taking baby steps and I hope these are things I can build on as time goes on:

  • Writing "I can" learning targets for each unit so students can self-assess regularly
  • Instituting a retake/corrections policy for all formative assessments
  • Offering a instant messaging office hours to give students another outlet to ask for help
I know the arguments....that kids need to learn responsibility and shouldn't ever be allowed to do corrections or take retakes. I don't disagree on summative assessments- there has to be some type of deadline in our 180 day calendar. However, that doesn't mean I can't help my kids see their learning as fluid (and growing) along the way. 

I know there are tons of resources on this out there, but this is the one that got me thinking:

Again, give me your suggestions!! How do you use assessment to send a growth mindset message to your kids? And how do you do this in a PLC environment if others don't necessarily agree? 

Thinking about growth mindset...want your best ideas! 
  • How do you use homework as a growth mindset learning tool?
  • How do you use assessment to promote growth mindset?

Monday, August 22, 2016

#MTBoSBlaugust Day 15: #ObserveMe Goals

Here are my #observeme goals for this year! 

I am still picking out a rubric I like and I'm not sure where I'll actually put this (maybe attach it to my back as I masterfully and gracefully float between classrooms? attach it to some currently unpurchased cart I wheel back and forth? get a tattoo of them?), but I love this idea so much. It is not only good for us as teachers to seek the feedback, but it models for our students that we should always been looking for ways to improve! 

My district orientation starts tomorrow and I can't wait! Wish me luck! 

Friday, August 19, 2016

#MTBoSBlaugust Day 14: Balloon Geometry

Time for a fun Friday post and a break from a lot of heavy curriculum lately! 

Every year my former STEM program put together a giant kickoff for our students. These events were designed to promote collaboration, trust, and community while getting to explore some awesome STEM ideas. One year we themed the entire kickoff around sustainability as our students would be engineering with repurposed materials in their design class. Another year, we had groups design boats out of cardboard and then we tested them out in a pool at the end of the day. 
SEAFARING STEM! from justin pierce on Vimeo.

Last year, we decided to go with a more diverse plan. Each teacher designed their own mini-PBL and students were able to select which they wanted to attend. It reminded me of the excitement of going to a big state or national conference- the hardest part was deciding what you should skip! This gave us all a chance to nerd out a little in our respective subject areas and do things we might not normally have time for with a diverse collection of grades and ability levels. 

I settled on using the time to have my kids explore Balloon Geometry. Besides spending two hours before school blowing up balloons and having incessant popping sounds coming from your classroom, it was fun & a great engineering challenge. I saw groups work together to problem solve, play to each other's strengths, and just have fun thinking critically about geometry. 

Here are my slides: Balloon Geometry

You could make this way more structured to ensure that kids are building "pretty looking" polyhedra, but this was only an hour activity and I liked seeing the kids work together to decide what figures would work the best. 

There are TONS of great resources online for this, but here are a fun of the ones I used:

Thursday, August 18, 2016

#MTBoSBlaugust Day 13: Geometry Learning Targets

Here is my draft of Common Core Geometry Learning Targets for this year. This is largely designed from the previous work of my PLC to unpack standards, so I want to spend some time going back and cross-referencing. And I tried to write these from scratch....exhausting (and impossible to focus on while you're immersed in the newest episode of The Night Of). 

My Calculus Learning Targets had me like:

With these, I'm feeling more: 

I'm still adjusting to seeing myself as a geometry teacher again- it's been almost 5 years. I love it, but it has a unique mindset from more algebra-based classes. I do, however, feel much more familiar with the curriculum as my PLC has interpreted it, which makes me feel more ready to be a team player. I'm ready to start working with some other teachers on this stuff....I always feed on that collaborative energy.

Under 3 weeks until Day 1!  

Wednesday, August 17, 2016

#MTBoSBlaugust Day 12: Mathematical Mindsets Norms Video

Somehow in my stream of consciousness Google clicking this week, I ended up on Cathy Yenca's (@mathycathy) blog post from 2013 on First Day Favorites. I loved the professional and engaging look of her video and it dawned on me that I could use this to convey a message I wanted kids to hear from me clearly and consistently.

