Here are the reflection and discussion questions for chapter 1. If you choose to comment on more than one, please use separate comments to keep the conversation organized. Comments for this chapter will be accepted until November 1st.
- Think about the instructional strategies you use most often. Which do you believe are most effective? What evidence do you have for their impact? Save these notes so you can see how the evidence in this book supports or challenges your thinking about effective practices.
- Identify one important mathematics topic that you teach. Think about your goals for this topic in terms of the SOLO model discussed in this chapter. Do your learning intentions and success criteria lean more toward surface (uni- and multi-structural) or deep (relational and extended abstract)? Are they balanced across the two?
- A key element of transfer learning is thinking about opportunities for students to move their learning from math class, to use their knowledge to solve their own problems. Think about the important mathematical ideas you teach. For each one, begin to list situations that might encourage transfer of learning. These might be applications in another subject area or situations in real life where the mathematics is important.
NH Seacoast Math PLC Book Discussion 
Hi everyone! I’m Michelle and I’ve just begun my 25th year of teaching at Exeter (NH) High School. This year I’m teaching Algebra Foundations and Geometry. I’m so glad you decided to join us!
Although I haven’t tackled chapter 1 yet, I did read the preface, and I wanted to share with you a quote that stood out to me on page 2, and that I shared with my students on the first day. “[Great mathematicians] knew that it was not exceptional talent that enabled success but the ability to persist; to enjoy the struggle; to see the growth of their learning as a function of seeking help and listening to others solve problems; and to try, try again.” If my students can embrace this growth mindset, I’m confident that they’d be well on their way to success!
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Hi all! I’m Jenn and I’m in my second year of teaching high school math (I taught elementary for 4 years previously and then stayed home with my kids). I teach Practical Math, Senior Math (which is an algebra survey class) and one Geometry at Pinkerton Academy.
Looking at the strategies I use in my classroom, I use some direct instruction (I try to do lots of think alouds and always ask my students why answers make sense during it), independent practice, group problem solving, use vertical non-permanent surfaces :), review games, student choice stations, discovery activities in groups, and tiered checkpoints.
The group problem solving around the room has been new to me this year and I and my students love it. Something about getting them out of their seats and to a whiteboard gets more buy in (especially with my seniors who are typically with me because they struggled at some point in math in high school) and helps them stay on task. I try to balance types of problems that we’ve covered in class with novel problems to develop their thinking before we start new types of learning.
Tiered checkpoints also seem useful but I feel like I’m not doing anything during them! (Which is maybe the point – I do set up the checkpoint and decide what is on it and who is going to share what answers). I have students work independently for about 7 minutes, with a partner for 7 minutes and then around the room in small groups to put up the answers. Students then do a gallery walk and ask questions when they reach a problem they didn’t understand. I try to direct those questions to the students who put those answers up on the whiteboard and sometimes we correct answers together as a class.
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Hi Jennifer! I love that you have your students explain why their answers make sense. If a student gives an incorrect answer, it gives them an opportunity to correct their thinking without the teacher pointing out the mistake.
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A lot of people celebrate mistakes because they go on to lead to deeper understand for MANY
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I feel like with a lot of my students the ability to think about whether an answer makes sense is where they get lost. If they make small calculation mistakes but end up with an answer that is ridiculously impossible, it should be easy to catch. Most of the time they will notice mistakes only when “the answer is a decimal” and sometimes those aren’t mistakes!
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Hi! I am Becky I have been teaching for about 2 years. I have taught middle school, college and high school. I currently teach at Pinkerton in Derry. This year I am teaching Algebra 2, Pre- Calculus and Repeater Algebra 1.
Some of my strategies that I use in my classroom include: team practice, turn and talk, direct instruction and interactive game practice. During team practice students might have an set of problems that they have to decide if they were completed correctly or incorrectly. The students enjoy this type of practice and many students enjoy explaining to there group where the mistake happened. Another team practice is matching activities, for example match the quadratic equation to the graph and to the table of values. Turn and talk has the student check their answers with a neighbor.
Everyday I want to encourage my students to talk about math and explain how to do the math to others. Students take pride when they can help others.
I am interested to learn more about the surface level of learning and how to proceed to higher levels of understanding using new approaches.
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Hi Becky! That’s great that you have students analyze completed problems to check for mistakes! It reminds me of these activities that I do in geometry (https://www.amazon.com/Whats-Wrong-Picture-Michael-Serra/dp/1559535849). I love that you have students explain the mistakes to each other. You know you really understand the math when you can explain it to someone else!
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Something that I do with my Algebra Foundations class is have them explore visual patterns (http://www.visualpatterns.org/) as a way to have them engage in algebraic thinking. We use a standard template for each pattern in which they have to draw the next step, state what they notice or wonder, and then complete a table that shows calculations for the 1st through 5th step, then the 10th step, the 27th step, and finally the more abstract nth step. I constantly ask them where they see the step number in the design so that it becomes easier for them to determine an expression for the nth step. These explorations are intended to be practice for more involved problems for which students have to describe numerical patterns, with the hope that they can transfer their learning to the more complex tasks. I’m happy to share these lessons – email me at mmorton@sau16.org if you’d like them!
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