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Chapter 2 - Option 1

01/11/2019 11:10 PM | Karen Campe

One of the reasons to use instructional routines in math class is to “help students and teachers build crucial mathematical thinking habits” (page 19).  Are there any thinking habits you already promote with your students or have tried to encourage?


  • 01/13/2019 3:07 PM | Anonymous
    One routine that I like to incorporate into my K-2 math intervention lesson is counting and writing numbers forward and backward. This is one way to warm up before leading into our lesson for the day. With this activity we are constantly making use of MP7 (Look for and make use of structure). I provide a simple number path 1-10 to support students who need it. Students are asked to notice the structure of the number path and apply it to numbers beyond 10. How is writing numbers 7-10 similar to writing numbers 27-30? This simple routine can be adjusted appropriate for the grade level I am instructing. My hope is that by guiding students to notice and understand the structure of the number sequence they will begin to look for and make use of structure in other math problems. I ask them to apply what you already know to help you plan to solve a problem you do not yet understand.
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  • 01/20/2019 12:24 PM | MINDY GOTTLIEB
    I have tried to encourage my students to read carefully and reread each question. I then ask students to understand
    1) What is this question about?
    2) What information do I have?
    3) What question is being asked?

    I ask students if they need any more information that would be relevant in answering the question.

    That being said I have to admit that I had trouble answering the question on page 27 since I did not read carefully and left poor Kate out of the problem thinking she spent $40 and that was all she had. I knew I was incorrect when my answer had dollars and cents. I also realized that I solve problem quantitatively.
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    • 01/20/2019 3:43 PM | Sarah Giaquinta
      I love that you have three questions that you have for your students to concentrate on before just diving into a problem and "seeing numbers." I find that when doing word problems, the materials I had to give the students always gave the information they need in a certain order, so the kids don't even read the problem! I have had to do a lot of supplementing to make them step back and have to think about what they were being asked and how to go about solving.
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      • 01/23/2019 9:35 AM | Michele Hanly
        I too liked the questions you ask. The questions are precise and concise. I think I will put them on a small poster board that I can just point to when needed. Thanks for the suggestion.
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      • 01/23/2019 10:25 PM | Karen Campe
        Sarah, I've had the same frustration with students just pulling the numbers out of the problem and calculating without thinking.
        Two strategies to address this are: writing numberless problems, so students have to decide what operation might be needed but can't actually calculate; and give a problem context including numbers but without the question, so students must read and think and suggest what questions could be asked.
        [And I think the routine in Ch. 3 will help on this point as well!]

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  • 01/22/2019 9:53 AM | Cortni Muir
    An instructional routine I try to incorporate into any lessons I do is the idea of Notice and Wonder (Thanks Max Ray-Riek and Annie Fetter). I think it is very eye opening when students participate in this kind of activity. I like to present a problem, often a word problem and ask students to think about what they notice in the problem and what they might wonder about a problem. I often encourage them to work through this in a think-pair-share format. I strongly believe that Noticing and Wondering helps give the teacher a look into how students are thinking about a problem and helps to maybe identify misconceptions they students may have about the problem. AS a coach I have been talking to teachers I work with lately about the importance of Notice and Wonder and often say it is a routine that we don't utilize enough in the classroom.
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    • 01/23/2019 10:28 PM | Karen Campe
      Notice and Wonder is a powerful routine, and I think it is applicable for all grades K-12+. And I agree that we don't utilize it enough in the classroom!
      You mention that it gives the teacher a look into how Ss are thinking about a problem... and I would say that if Ss record their Notice & Wonder, that helps the teacher "capture" the thinking of more students than they otherwise might.

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  • 01/23/2019 8:09 AM | Marianne Springer
    When introducing any new algebraic content, I always focus on having students connect the new and often abstract algebra to something they have seen before. For instance multiplying complex numbers looks alot like multiplying binomials. Also, making an algebraic expression simpler to work with -- what if the x were a number (pick any reasonable number based on the context), how would you handle this? Over time, students develop the capacity to do this naturally and independently.
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    • 01/23/2019 10:31 PM | Karen Campe
      Hi Marianne,
      I like your two strategies:
      Connecting to previous knowledge is a great strategy to build conceptual understanding and help with learning retention too (#MakeItStick).
      Solving a simpler problem is a classic problem-solving/modeling approach.

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    • 01/24/2019 8:07 AM | Todd Butterworth
      I try to do a similar idea as on of the instructional strategies I use. I find it easiest in Algebra or Calculus (you can certainly do it in Geometry, there's just a lot of content there and sometimes connecting things gets a little tricky). I try to get my calculus students to build their understanding upon old understanding. For example, if they want to find the derivative of some new function, how can they use prior knowledge of derivatives and algebra to get there? If I can get them to understand how things are built, then if they are to forget in the future, they can rebuild that knowledge. Makes life hopefully easier for all.