Thinking back to my readings about math class norms from Mathematical Mindsets, I decided to create a video to summarize what I want my students to walk away from the Post It Activity knowing I believe about them. It's brief and will ensure that all my classes are hearing a consistent message from me. Once we wrap up our class discussion, I'm planning on playing this for them and having them reflect as an exit ticket.

I have the file saved if anyone wants me to send it so it can be tweaked! Like Cathy, I used the free trial of VideoScribe to create this! It's super user-friendly!

Tuesday, August 16, 2016

#MTBoSBlaugust Day 11: AP Calculus AB Learning Targets

Here's my first draft of my AP Calculus AB Learning Targets for this year. My goal is to add these to my Student Unit Organizers so students have a road map as we go through the unit. In addition, these will help me design my assessments and my study guides- the next 2 tasks on my list. (How do I already feel behind when there are still 3 weeks left until I see kids?!?!?!)

These are a compilation of my own 2015-2016 course calendar, information from my APSI last month, the AP Curriculum Framework, and reading through other teacher's course calendars for student-friendly wording (This one in particular was helpful). They align to Calculus of a Single Variable, 8th Ed. by Larson, Hostetler, and Edwards. 

I've made a few big changes from other teacher's that I've read, the book, and some things I didn't like last year. The biggest ones are:

  • Weaving transcendentals and trig throughout the units, rather than separating them like the textbooks and many other teachers do. I am still trying to wrap my brain around late transcendentals- I feel like the more practice kids can get with these intricate functions the better. If someone wants to convince me otherwise, please please please do. I am interested in hearing the other side. 
  • I switched the order I taught integration. Last year I started with the "area problem" as a motivation and then switched back to general antiderivatives, but starting with antiderivatives seems more of a natural flow and allows us to revisit u-substitution multiple times, rather than just once. It's my major change for this year, but I'm excited about it. This also would logically put differential equations in the middle of the integration unit, which I think will be a nice break for the kids. 
  • https://www.lookhuman.com/design/
  • (Side note: I just ordered the shirt at right...while I was writing these learning targets.... I need to start buying back to school clothes, but this was so much more fun.)
  • I moved volumes of known cross sections to after disks and washers, but I'm not sure if I'm going to keep it that way. Disk and washer were simpler cases for my kiddos last year since they are always the formula for a circular cross section; I saw so much more struggle in using the formulas for other shapes.  I'm considering testing it out this year to see how it changes the understanding of the kids. Nothing set in stone here yet. 
  • L'Hopital's isn't an "after exam" topic anymore- it's right in there, during my derivatives unit! Excited to get to spiral in some limits there to review. Also excited that it's only the simplest case, not all the other wacky indeterminant forms we'd normally get into after the exam. 
Let me know if you see anything I missed or have any sequencing tips that made a huge difference in your students' understanding! 

AP Calculus AB Learning Targets


Chapter 0: Pre-Calculus Skills
  • I can identify minimums, maximums, intercepts, intervals of positive/negative, and key values from a graphing calculator
  • I can sketch all parent functions by hand and identify their domain and range
  • I can write the equation of a line given a point and a slope
  • I can rewrite an absolute value function into a piecewise function
  • I can rewrite expressions using factoring
  • I can rewrite expressions using rational operations
  • I can rewrite expressions using long division
  • I can rewrite expressions using completing the square
  • I can solve equations and inequalities graphically and algebraically
  • I can find the inverse of a function algebraically
  • I can compose and decompose functions
  • I can use properties of logarithms to rewrite expressions and solve equations
  • I can identify exact trig values of important angles in the unit circle and use them to sole trigonometric equations

Chapter 1: Limits & Their Properties
  • I can evaluate the limit using a table  
  • I can use a graph to evaluate the limit
  • I can evaluate a limit using properties  
  • I can evaluate a limit by using direct substitution  
  • I can evaluate a limit algebraically  
  • I can write a simpler function to evaluate a limit  
  • I can evaluate a limit using two special trigonometric limits  
  • I can evaluate a limit using the squeeze theorem**
  • I can evaluate a one-sided limit
  • I can determine if a function is continuous (satisfy 3 conditions)
  • I can discuss the continuity of a function on a closed interval  
  • I can identify the type of discontinuity by name  
  • I can use Intermediate Value Theorem (IVT) to analyze function behavior in an interval
  • I can write the equation for a vertical asymptote  
  • I can evaluate limits with function values approaching ±∞
  • I can evaluate limits as x approaches ±∞
  • I can find the horizontal asymptotes of a function

