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Computations Versus Communication

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by Aviva Dunsiger

As I’ve mentioned in previous posts, communication in math is a focus for me as part of my Annual Learning Plan. Since returning to school after the holidays, I was thrilled to see so many of my students communicating so much more in math. They are really elaborating on their answers, and sharing their thinking in both their written and oral work. When completing words problems in groups and independently, students are showing their calculations as well as explaining the individual steps. They are breaking down what they’re doing and why they’re doing it. Since September, the emphasis has been on communicating more, and this constant focus on communication, as well as the time spent modelling and practising this skill, seems to have helped. I couldn’t be happier!

For the past couple of days though, I’ve noticed a new problem that is starting to bother me. Students are clearly explaining their mathematical thinking, but their calculations are incorrect. Yesterday for Multiple Choice Mondays, I noticed a number of students going to the math cart to get the manipulatives that they needed to answer the questions. This has never happened before without me prompting them to do so, and I was just thrilled to see this change. When these students tweeted their answers to the multiple choice questions, they added and divided wrong, so their solutions were also wrong. I saw the same thing happen today as students solved a perimeter problem. They multiplied incorrectly, and got the incorrect answer. Yes, they know what to do, and yes, they explain every step, but how does this factor in when the solution is wrong ?

 I’ve tried sending home website links and app suggestions that review addition, subtraction, multiplication, and division facts. In the classroom, I pull small groups to also work on these skills. Maybe I need to devote more of my math class to reviewing mental math skills. Almost all of the students struggle with calculations to some degree. I don’t want to take a step back though when it comes to math communication.

How do you reinforce computations while also emphasizing communication in math? Should we be devoting an equal amount of time to computations and communication in math class? How do you determine a good balance ?

 

 

 Aviva Dunsiger taught Junior Kindergarten to Grade 2 for 11 years before moving to Grade 6 this year. She’s passionate about using technology in the classroom to support student learning, and she’s presented on this topic numerous times both online and offline.

She enjoys maintaining her blog, Living Avivaloca: My Many Musings on Life and Learning. Aviva’s reflective writing about her professional practice inspires communication between educators, administrators and parents.  

 

 

 

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  • http://teachingisagift.blogspot.ca/ Ms. M

    Aviva,
    Being a teacher of gifted grade 6 and a parent of a student in grade 7 gifted I can tell you one thing. The students won’t all have the computations down pat. My daughter has struggled for YEARS with getting the “right” answer. She too can give you all the steps, and explain her thinking. I personally and professionally believe that her being “numerate” is more important than her being “mathematical”. I have fought with her school to allow her to use manipulatives and a calculator. I have gone so far as to demand that it be added to her IEP. I allow all students in my classroom to use a calculator and manipulatives when they are working. Don’t we use tools when we work? Don’t we use calculators and computers to help us confirm our answers, or just to make the work more efficient? I am NOT saying being mathematically capable isn’t important…I am saying I think it is important to value all parts of problem solving. I use a 4 point scale when assessing student work in math. I give them one point for the right answer, one point for the proof, one point for the explanation, and one point for a connection (math to math, math to self, math to world). I want my students to know that there is more to life than getting the right answer. When they learn how to “show what the know” they are often able to go back and self-correct their answers. They have a “paper trail” to follow, rather than just “I don’t know how I go that answer” or the “that’s what the calculator showed”. I think it’s a tension in teaching that we have to embrace, some students will be highly mathematical and other highly numerate and our goal is to try to help them all become BOTH.

    • Aviva Dunsiger (@avivaloca)

      Thank you so much for your comment! You make a very valuable point here. I wonder if it’s more important for students to realize if an answer makes sense or not versus being able to do all computations in their head. I have no problem with students using calculators and I encourage them to use manipulatives. I get more concerned when they don’t realize that an answer is unreasonable. Maybe this comes down to real “number sense.” This is much harder to do when their answer is close to the real one, but not correct. I wonder how we can best address this problem. What do you think?

