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Teaching Numeracy, Critical Habits 8 & 9

This week we finish up the final two critical habits.

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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

Habit 8: Develop Vocabulary

“Understanding the language of math gives students the proficiency they need to think about, confer, and integrate new math concepts as they are presented.”

Academic vocabulary is difficult for all students, and it is particularly hard for ELL students, making this an important chapter. I liked the idea of helping students form Vocabulary Habits (p 103), because our goal is for students to become more independent learners. Unfortunately, many students don’t get past the first habit–identifying when understanding has broken down and realizing they have to do something to move on. The authors made a great point that teachers need to plan think-alouds to show students what the habits look and sound like in practice. The whole idea of teacher think-alouds in math instruction has been a recurring theme throughout this book. I think this practice is so much more common in reading instruction, and math teachers have yet to tap the power of this instructional practice. If we want students to develop their own vocabulary habits, we need to model and teach the habits.

The second bullet on page 105, about words that have different meanings in math than in regular conversation, caught my attention. I attended a vocabulary session with Christine Moynihan, author of Math Sense, at CAMT, and she talked about this very thing. Words such as right, plane, and reflection have more familiar meanings unrelated to math. She also pointed out that even within a math context, some words have multiple meanings. Words such as round, square, and second. The list under Be innovative in your vocabulary instruction on page 107 is extremely comprehensive and will be a valuable planning tool. The second bullet, Use the words in your own speech, requires teachers to develop habits of their own! First and foremost, we need to be precise in our own mathematical language. It is a sum or a product, not an “answer”. Consider having someone videotape one of your math lessons and analyze your use of language as you view the video. Videotaping can seem very awkward at first, but it is a great reflective tool and no one needs to see the video but you!

Habit 9: Collaborate to Learn

“When collaborative moments are built into your lessons, your students will learn to appreciate each other’s thinking.”

For me, the true gold in this chapter came on page 118 with the statement, “True collaboration is not what some consider to be ‘group work'”. Amen! You can probably put this into the context of your own work experiences. Many teams do team planning, yet not all team planning would be described as truly collaborative. As the authors point out, true collaboration requires planning, the establishment of community and group norms, and an equal commitment from all members. True collaboration is difficult for adults, so I’m sure we realize how much support students will need to effectively collaborate.

If you are not sure if your instructional style is fully supporting student collaboration, you might use the list of key ideas on pages 121 and 122 as a reflective tool by turning each statement into a question and rating your answer using a scale. For example:

  • Have I arranged my desks so that students can easily talk and listen to each other?
  • Do I encourage students to generate questions and direct their questions to the rest of the class, not simply to the teacher?
  • Do I maintain an atmosphere of acceptance and freedom?

You will probably find that you are already doing many things to foster collaboration in your classroom, but you might find a couple of new ideas as well.

And Now for Something Completely Awesome and FREE!

Greg Coleman, aka Mr. Elementary Math, was inspired by the question prompts in Habit 6, and he created this amazing set of questioning prompts.  Click here to head over to his blog and download them!  Thanks so much, Greg.  You are one talented dude!

Please add your thoughts about these two chapters in the comments!

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  1. Good evening everyone! I really enjoyed the vocabulary chapter because it reinforced some of the information I gained in recent PDs. Last year, I attended a training that covered various strategies from Marzano’s Classroom Instruction That Works. We did several of the vocabulary activities that are discussed in the book and I especially liked the Frayer Model. It is important for kids to have visuals because some of the concepts can be really abstract. Also, providing examples and non-examples helps students that may need to make connections to their prior knowledge.

    Mr Elementary Math Blog

    1. The Frayer Model is such a powerful tool, Greg! I agree with you about the importance of the visuals.

  2. Cultivating a deep sense of understanding means providing moments for students to interact with math vocabulary. For some time, I thought that meant simply me making a word wall. Then, I realized that my word wall was about as useful to my students as the trash basket. We put things on it and left them there to waste away.

    That is when I started playing around a bit with the idea of making an interactive word wall. First of all, I stopped making the words and had the students create the vocabulary using a Frayer Model. I infused the “working word wall” into my daily lessons using questions prompts and discussion ideas, and voila, the words came alive to the students in a whole new way.

    For example, I might ask small groups to choose three words that would connect to today’s learning and prove their decision in some way (CRA). I really like using closed word sorts and open word sorts, which you know students love both.

    At times, I liked to hand out the words, one to each student and ask them to stand-up and form groups that make mathematical sense, then challenged them to create a title for their group of words and justify that title. I might also challenge groups to decide which two groups might be included in the same math news article and again, defend their decisions.

    I’d love to get your thoughts on how a working word wall works in PreK-K.

    1. I think the shift toward interactive word walls is following the general trend of shifting more of the responsibility for learning to the students, with the teacher’s role being that of facilitator. It’s so exciting! Kids talking about math, writing about and drawing math, DOING math!

