Association of Teachers of Mathematics in Maine

Chapter 1 Response Choice 1

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  • 24 Nov 2018 8:38 AM
    Message # 6930557
    Anonymous member (Administrator)

    Identify one important mathematics topic that you teach. Think about your goals for this topic in terms of the SOLO model discussed in this chapter.

    1. Do your learning intentions and success criteria lean more toward surface (uni and multi-structural) or deep (relational and extended abstract)?

    2. Are they balanced across the two?

    3. What can you do to create a balance within this topic? Or do you think a balance isn't necessary? 

  • 25 Nov 2018 3:33 PM
    Reply # 6931775 on 6930557

     In my teaching, I try to create a balance between surface and deep learning when appropriate.  I try to start enrichment classes with a problem of the week to warm-up student thinking in math.  These questions are usually more surface-level, but help to inform what students understand and need to understand about in solving a problem.  I also try to allow for experiences where students are able to talk about how they got to a particular answer.  Recently, I've tried to allow for the balance of content instruction when needed, with deep discussion of the problem-solving process.  In my situation, I work with students for one hour each week in a class based on problem-solving, they have a regular classroom teacher as their teacher of record so I have the ability to decide what I teach and what it looks like for my learners.  I'm working with one group in particular to teach them how to explain their thinking, and how to listen to and learn from the input and different ideas of their classmates.  This has been a struggle because the group is quite competitive and not always open to other ideas.


  • 26 Nov 2018 8:10 PM
    Reply # 6934042 on 6930557

           In Kindergarten most of the instruction I give leans towards surface learning. Students are being introduced to a topic for the first time. For example, Geometry begins by introducing a shape and describing its attributes.  Once they can identify and name the attributes of the shapes they can then relate them to real life and be given the higher-order thinking questions to allow for a deeper understanding. However sometimes the surface learning takes longer for this age group because of their limited schema. There is more of a balance between surface and deep learning once the student has an understanding of the topic. I think a balance between the two is crucial to the students and their future learning. Perhaps at my grade level, deep learning can be promoted immediately after the surface learning- almost like a response- to get them used to the vocabulary and thinking beyond the facts of the topic. 


  • 26 Nov 2018 8:11 PM
    Reply # 6934043 on 6930557


    Reading about the SOLO model reminded me of the learning progressions that my district (South Portland)  has asked teachers to make for students.  The progressions start off at the surface level and progress towards the deep. These are based on Jan Chappuis' work with Assessment for Learning. 


    For example, this is a learning progression that we created for dividing decimals:


    I can...

    • divide non-decimal multi-digit numbers
    • estimate the quotient when dividing decimals
    • convert decimals to fractions with common denominators and divide the numerators to solve decimal division problems
    • divide a decimal by a power of 10 (i.e. 0.01, 0.1, 10, 100)
    • solve division problems with whole number divisor and dividend, but decimal quotients (i.e. 15 ÷ 2)
    • solve division problems with decimals only in the dividend (i.e. 1.5 ÷ 2)
    • solve division problems with decimals in the divisor and dividend (i.e. 1.5 ÷ 0.2)
    • recognize and solve word problems that involve dividing decimals
    • find and explain errors in given decimal division word problems

    I suspect that this progression leans more on the surface level of learning since only the last two bullets really emphasize deep learning.   But, I feel the steps leading up to the deep learning are all necessary.

  • 27 Nov 2018 4:31 AM
    Reply # 6934430 on 6931775
    Anonymous member (Administrator)
    Anonymous wrote:

     In my teaching, I try to create a balance between surface and deep learning when appropriate.  I try to start enrichment classes with a problem of the week to warm-up student thinking in math.  These questions are usually more surface-level, but help to inform what students understand and need to understand about in solving a problem.  I also try to allow for experiences where students are able to talk about how they got to a particular answer.  Recently, I've tried to allow for the balance of content instruction when needed, with deep discussion of the problem-solving process.  In my situation, I work with students for one hour each week in a class based on problem-solving, they have a regular classroom teacher as their teacher of record so I have the ability to decide what I teach and what it looks like for my learners.  I'm working with one group in particular to teach them how to explain their thinking, and how to listen to and learn from the input and different ideas of their classmates.  This has been a struggle because the group is quite competitive and not always open to other ideas.


    Carolyn, 

    It looks like you do have a great opportunity to include a balance of deep learning in a problem solving class like this. If anything, I think it would be harder to include surface learning, like vocabulary. Using discussion is a powerful way to increase their mathematics vocabulary. I have found that using discussion hand signals, like those found on page 149 & 150 have helped my students have a voice without speaking. On page 147 are some sentence starters that can help students who need scaffolding with how to speak to one another. I have a poster with sentence frames posted in the room and we refer to them especially when a student disagrees in a negative way, and we practice restating in a more positive manner. I have found that having tools like these are very valuable. 