Chapter 2: Differentiation
  • I can explain how the slope of secant lines can approximate the slope of a tangent line
  • I can use the average rate of change (slope formula) to approximate the derivative of a function
  • I can identify derivative as an instantaneous rate of change  
  • I can find the equation of a tangent line at a specific point  
  • I can find the equation of a normal line at a specific point
  • I can find the general derivative using the limit process
  • I can find the derivative at a point using the limit provess
  • I can explain the relationship between the limit definition formulas (at a point and general) and the slope formula from previous courses
  • I can use a graphing utility to find the slope at a specific point, sketch a possible graph of the derivative of a function  
  • I can apply to alternative form of the derivative  
  • I can find where a function is differentiable
  • I can differentiate using the power rule  
  • I can find where horizontal tangents occur
  • I can find the derivative of sine and cosine
  • I can understand how the derivative applies to Position/Velocity/Acceleration
  • I can differentiate using product rule  
  • I can differentiate using quotient rule
  • I can find the derivative of tangent, cotangent, secant, and cosecant  
  • I can differentiate using chain rule  
  • I can differentiate using more than one rule
  • I can understand function notation to find derivatives, including differentiating from a table
  • I can find derivatives implicitly
  • I can find the second derivative of an equation implicitly  
  • I can find horizontal and vertical tangents of an implicitly defined function
  • I can identify when L’Hopital’s rule applies to an indeterminant form (p.567)
  • I can evaluate a limit of the form 00 or using L’Hopital’s rule (p.567)
  • I can evaluate (f-1)'(a) (p.341)
  • I can find derivatives of functions involving the natural logarithmic function
  • I can find dy/dx using logarithmic differentiation(p.322) **
  • I can find the derivative of the exponential function (p.350)
  • I can find the derivative of a function involving a base other than e  (p.360)
  • I can find the derivative of an inverse trig functions (arcsin and arctan must be memorized)

Chapter 3: Applications of Differentiation
  • I can apply the extreme value theorem  
  • I can find critical values of a function  
  • I can find relative extrema of a function  
  • I can find absolute extrema of a function using the closed interval test
  • I can use the First Derivative Test to find relative extrema of a function
  • I can relate the First Derivative Test to the second derivative  
  • I can find points of inflection of a function  
  • I can find intervals of concavity of a function
  • I can sketch the graph of f ′ and f ″ given the graph of f(x)  
  • I can sketch the graph of f(x) given the graph of f ′ and f ″
  • I can use a tangent line to approximate function values  
  • I can use differentials and the graph of f to approximate values**
  • I can verify that a the criteria for Mean Value Theorem apply
  • I can apply the Mean Value Theorem
  • I can write an argument to justify my use of Mean Value Theorem
  • I can apply Rolle’s Theorem
  • I can apply the Second Derivative Test to find extrema
  • I can solve applied minimum and maximum problems
  • I can identify important quantities and equations in a related rate problem
  • I can solve related rate problems involving distance
  • I can solve related rate problems involving area and volume

Chapter 4A: Integration (General Antiderivative)
  • I can find the general
  • anti-derivative of an algebraic function  
  • I can recognize why we need a constant of integration  
  • I can define the indefinite integral and its parts
  • I can find the general anti-derivative of a trigonometric function
  • I can find the original function from the graph of the derivative  
  • I can find a particular function given certain conditions  
  • I can find the anti-derivative of a natural logarithmic function (p. 332)
  • I can find the anti-derivative of a function involving a base other than e
  • I can find the anti-deriative of an exponential function
  • I can integrate functions whose antiderivatives involve inverse trig functions
  • I can use the method of completing the square to integrate a function
  • I can integrate functions using u-substitution
  • I can integrate functions using long division

Chapter 6: Differential Equations
  • I can sketch the slope field to represent a differential equation  
  • I can sketch the solution curve to fit a given slope field  
  • I can choose a differential equation to fit a given slope field
  • I can use separation of variables to solve a simple differential equation  
  • I can use exponential functions to model growth and decay in applied problems
  • I can use exponential functions to model compounded continuously problems  
  • I can identify a problem as exponential (y=Cekt) when it discusses the rate being proportional to the amount present
  • I can find the general solution of a differential equation
  • I can find the particular solution with conditions