      Thanks for adding to this conversation!
      Aviva

  • http://rothinks.wordpress.com Thomas Ro

    Great article Aviva and a great problem of practice. I think it is great that you are focusing on communication as you teach and learn mathematics with your students. As your students are focusing on communication I was wondering how they know if or when they are achieving success at communicating? Do you have a math communication learning goal and success criteria that they can refer to?

    Here are some of my thoughts on your great questions that you posed in your article:

    How do you reinforce computations while also emphasizing communication in math?

    I think you can do this by consistently focusing on some of the mathematical processes (pg. 11 of the Ontario Math Curriculum) like problem solving and selecting tools and strategies. When it comes to the problem solving process, it sounds like your students are fine with understanding the problem, making a plan, carrying out the plan, however if they are coming up with the wrong solution due to computational errors and are unaware of their incorrect answer, perhaps one way to reinforce procedural computations would be to focus on the last part of the problem solving, Looking Back at the Solution. Are your students checking the reasonableness of their answer? Are they reviewing their strategy/method used? Another opportunity to reinforce procedural operations and mental math strategies would be during the Reflect and Connect or Consolidation as a class where these computational mistakes could be identified and be used as learning opportunities for all.

    Should we be devoting an equal amount of time to computations and communication in math class? How do you determine a good balance ?

    I think there definitely should be a balance of Knowledge and Understanding (procedural skills, facts, and terms) and Communication but we should also include Thinking (problem solving) and Application (making connections, transfer knowledge) to the mix. The achievement chart in the Ontario Curriculum is always a good reminder to ensure that math programming is well balanced. There may be lessons where the focus is on introducing a bid idea or concept where the balance may shift more towards problem solving and communication. There may also be lessons where the focus is on purposeful practice and reinforcing strategies and procedural skills where the balance may shift towards knowledge and understanding. After reading your article it definitely looks like you are implementing and achieving a pretty balanced numeracy program. Thanks for sharing your thinking and practice Aviva!

    • http://adunsiger.com Aviva Dunsiger (@avivaloca)

      Thomas, thanks for such a detailed response! I’m glad that we could also extend our conversation on this on Twitter last night. I think that the major problem that my students are having is that their answers, if not correct, are incredibly close, so checking for reasonableness doesn’t help them out. Their responses are reasonable, just not right.

      I do like the idea of reinforcing computations during the Reflect and Connect stage in problem solving. I can definitely see this working. As we discussed last night, maybe trying to balance this with some home review as well as small group support will help. It is definitely a balancing act.

      Thank you for always getting me thinking more about math!
      Aviva

  • Kristi Bishop

    You’re right, Aviva – math is awfully complex and for us to do it really well we need to put lots of skills together: an ability to do computations, estimations, problem solving, use of tools and strategies, and communicate our thinking. Communications is only one of the process expectations. Any one in isolation doesn’t do it all. If communication is a strength for your students, I wonder if even using a simple prompt like “how do you know that’s the answer?” might help them consider their response. Focusing some time on them practicing reasonable estimation strategies for different computations will not only get them thinking about the answer but also increase their understanding of number and number sense. That said, students do need to understand computations. Understanding numbers and how they are manipulated by computations should come with thinking about them, talking about them AND practicing them. In other words, keep doing what your doing!

    • http://adunsiger.com Aviva Dunsiger (@avivaloca)

      Kristi, thanks so much for the comment! Your prompt, “how do you know?,” is one of my favourite ones to use, and was actually suggested to me by my math facilitator last year. The problem I’m having with the students now is that their answers are close (e.g., they might write down 45 instead of 50). Usually their answers do seem reasonable, so estimation skills don’t work. I think that many students are actually unsure of some basic math facts, and while I’m not a fan of “drill and kill,” I think that some students need this time to learn their addition, subtraction, multiplication, and division facts. I know that some parents are starting to review these facts at home with their children, which helps. My thought was to continue to emphasize problem-solving, but also work on the computation skills in a small group setting (when necessary). I was speaking with another educator on Twitter last night, and he suggested trying to review these computation skills as part of the Reflect and Connect piece of a Math Congress. I liked that suggestion. What do you think?

      Thanks for getting me thinking!
      Aviva