      I also try to get kids to answer each others questions. Usually this develops over the course of the year because at the beginning of the year they are dependent upon me to guide them, but as we progress through the year, I try to listen to a kids question, perhaps restate or rephrase the question, then see who can explain the answer. Then I'll get other kids to clarify the answer, eventually trying to get the original kid to re-explain to see that they understand at the end.
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  • 01/24/2019 7:09 AM | Karen Campe
    There are several “Habits of Mind” that I’ve encouraged in my students (high school & middle school)
    (1) What changes & what stays the same? For this, I ask my students to focus on the consequence of a mathematical operation, or compare & contrast features of a graph or geometric shape, or see what quantity or property doesn’t change.
    (2) Can we look at it another way? Here, we make connections between different representations, such as a graph, an equation, or a table of numerical values (where in the equation can you find the x-intercept? what happens in the table at that point?, etc. )
    (3) What If? These questions are follow-ups in which we change something about the situation, how would it change your graph, your solving method, or other detail. (What if slope was -2 instead of 2, or how do we solve (1/2)x=10 if we know how to solve 2x=10, etc.)

    For more on "Habits of Mind" there was a series of articles in the NCTM journals in May 2010 (all 3 grade levels) by Cuoco, Goldenberg & Mark. The thinking habits I mention above relate to those discussed in the articles, specifically: experimenting, connecting representations, finding invariants, looking for patterns/generalization, doing/undoing, mathematical language. [Let me know if you want these articles but can't access them.]

    I also write a blog, and a recent post is about using technology’s multiple representations to deepen understanding of mathematical relationships in high school math. https://karendcampe.wordpress.com/2018/12/19/how-else-can-we-show-this/
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    • 02/09/2019 6:22 PM | Cindy Noftle
      Thanks Karen for pointing out the series of articles in the journal. I am looking forward to reading them. I have been using the second HOM it can be hard to get them started. I will look at your blog too. Thanks for sharing.
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  • 01/25/2019 11:07 AM | Jennifer Rianhard
    A few instructional routines that I try to incorporate when working on math word problems in my 3-5 math classes are:
    1. Understand the problem, what is it asking?
    2. Plan, what's the strategy and steps you are taking?
    3. Reflect, Does this strategy and math work make sense?
    4. Explain, write a detailed paragraph explaining your math thinking and use the anchor charts to help you

    The students have these four instructions hanging on the board to use when solving problems. They also have anchor charts that include some sentence starters, a scaffolded writing template, and math toolbox strategies.

    I have been working on problem solving for about 2 months now and the students use all of these ideas to help them solve and write about their math thinking. I'm happy about their progress so far.
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  • 01/28/2019 1:31 PM | cindy noftle
    Whenever I pose a problem to my students, I ask them to think about what they already know. I pose questions to to encourage them to make connections to their prior knowledge. They seem to be looking at the topics as discrete things that have no connection to any other math topics. By encouraging them to ask me and themselves what they recognize within the problem gives them insight into solving the current problem.
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  • 01/31/2019 9:55 PM | Walter Pohle
    When it comes to story problems, even my best mathematicians make careless mistakes because they don't read the story carefully and rush right into multiplying for example when they should be dividing. When confronted with a story problem my students are instructed to put their pencil down, read the story carefully three times while painting an image in their minds about what the story is about. After they do this, they pick up their pencils and underline the key vocabulary word(s) that indicate what operation should be performed. I have found that this practice forces the students to think more critically about the math found in each story.
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  • 02/07/2019 7:54 PM | Katie Chuchul
    One thinking habit that I promote in my classroom is asking students to share noticings about a problem before solving it. I incorporate this habit often (in discussions during a launch or wrap-up of a lesson), but especially at the beginning of a unit or when introducing a new concept within a unit. I started using this routine after teaching Contemplate then Calculate last year. I saw an improvement in students focusing on the process rather than solely the right answer if I prompted them to share what they noticed first. This has also helped students make connections to other problems and units they have worked on.
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  • 02/09/2019 11:28 AM | Anonymous member (Administrator)
    Post moved from Reminders:
    02/03/2019 10:05 PM | Cesar Llontop
    chapter 2 Option 1

    As students enter the classroom, there is always a five minutes warm-up question for students to solve on their own. Once the five minutes is up, I ask the students to work in groups (already assigned by the teacher) to discuss their thoughts as to how they approached the question. This discussion takes 1 minute at most. For the next 2 minutes, I asked multiple questions to find out the various approaches students must have taken in order to solve the problem.
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