Chapter 4B: Definite Integration and the Fundamental Theorem of Calculus
  • I can estimate the area under a curve using a Riemann Sum  
  • I can estimate the area under a curve using the Midpoint Rule
  • I can approximate the area under a curve using the Trapezoidal Rule  
  • I can compare Left, Right, Midpoint, and Trapezoidal approximations of the area under a curve
  • I can evaluate problems involving summations both with and without calculators
  • I can identify the limit definition of the definite integral
  • I can represent the area of a region using a definite integral  
  • Ican recognize that the value of a definite integral can be found using geometry
  • I can use properties to help evaluate definite integrals
  • I can use the Fundamental Theorem of Calculus to evaluate definite integrals
  • I can accurately calculate a definite integral using u substitution and change of bounds
  • I can evaluate a definite integral using a graphing calculator  
  • I can find the average value of a function using the Mean Value Theorem for integrals  
  • I can use the Second Fundamental Theorem of Calculus to find the derivative of a definite integral
  • I can use the differential equation and a given point to find the function
  • I can use an accumulation function to answer application questions

Chapter 7: Applications of Integration
  • I can finding area between two curves
  • I can use the disk method to find the volume of a solid of revolution
  • I can use the washer method to find the volume of a solid of revolution
  • I can use the shell method to find the volume of a solid of revolution**
  • I can find the volume of solids whose cross-sections are known

Monday, August 15, 2016

#MTBoSBlaugust Day 10: Mathematical Mindsets

Just finished Jo Boaler's incredible Mathematical Mindsets. Can you tell it gave me a few ideas? 
For anyone who hasn't read it yet, Boaler does an incredible job synthesizing recent research on everything from the influence praise has on toddlers to the influence assessment and classroom environment have on students. She looks at achievement from many angles and offers tons of practical advice and strategies for all grade levels. I feel this insane desire to put one in the mailbox of every elementary teacher I've ever met who told me they "weren't math people." It's that kind of read. 

I wanted to go through some of my favorite ideas in the book and try to marry those to some ideas for my classroom, so bear with me here. Feeling a lot of inspiration mojo today. 

1. No one is "born" with a math-phobia
My brother is a computer scientist and my sister-in-law is a nurse. They both work in extremely math-centric careers and have a large amount of formal math training. Yet the insist that my 2 year old niece already needs me to set some free time aside to tutor her in high school because they won't be able to help and she'll probably struggle just like mom and dad did. It drives me insane. Math phobia is learned (maybe even- dare I say- taught) and I never want her to experience that. I see the unbounded love she has of experimentation right now....I never want her to lose that. 

This particular passage shot out at me the minute I read it...both when thinking about my own family and thinking about my kiddos:
"...researchers concluded that the difference between high- and low-achieving students was not that the low-achieving students knew less mathematics, but that they were interacting with mathematics differently. 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 didn't 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. The researchers pointed out something else important- the mathematics the low achievers were using was harder mathematics."
The frustration so many students that have been labeled low face is that they have always trusted that the procedural way a teacher taught them was the only way. When that procedure became too complicated, too distant from their own intuition, they began to think of themselves as failures. And no wonder they've lost trust in themselves and their math teachers by the time they get to high school. I just imagine that kid in the back of the room who refuses to do what's asked of him because he's defeated before he starts....that's the kid who has been trying to keep up by doing harder math all along. Your heart just breaks for them. Of course they hate math. 

2. Homework isn't just a question of practice, it's a question of equity
My husband has always refused to assign homework in his science classes and as a math teacher I've never been able to go quite get there. I was different than many math teachers I've met in that I assigned only a small amount of homework and gave my students a talk on the first day that if they were struggling after ____ amount of time on homework (depending on the grade level), they should stop and come in the next day with questions. But this book really pushed my thinking on the topic.

What was particularly interesting to me was to see the amount of research backing up the neutral or negative effect of homework on student achievement, as well as the discriminatory effects of homework grading practices. In a sense, backing up what I have seen every day since I started teaching. I have taught those kids who have a job (or jobs) to help support their family, don't really eat when they aren't in school, and more or less raise their siblings when a parent is absent, working long hours, or deceased. I've always had a positive enough relationship with these kids to work one on one with them and decrease their amount of work or give them an extension on it. But I saw in their eyes that it stressed them to know that I was making an exception for them. Seeing these observations confirmed with so much research was huge for me. 

