Association of Teachers of Mathematics in Maine
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Chapter 4 Response Choice 2

24 Jan 2019 5:47 PM | Anonymous member (Administrator)

Consider the strategies you use, and the strategies you've read about and tried from this chapter to solidify surface learning. What are some effective ways to build surface learning, and why is that necessary?

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  • 27 Jan 2019 7:06 PM | Ann Luginbuhl
    In reading this chapter I would say that the math books I use do a pretty good job at introducing and reinforcing surface knowledge. They guide me to introduce topics with manipulatives, they have clear introductions of vocabulary, they provide good worked examples, they have good questions for me to use in class. I also like that they have a section of spiral review to reinforce material we have learned previously.
    I certainly use Mnemonics- Long division- DMS down. (divide, multiply, subtract, bring down). nUmerator-up, Denominator Down. The line in a fraction is a division sign and OF means times are just a few of our class mantra.
    My biggest take away from this chapter is the section on mathematical talk. The encouragement of use of the words "I" and "because", really spoke to me. I have been doing daily number talks since our first face to face meeting and I am going to start pushing my students to include those words in their NumberTalk responses.
    I certainly understand why surface learning is important! A perfect example is the memorization of multiplication facts- I have many kids who really understand the concept of multiplication and compute 7X8 by repeatedly adding 7- but with out that foundational memorization of facts they are struggling mightily when it comes to adding fractions with unlike denominators or reducing fractions to lowest terms.
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  • 29 Jan 2019 6:09 AM | Anonymous member
    The text emphasizes the importance of questions and discussion in the classroom. These questions need to be planned, anticipating potential misconceptions, choosing questions that will encourage rich discussion. My students enthusiastically participate in math discussions responding to how and why questions. I want to push them to think more about their problem solving and encourage more deliberate metacognitive strategies.

    I ask my students to correct their errors on assessments. I also review problems done incorrectly with the whole class. Some students share where they went wrong and what caused their misunderstanding. The students seem to appreciate hearing where others went wrong especially if they had a similar misconception.

    The section on vocabulary strategies was interesting. I have used a Frayer model graphic organizer occasionally but after reading this I plan to use this and other vocabulary activities more often. I do wonder about the Word Wall idea. I read another math education book that talked about visual “noise” in a classroom and how distracting it can be for some students. I would appreciate reading about how other teachers use a word wall and its impact on student learning.
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  • 02 Feb 2019 4:53 PM | Anonymous member
    I loved the concept of surface learning - hadn't thought of it that way before, but it makes total sense. The house needs a frame before you stuff it full of furniture. Otherwise everything ends up in the basement when the floor caves in. That's what it seems like surface learning's aim is: provide the frame, the big-picture concepts, the vocab, the rudimentary skills, and then the kids will have an excellent support for the learning that comes next.

    One thing I've found necessary more than any other is the distributed practice idea. Holy cow is that vital to memory! New learning so easily slips out of mind unless it's called back up again and again. I haven't used a word wall before, but I was thinking while I was reading, "how dumb of me not to have used a word wall yet". How many times could I have had the kids partner up and then fire off questions like, "Partner A, give an example of <vocab word>." "Person B, draw three shapes that exhibit <vocab word>". Word walls are themselves opportunities for distributed practice.

    I liked the worked-out example also. I'm definitely a proponent of letting kids get messy in math class - trying to find all kinds of ways to solve a problem. But I think it's also important for them to be still and watch how a mathematician lays out a problem - what to show and what not to show, how to organize the thinking, how to organize the writing.

    Besides for word walls, I'm going to go google "number talks for high school math" and see what comes up. I could totally see it being good for warm-up problems at the start of class. But that's also such a great opportunity to, as they say, activate prior knowledge, I'm not sure I'd want to trade away that time.
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  • 03 Feb 2019 3:03 PM | Anonymous member
    Recently, I've tried to activate surface learning by using a warm-up questions, or problem of the week question to try to determine what students already know, or do not know about a topic. I've also found the Sentence Frames that Can Build Metacognitive Thinking on page 121 to be very helpful. I was already using some sentence frames from another resource with my students that related to the Planning and Monitoring aspects of metacognition, but I didn't have a resource that looked at the evaluating piece as well. I have found that sometimes my students know the process, or can problem-solve their way through a math problem using logical reasoning, and other math problem-solving strategies, but if they lack the math vocabulary, and properties when it comes to geometric thinking, then they may not even try a question due to lack of confidence. I've been incorporating more number talks that relate to math concepts and thinking and to elicit student ideas. One middle school group with which I work has just gotten to the point where they are understanding the value of math talks which I see as a big win as a teacher.
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  • 18 Feb 2019 9:29 AM | Anonymous member
    I was pleased to find as I read this chapter that I use many of these suggestions in this chapter to enhance surface learning. For example, a word wall for our current unit, graphic organizers for both vocabulary, and for planning solutions to problems. We are currently using Mnemonics to remember our steps for long division. I make the students say each step out loud and check it off as they complete it ("Divide, Multiply...). The chapter gave me more ideas for discussion and feedback to improve student understanding, and it also reminded me to slow down and allow for more self-assessment and metacognition. I use to do this every day or two and find myself rushing to finish covering topics. Also, I use manipulatives in many units, but as I read this, I realized I could have used them more often and more effectively, but again did not due to the rush to cover material. These steps to deepen surface learning will help my students move toward deeper understanding and application of these concepts and when used for real-life problem-solving.

    My biggest take away that I want to share with my colleagues is the 2-4-2 strategy for math homework. I would use this strategy for math morning work as well as (or instead of) homework. I review prior concepts weekly to strengthen the skills so that they become second nature, but I loved the set up of this strategy, including the 2 reasoning problems at the end.
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  • 19 Feb 2019 3:01 PM | Anonymous member
    Consider the strategies you use, and the strategies you've read about and tried from this chapter to solidify surface learning. What are some effective ways to build surface learning, and why is that necessary?

    I like how the chapter focused on the different ways to build on the surface learning and using the surface learning as the jumping point for the "deeper" learning and thinking that takes place. I feel that building on the surface learning is necessary in order for students to understand how they got from point A (surface learning) to the abstract (deeper understanding) of the problems

    I have been trained in several of the strategies described in Chapter 4, but given the constraints of "teaching to a program" it can be difficult to find the times to dive deeper within the context of scripts and "expectations" through the programs. This year I feel that, even though a lot of what I feel I do is "surface learning", I try to make more opportunities for students to explore, try, fail, and revise their thinking within the context of our program. A warm up involving number talks is a great way to get students thinking about the concepts and how they would apply tools and strategies to solve simpler problems. From there they can build upon their knowledge through applying the language of math, understanding the background of the vocabulary, exploring it's meanings, what it is, what it isn't , and then from their applying that vocabulary and what they learned in their number talks to help them solve a applicable "real-world" problem that allows them to practice and apply their learning.

    Each part of a lesson has a lasting role in students being able to derive meaning and understanding about what they are learning. IF they are actively involved through practice, questioning, and revising their thinking, the learning becomes more personal and meaningful for the students.
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  • 04 Mar 2019 7:38 AM | Anonymous member
    I have loved implementing Number Talks as a math warm up. In my 2nd grade classroom we finished a unit on addition and subtraction of 2 digit numbers and are currently working with 3 digit numbers. As they share their thinking, I have a particular student who is struggling with addition and subtraction and when he shares his thinking he is not accurate and he does not self correct. I record his thinking, but he does not see his mistakes. Other students don't always speak up to say he is wrong and I don't but I do record others thinking. I use the time to record and show their thinking and it is a chance for me to do formative assessment.
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