Glad to see you’re back for more great math discussions!
This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.
If you’re just joining us, we’re reading and discussing Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking, by Margie Pearse and K. M. Walton.
Reading Schedule
- Preface and Introduction
- Critical Habits 1 & 2
- Critical Habits 3 & 4
- Critical Habits 5 & 6
- Critical Habit 7
- Critical Habits 8 & 9
- Essential Components 1, 2, & 3
- Essential Components 4 & 5
Habit 7: Summarize, Determine Importance, Synthesize Using Note Taking and Journaling
“Writing shifts the responsibility for learning away from the teacher and toward the students by encouraging personal learning”
As the authors note early on in the chapter (p 79), the three skills discussed in this chapter–summarizing, determining importance, and synthesizing–have “the power to force students to own their mathematical thinking and be able to take it with them into the real world.” Of course, these are not skills that only support math learning. In fact, they might be more often thought of as language arts skills.
Although we don’t use textbooks for math instruction on my campus, I have used the textbook scavenger hunt idea with science texts in the past, and I think it’s a great way to introduce students to the features of a nonfiction text.
Likewise, because we are an elementary campus, we don’t do much note-taking. When I’ve seen it in the classroom, it has most often taken the form of the Interactive Cloze System described on page 86. The teacher prepares an anchor chart prior to the day’s mini-lesson, with blanks in place of keywords and phrases. Students have a printed copy of the same anchor chart. Students interact with the teacher during the mini-lesson to fill in the missing words. After the mini-lesson, students glue their completed work into their math journals. I’m curious to hear what other elementary teachers say about note-taking.
From note-taking, the chapter moved on to journaling. Journaling is huge, in my opinion, and should be an ongoing part of math instruction at every grade level. I particularly liked when the authors referred to the concrete, representational, abstract sequence of instruction (p 92) and the way that math journals can be used to move students from the concrete to the representational and abstract. It’s so important that those stages overlap, and journaling is the perfect way to connect them.
The authors addressed and dismissed the elephant in the room–the time required for journaling–by citing research that journaling can help reduce the need for review and reteaching (p 93). I think that underscores the fact that when students put their thoughts in writing, they “clarify their thinking, and as they write, they expand their knowledge of the math.” (p 92). In other words, learn it deeply the first time around and you won’t need to review and reteach.
I loved the sentence starters on page 96, because students often just don’t know where to start to put their thoughts in writing. And, I think, teachers can fall into a routine and overuse certain prompts. I knew Margie wouldn’t mind, so I took the liberty of creating a poster with some of the prompts. Like the Math Fix-Up Tools from Habit 1, I also made a smaller, B&W version students can glue in their journals. Grab the writing prompts poster here.
If you are not using exit tickets in your classroom, be sure to read pages 96-97 and give them a try. They are a quick, easy, and extremely powerful formative assessment tool. Once you have the stack of exit tickets, you can easily sort them to create your small groups for the next day’s instruction. You don’t need fancy forms for the exit tickets–plain index cards work great.
While there were many practical activity suggestions offered on pages 98-101, my favorites were the 3-2-1 Journal Entry (p 98) and having students Compose Problems (p 99).
I have used the 3-2-1 format with adult learners in professional development sessions, but I like the idea of using it with students. I also like the suggestion provided for changing up how to use the 3, 2, and 1 (examples of learning, nonexamples, ways to tell the difference).
An activity I have used extensively is what I call You Write the Story, which is a fancy name for having students compose problems. You give the students an equation, such as 24 x 6 = ?, and they must write a story problem that can be solved using the equation. This is a VERY difficult activity for some students and takes a great deal of modeling, but it really does shine a spotlight on their understanding of the operations. You can easily differentiate the activity by using larger or smaller numbers; different structures, such as 68 + ? = 133; and even two-step equations, such as (24 x 6) – 32 = ?.
Check out this post from Mr. Elementary Math for some great question prompts!
I really enjoyed this chapter because it demonstrates how we can infuse comprehension strategies into mathematics. My wife is a reading coach and we always get into deep conversations about the link between reading and math. The statement that “one must synthesize the information to summarize it” is powerful because it shows the relationship between summarization and synthesis. I have found teaching summarizing to be one of the most challenging skills to teach because students tend to copy sentences from the text verbatim. Once student can summarize effectively, especially in writing, you know that they have a good grasp of the material. That is why I really found the section on journal writing to be helpful. The explanation of the different journal prompt purposes and example questions was excellent. Can’t wait to read the next chapter!
