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Ben Graber

Chapter 6 is full of resources to explore.
Tell us what you find and share your experiences putting them into practice!

I took this chapter as an opportunity to challenge myself to develop low threshold, open middle, high ceiling problems. I'm moving into exponential functions and have decided to revolve the unit around applications of exponential growth. I am going to show my students a video on artificial intelligence and ask them to consider whether technological development is linear or exponential, and include a mathematical defense of their perspective.

I love, love the "Notice and Wonder" strategy because this makes mathematical problems have a threshold of zero. Anyone can notice things about a picture or problem, even if they are two years old and have never stepped into a classroom. I've been using this strategy to engage the learners who don't think of themselves as "math people". Regardless of their own personal challenges with (procedural) math, I want them to know that they are welcome in my classroom and can participate at equals despite their past history.

Part A:
Which instructional strategies caught your attention (pages 81-104)? Why? (be sure to reference the page your strategy can be found)

I really liked the strategies for helping students make estimations. I have tried to get my students to estimate, but like the book mentioned, I have found it to be a hard sell. Because of this, I found a lot of value in the warm-up describing WHY a particular answer would be unreasonable (and encouraging estimation).

Part B:
Share one of your experiences (as a student or educator) that came to mind when you read through Tracy’s “Misguided Approaches to Precision” beginning on page 104.

I get stressed out by timed tests because I feel like it limits my ability to think through problems and double check my thinking. The first time I took the PSAT as a high school student, my scores were significantly lower than when I took the SAT a year later, simply because of the stress of a high stakes timed test. When I took the SAT I was able to destress better and performed much better.Timed tests are very poor indicators of students' abilities!

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1.How does your own experience as a student compare to Tracy’s?

For as long as I can remember, I have been a perfectionist that has a hard time dealing with my own mistakes. I had low self-esteem as a teenager and I was very judgmental of myself when I made mistakes. This was not just in math and began through my own social insecurities. Because of this past history, which I am finally just now beginning to overcome in my 30's, I am very passionate about this topic. It is extremely important to me to help students understand the power of learning from mistakes and accepting themselves without judgment.

2.What are some of the instructional strategies/resources that help STUDENTS see that mistakes are part learning? (if possible, share links to your resources)

In my perspective, this starts by having a classroom where everyone is accepted and welcomed without judgment. This culture is vital in any classroom, but especially in the math classroom. I am open with learners about my own mistakes and my own journey of improving as a teacher.
I also begin the year by talking about growth mindset and the importance of perseverance. I use resources from Jo Boaler's Mathematical Mindsets and her online student course here: I also begin the year with a grit activity like this one:
One strategy that I have used this year is trying to help kids focus on improving and learning from mistakes rather than a grade. After kids have taken a test, I return the test WITHOUT a grade, but instead with feedback. I give the kids an opportunity to reflect and respond to this feedback before giving a grade.

3.What are some of the instructional strategies/resources that help PARENTS/GUARDIANS see that mistakes are part learning? (if possible, share links to your resources)

I have talked to parents about Growth Mindset at our school's open house. In our parent-teacher conferences, we try to focus on habits of mind rather than grades. It takes work to help parents see differently, but when they can see the importance of these habits, they buy into our vision.

Three reasons students are afraid to take risks:
1. Most students don't see themselves as mathematical thinkers. They don't have the confidence to try playing with mathematical concepts and understanding these concepts at a foundational level. This requires a certain level of emotional maturity that they aren't trained in.
2. Taking risks requires perseverance and grit, and is genuinely hard work. Students have not been trained in pushing through the grit required to take mathematical risks. And some students don't have the work ethic necessary for these risks; it is easier to sit back and let other students take the risks.
3. Students don't want to make mistakes because they see mistakes as a bad thing or an indicator that they are "not good enough". This fixed mindset suggests to students that their self-worth is based on their achievement, and mistakes indicate low self-worth. If they don't try, they won't fail.

Two strategies for taking risks:
1. I have found it helpful to encourage students that mistakes as part of the learning process. I give learners constructive feedback while celebrating the effort that they give when they take risks. This is all an attempt to help learners develop the growth mindset and see mistakes as a good thing.
2. I encourage learners to use a variety of mathematical strategies for approaching problems. This allows them to see that there are many different ways to apply mathematical strategies and there is not just "one right way" to think mathematically. They also see that different students have different mathematical strengths.

I really appreciated the suggestions for encouraging risk on pages 51-53. "It is recognized and celebrated that there are different ways to approach problems. It is also understood that not all solutions work equally well, and rich discussions can grow out of different methods... Students are encouraged to make sense out of mathematics in an active way and to push the boundaries of their thinking. They should only accept a claim in they are satisfied by a convincing mathematical argument."

I am a freshman math teacher at the NIHF STEM High School in Akron. I love teaching at STEM and working with inner-city kids, but I have been experiencing some teacher burnout this year. My hope is that this conversation will be able to keep the passion lit and help me work through some of the burnout.

Unlike most math teachers, I did not always like math as a student. In middle school I was extremely frustrated by algebra and the introduction of letters into math. I was never good at memorizing procedures and got frustrated when I didn't understand the "why" behind math concepts.
I didn't begin liking math until I was a sophomore and was able to begin visualizing mathematical concepts. Once I could visualize concepts, then I understand the underlying concepts and began doing very well in my math classes and enjoying math.
I am open with my students about my math story, and use it as a starting point for building a relationship - regardless of their past history with math, I believe that every student can come to appreciate math and understand the underlying concepts.

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Teaching at a STEM School
The past semester has been the busiest season of my life as I became a part of my dream school. I am a mathematics coach at a STEM high school in northeast Ohio, where I am a mathematics coach who guides and inspires all of the freshmen in their journeys in...
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Surface area and volume in olives (Greenr article)

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