    ~Holly

  • 27 Nov 2018 4:48 AM
    Reply # 6934434 on 6934042
    Anonymous member (Administrator)
    Anonymous wrote:

           In Kindergarten most of the instruction I give leans towards surface learning. Students are being introduced to a topic for the first time. For example, Geometry begins by introducing a shape and describing its attributes.  Once they can identify and name the attributes of the shapes they can then relate them to real life and be given the higher-order thinking questions to allow for a deeper understanding. However sometimes the surface learning takes longer for this age group because of their limited schema. There is more of a balance between surface and deep learning once the student has an understanding of the topic. I think a balance between the two is crucial to the students and their future learning. Perhaps at my grade level, deep learning can be promoted immediately after the surface learning- almost like a response- to get them used to the vocabulary and thinking beyond the facts of the topic. 


    Hi Amy, 

    I agree that naming a shape is surface learning, but describing the attributes can be deep learning. Especially if you have the kids describe what they notice, and then give them the name for it. As we keep going in the book study, Chapter 5 will give you a bunch of ideas to help with deep learning. I bet you are doing many of them now! 

    ~Holly

  • 27 Nov 2018 7:50 AM
    Reply # 6934603 on 6930557

     

    As a RTI K-2 teacher  I strive for my students to want to deepen their math understanding and view our math time as fun, engaging, challenging, and worth while.  I teach small groups of students 1-3 at a time and encourage a lot of talk between students with probing questions like: "What do you notice?"  "Can you solve that another way?"  "What do you understand about ____________?"  I think I dance between surface and deep, however I will pay more attention as I continue to read on and increase my own understanding of meaningful math instruction.  


    I am unsure of my skillset with my K students as we are focusing on oral counting, number writing, one to one counting, and what is "five-ness".  I do a lot of subitizing, but at this time all of my work with them seems surface level.  I would welcome suggestions to make my intervention time more meaningful. 


    One take away from chapter one, I will now have my students name their "I CAN" learning progression statements and provide evidence of learning.  



  • 27 Nov 2018 11:04 AM
    Reply # 6934912 on 6930557
    Anonymous wrote:

    Identify one important mathematics topic that you teach. Think about your goals for this topic in terms of the SOLO model discussed in this chapter.

    1. Do your learning intentions and success criteria lean more toward surface (uni and multi-structural) or deep (relational and extended abstract)?

    2. Are they balanced across the two?

    3. What can you do to create a balance within this topic? Or do you think a balance isn't necessary? 

    I feel that in my current work as a 6th grade teacher, our learning targets and success criteria lean more towards surface learning initially, and then delve deeper as we progress further in the topic. Right now they are dictated by the Learning targets connected with the math program that we use, but I do see the potential to "dig deeper" in development of more powerful success criteria. Initially we start with the basics and build from there ... and the "digging deeper" comes when we focus on the word problems/real world application and relavence, and explaining our answers, which many students struggle with if they have not used the reasoning strategies all along.


    There definitely should be a balance between the two, as the surface learning, I feel, provides the foundations for the abstract learning. Without the concrete skills, the students are not able to support their reasoning. The "surface" learning places the building blocks so that students can provide evidence of their reasoning. Therefore, creating a balance means that educators could spend the time on learning targets and success criteria that build the foundation, and then take the time to really apply the skills using real-world problems to solve, so that students are able to make the connection that what they do matters and they can apply it outside the classroom. 

  • 27 Nov 2018 2:17 PM
    Reply # 6935164 on 6930557

    When thinking about the Quadratics Unit I am about to start, I see the surface level learning that will need to happen as the foundation FOR the deeper learning that will happen once they understand what a quadratic equation is, and how each term contributes to the graph/real life situation represented. Once my students explore/understand these basic concepts we will be able to dig deeper into more problems that can be represented/solved using quadratics. 

    We begin each class with a challenge problem or two for the tables to discuss and formulate solutions to (The first day I put three parabolas on the board and ask for 2 similarities, 2 differences, and 1 question they want to ask). It is fun to see them put their heads together... even when earning the basics... and see them come up with various ways of looking at the situations and share their thoughts. The learning may be of basic facts that they need to build understanding of quadratics, but their discussions typically go deeper than I expect.  The way you phrase a question can often times lead them to not only scratch the surface, but also tap into their "what if..." gene causing them to create more questions than answers to the challenge problems. Love it when they make those statements that lead them where you wanted them to go!


  • 27 Nov 2018 7:49 PM
    Reply # 6935627 on 6930557

    Overall there should be a balance between surface and deep level learning, but as I move through lessons and units, where students are and their needs directs how the learning progresses.  My learning progressions start out as surface-level learning.  As students move through the math standards, the work requires them to delve deeper into topics, taking on the challenges of solving word problems and making math connections to everyday life.    


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