    2. As a K/1 teacher, I love the interactive word wall (although I am still working on it in my own room). I always make sure to make my words easy to remove. I have used magnets, and now that I do not have a magnetic wall, I have them attached with velcro. That way I can easily pull them off, rearrange them, hand them to a student, etc. In my own goals I want to have them student written, and I want more content words – actual VOCABULARY- and fewer sight words. And I want to pair student drawings/representations with the text on the word wall cards. So, I love the concept and have some improving to do to get where I want to be with it.

  3. HI all,
    I love Margie’s idea of having kids choose words that relate to the current topic and to justify their thinking! I am always looking for ways to help kids make more connections with a word. The Frayer model is a great way to organize these connections. Chapter 9 really inspired me to work hard at planning more student collaboration into my small group time next year. As an interventionist, I have such limited time with students and sometimes fall into the trap of trying to move ahead with my lesson plan without taking time for this critical piece. This prompted me to read Math Exchanges (Wedekind) which further explores this idea.

  4. Vocabulary has been my school’s PD focus for the year. We have been sharing vocab ideas around the classrooms, and have had much discussion around Marzano’s work. So this read was exciting for me – I love it when the pieces all seem to connect!

    I was very excited about the “Vocabulary Grab Objects” activity. I think pairing math and drawing is natural and incredibly engaging. For several years now I have done formal drawing instruction with my students once a week. I teach them one way to draw something (one way to draw a person with clothes, a way to draw a dog, a way to draw a castle, etc). I ensure that they know that there are many ways to draw each of these things. Then, as I teach them the drawing, I embed LOTS of math vocabulary into the instruction. For example, “In the top half of the paper, draw a horizontal line. Draw another parallel line just below it.” I also teach them shading techniques to make their objects look 3D, and I do this by having them learn to shade 3D objects (cone, sphere, cylinder, and cube). The kids begin to understand things like “quadrant,” “half,” “semicircle,” etc because they are embedding them in drawing. And I often let the kids choose what we are learning to draw, so the motivation is HIGH. When I read the Vocabulary objects idea, it gave me one more option on how to put these pieces together. Having them take a drawing (one they did, or one in a coloring book), and label it with math terms! Great idea.

    I also really enjoyed the collaboration chapter. I think my main focus here is going to be to teach the kids how to question one another for further understanding. I have partnerships and turn and talk moments regularly, but I know that my students (K/1) need lots of instruction on HOW to talk to one another. Giving them sentence starters will be a great tool.

  5. Vocabulary has been a focus of ours lately. The problem has been picking which words to focus on so it is consistent across classrooms, grade levels, and schools. Is it CCSS? District curriculum? Marzano’s list? I also like the idea of student choice that Margie referenced above. The vocabulary lists get quite lofty and then the expectation becomes unrealistic for students. And teachers get overwhelmed with what words to teach when. We are still in the process of figuring this all out.

    When reading Habit 8, the key Vocabulary Habits stuck with me. I think with explicit instruction and modeling these habits can become part of classroom learning. The transference of understanding the meaning of these words is huge! I feel a conscious effort needs to be made in planning for vocabulary instruction in math and not hope it just happens. There were many ideas shared in this chapter that I hope to pass along. For some reason, the Greet and Go activity on pg 112 made it to my list of must-dos. I love the idea of students having their brains loaded with words…it’s like priming their brain for what learning is to come.

    In Chapter 9, Collaborate to Learn, I really liked the focus on listening (pg 118) as a metacognitive process. Not only are students processing information from the listener standpoint, but the speaker is processing his/her thinking. Sometimes being an attentive listener during collaboration is difficult for students. It is something that can be practiced and encouraged. I also like how the chapter pointed out that true collaboration is NOT what some consider to be “group work.” This might make an interesting talk point for teachers to help see the difference between cooperative learning, group work, and collaboration. Changing the statements from this chapter into questions like Donna recommended above is an awesome idea. It is a great way to reflect upon one’s teaching to ensure that the classroom environment is conducive to student collaboration. Two lasting thoughts are the reference to Rick Wormeli: Learning occurs in “compelling disequilibrium,” and the statement, “Let confusion linger for a while (pg 121).”

  6. Ug…I’ve fallen nearly a week behind! I really enjoyed Habit 8 Vocabulary because I feel like this is an area where I am weak. I don’t have a good set of vocabulary activities to fall back on. And now I do! I found myself counting down the pages to the section on implementing in the classroom. I continue to be struck by the similarities in the ideas presented and the connection to informational texts standards (CCS). I love the idea of using sorts for math vocabulary.

    One advantage to being late to response, I was able to read and reflect on the other responses while finishing up my reading. Karen, I love your idea to incorporate more concept words in your interactive word wall. I literally just finished putting magnets on my letters last night in preparation for moving to an interactive word wall. I hoped to make it more student centered by putting up words that they generated through their writing and speaking. What a great idea to add concept words too! And I see it being an important resource for writing more about math. Its so hard to expect young students (I teach 1st) to write concept words if they aren’t readily visible.

    One last take away from Habit 8- a pet peeve of mine is how primary teachers use cutesy words rather than true vocabulary and I find this true in math more than other subjects. Switch-a-roo facts and alligator signs are two that come to mind. Then we wonder why students can’t understand directions on standardized tests!

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