Greg
Mr Elementary Math Blog
The connections between reading and math are becoming more prevalent in literature, Greg. It seems that nearly every book I’ve read lately on math instructional practices has referenced the similarities between the two. I just pulled Laney Sammons’ book Building Mathematical Comprehension off the shelf, and it looks like I’ll be rereading Chapters 6-8 which are on the very skills we’re talking about today.
I love that you and your wife discuss the links between math and reading. I wonder how often conversations like that take place between math and reading teachers? With research showing such strong connections, you’d think there would be more collaboration across content teachers, but I’m not sure I see that happening. Do you?
I don’t see as much collaboration across content areas as I would like. That is why I think math journaling is a great instructional strategy to use in math. We are getting a new test in GA that is replacing the CRCT and we just sat through a presentation this week. We were able to see some sample questions and the new assessment, GA Milestones, will have many open-ended questions. Students will have to write an explanation of how they know that their answer is correct. Also, the sample problems were all word problems. You really had to have good reading comprehension skills to understand what the problem was asking you to do (determining importance). With these new shifts in assessment, there is a definite need for across content area collaboration.
That sounds like a great way to assess students, Greg! Our state test has always been all word problems, but no written component yet.
PS Thanks Donna for the math journal handouts. I’m still working on the questioning poster from last chapter.
Greg
Mr Elementary Math Blog
Thank you, Donna, for creating the “I can put it in writing” poster. I love it! I already printed them out and made copies for all my students.
From my experience, developing inference skills in academia are quite difficult for students, but reading the world outside of the classroom seems to come naturally to them.
Even now, as the Coordinator of a Math Resource Center in higher education, I introduce this idea by asking students how and when they know it’s a good time to call home and ask for money. Conversely, I also ask them how they know when not to do this. The conversation is often lively and fun. I then collect their ideas and draw their attention to an equation that is always in the front of any class I teach: BK + TC = I (Background Knowledge + Text Clues = Inference).
My goal is for students to go beyond the “I just figured that…” to “I made an inference because I already know…and the text is showing…so I can infer that…”
It is sometimes challenging to use this language in math, but it is so vital for students to be able to name and claim how they “just figured…” something.
Margie, I love your “equation” for inferring and the sentence stem!
Oops, sorry. I got so carried away with my thoughts on making mathematical inferences that I forgot to also add my responses to the new chapter.
I have found taking the time for proper summarizing to be the first habit I dismissed in math whenever I ran out of time. And every time I did that, the learning had no real chance to congeal and my students and I were left not exactly being sure what they knew and how they knew they knew.
I shared this frustration with a good friend and she gave me a great idea. I recently made four large stop signs. Inside the stop signs I wrote “STOP! 1 minute to reflect on what you learned so far.” I colored them, laminated them, put two back-to-back, stapled them together and pushed them into two meter sticks to create two stop signs.
Now, they are visible to me and whenever I need to stop and provide those moments for summarizing, reflecting, debriefing, and synthesizing, I hold up one of the stop signs, sometimes even toot a short traffic whistle and take a moment out to determine importance synthesize, and summarize.
The idea of having the two stop signs in front of me also keeps me accountable.
I love this idea Margie! I am also guilty of letting summarizing go when I feel like I am running out of time. Your tip about the stop sign is something I think would work well for me!
Tara
The Math Maniac
I have just joined this book discussion and am enjoying the comments and insights from Donna, Margie and others. I am providing math intervention for K/1 students. I usually work with students in small groups outside the classroom on foundational skills and/or concepts. Although I have used journaling before when I was a classroom teacher (I used to use the 3-2-1 a lot in science journals back in the day!) it hadn’t occurred to me to consider them in small group work. My students often struggle when trying to represent their thinking or their solution to a problem. Throughout the year, they are introduced to many different ways to represent numbers (PPW charts, diagrams, manipulatives, ten frames, etc) and have a lot of difficulty making connections between representations and seeing ways that they are the same and different. Using a journal would allow us to explore these representations and to keep tabs on the progression of their thinking.
My position is somewhat ill-defined and my duties are a moving target! My primary focus, however, has always been early numeracy skills. The discussion in the first chapter on the definition of numeracy was really helpful in clarifying just what these skills are and why they are so important!
I always flip through a book before I begin reading to get a sense of the layout and the main ideas in each chapter, similar to what was described on page 82! I look forward to the second half of the book and the discussion that will follow.
Sandy, I’m going through the same thought process as you regarding journaling! I am moving into an intervention role next year, K-5, and I’m also thinking about having my kiddos journal.