What I also loved was that Boaler gave an alternative if you are at a school that requires homework. Instead of giving a list of problems from the book, use that time to help students reflect and self assess. Boaler's homework reflection questions can be found here

Boaler also offers 6 strategies to purposefully make math class for equitable for all. Homework is only one part of a much bigger puzzle. I created this graphic so I can hang it right above my desk. I want these challenges nearby whenever I'm planning. 

Equity is how we better kids lives. It's the whole point of education. I'm excited that I'm becoming more cognizant of it through studies like this. 

3. The 5 C's of Mathematics Engagement

Love these. Some things to shoot for every day. 

4. Designing & Adapting Math Tasks
Boaler offers 6 questions to ask yourself to try to adapt a mathematics task to your classroom and I love them! Another little graphic for my desk so they're never far away! 

5. Heterogenous Grouping Helps All Students
So often when a student is grouped with those deemed "outside his or her ability level," you run into issues with the outside world. Parents worry their student will be left behind or not challenged enough and can be extremely vocal about expressing it. Boaler emphasizes that this has been disproved many times and it's helpful to read some of the research to have for discussions with parents and administration. She also discusses Complex Instruction, which examines student engagement in relation to their (actual or perceived) status in a group and works to directly create equity and student accountability.

One thing I will take from this is more of an emphasis on the use of group roles. I used them when I taught middle school, but have moved away from them in high school. I want to give them another go this year with this framework to help and see how it works. I think it might be especially helpful in my standard level classes, where group work can be more of a struggle. 

I particularly loved this quote from the section on Complex Instruction...it was a huge part of my STEM group norms at my last school:

6. Assessments Shape Mindsets
Students label themselves by their test grades and this identity can be such an impediment to mathematical growth. In such a performance-centric world, Boaler encourages a complete reexamination of assessment practices. 

One strategy I loved was one a 20 year veteran teacher had shared with her. Students were told to answer as many questions on an assessment as they could, then draw a line across the page when things got too difficult. Any questions below this line could be answered with the help of a textbook. The work beneath the line then became the fodder for classroom discussion. This was more about assessing students in an effort to continue their learning journey- a true example of formative assessment. 

Boaler also discusses Assessment for Learning (in contrast to assessment of learning). This demands:

  1. "Clear communicating to students what they have learned"
  2. "Helping students become aware of where they are in their learning journey and where they need to reach"
  3. "Giving students information on ways to close the gap between where they are now and where they need to be"
I love the idea from this section of generating "I can" statements for each unit of your course and having students use their as a self-assessment. If anyone has geometry or AP Calc AB resources for this, please feel free to share :)

Boaler gives lots of advice on grading and I'm still working on wrapping my head around the practicality of a lot of these. One that will particularly influence my grading scheme is the idea of a 10 point separation between letter grades A-D, then a 60 point separation to an F. She suggests using a point scale of 0-4 to keep grading more mathematically fair and I like this system for homework. 

7. Growth mindsets can be built by teachers
The final chapter of the book is strategies for growth mindset teaching and they are helping me shape my first day activities that I shared previously. In my Post It Note activity from a previous blog, I was still working on shaping the questions I wanted students to answer. Boaler gives a list of the positive norms she encourages in class and I am going to frame my questions around these.
Read more about here norms HERE

She also talked about participation quizzes, a method to encourage productive group work. This fits perfectly with my previous post about AP Calc study groups and I'll definitely be using it with them. Here's a summary of the strategy.  

Lastly, she talked about the way that teachers interact with students in the classroom. I want each of my students to truly believe I think they can learn and I want to make a conscious effort to give growth praise and help, not fixed praise and help. Praising my kids for their efforts, their specific strategies, and their failures will be more beneficial for them and provide me better information about my kiddos in the long run. It will make me a better aunt and (someday) a better parent, too. 

To anyone who hasn't read the book yet, I highly encourage it. It is a game-changer for anyone who feels like they're in a rut or wants some new ideas and it contains tons of research and strategies for your benefit, no matter the level you teach. 

Next, I'm diving into Make It Stick! My kids won't know what hit them this year! 

P.S. Anyone else feel like we need to start an MTBoS Book Club? Do some online book studies?