Donna, I hope you post about it next year! My role is changing a bit as we move to a co-teaching model in my school. I will be in the classroom more, which makes journaling more difficult. Being in the classroom poses some logistical challenges, but I am finding some great strategies from the book that I will try. One of the most important is activating background knowledge prior to a lesson. Many teachers do this, but some do not, and I can observe students “glazing over” as they struggle to remember the previous day’s lesson without a warm up. If I am scheduled to be in the classroom for small group work time, I will have missed the opportunity to preview with my kiddos. As Margie points out back in Habit 2, one of the important benefits of activating background knowledge is confidence and active engagement in learning. I need to do some more thinking/researching this summer to figure out how to be most effective.
Oh, I most definitely will, Sandy! I can’t wait to take on my new role!
My big take away from this chapter was to teach kids to take notes that make sense to them, NOT to copy or write exactly what they read or are told. This immediately struck a chord with me. All through college I was meticulous with my highlighting and note taking in my textbooks, but not very good at it. I had a system where I highlighted every definition and underlined meaningful sentences, and then wrote notes on the side. The highlighting and underlining was absolutely useless. I did not process any of that information in a way that I retained, and I might as well have saved myself the highlighters. However, the little notes I scribbled in the margins DID help. They were the personal connections or examples that I came up with that helped me to connect the information and make sense of it. So, in reading about note taking, I really can testify to how important it is for kids to learn to sum it up in their own way.
I am now on board with the idea of math journaling (I have never done it before.) I just need to get started with my students! I think the best way for me to start will be to create my own journal and have them watch me think aloud as I do it. Of course, I will need to be clear that their journal should not be EXACTLY the same as mine. Once they grasp that (which they should do now, as we have been through that in writing a thousand times already!), I think it will be powerful
Yes, Karen! I’m big on margin notes. Hard for students to do with textbooks, but I think that’s why our language arts teachers use sticky notes a lot.
I also love margin notes. My students had textbooks, so they were unable to write in the margins. To get around this, I created lined strips of paper and called them “Textbook Talk-back Notes.” The students used double-stick tape (which will not rip the pages- thankfully, and the kiddos thought it was novel).
As a debrief, I would have them remove the talkback notes and put them in their journals responding in some way (writing a synthesis, sketching a summary, defending why what they wrote was important, etc.). Sometimes, I had them share with a partner and come to a consensus on one most important sentence that represents their learning and then share that with another set of partners.
The ideas are endless.
Love that idea, Margie! I also did not know that double-stick tape was removable. Learn something new every day! Ha ha.
This chapter gave me a lot to think about. Sometimes to begin a lesson, I have students do an example walk. From that, I ask them to “take notes” on what they observe in their journal. From there students can pair-share their thinking. The lesson can then begin. At this point, their brains have been primed and have a mental framework that can be added to during the lesson. One thing I noticed on pg 97 was the idea for students to revisit and revise an old journal entry. I could have students revisit their original thoughts from their example walk after learning has taken place and add/revise using a different color. In this way, students can track their before and after thinking.
Note taking in its purest form is tough for some students. “Verbatim note taking is, perhaps, the least effective way to take notes (pg 84).” This statement rang out as I read this page because this is what so often students do. I sometimes feel note taking is a skill that is constantly evolving. Even when students are asked to annotate text with a highlighter, the pages become more colorful than they are white. We have a saying, “Don’t be highlighter happy.” In order for students to be able to summarize and synthesize, they have to be able to pick out the kernels of understanding. To help students with that, I really liked the ideas of Summaries in Headline Fashion (pg 98) and Four to Six Word Summary (pg 100). I think this will take a lot of modeling and practice, but if students can work towards this way of synthesizing a lesson it might help with the retention of learning. As William Zinsser said, “Writing is how we think our way into a subject and make it our own.” We want our students to own their learning, and this chapter gives many wonderful ideas to help students get there.
I LOVE the example walk idea, Pam. What a great way to get students thinking! I had to laugh at your description of students being “highlighter happy.” I’ve watched students take tests on reading passages and practically the entire passage is yellow!
Chapter 7 was my favorite chapter so far. Mainly, this is because I am a BIG fan of math journals and justifying your answer. I like to know what students are thinking. One easy way to do this is through their writing. I do not want them to simply take in information – I want them to process it, digest it, and send it back to me.
I like to have students write in their journals about a topic that has been studied recently and then pass it to a friend. I ask the friend to respond (we teach this skill in the beginning of the year). If time allows, we do this one more time. We close with a few people sharing their thoughts and aha moments! I try to have the students do this at least one for each major concept. It really helps everyone clarify some misunderstanding that might exist AND justify the time spent on writing in their journals.
I loved seeing the exit ticket information. These were a staple in my classroom for years. They are quick, they give students a reason to listen, and they gave me a quick peek at what I needed to reteach.
Thank you so much for share your insight.