Week 5 (February 8-15) Chapter 4-Building Sensible, Sense-Making Mathematics: What to Encourage and Implement

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  • 27 Feb 2013 12:44 PM
    Reply # 1229024 on 1203886
    Peggy Weeks

    When a list of basic skills of mathematics like this is given, it is often unclear how deep some of the topics are.  For example, “Creating and solving equations and inequalities for variable situations” could represent a large range since equations can be linear, quadratic, logarithmic, trigonometric, etc.  To be able to solve, manipulate, and interpret these types of equations, students need a depth of skills.  Therefore it is feasible that accomplishing the skills on this list would require mastery of a set of prerequisite skills. 

    I understand the push to de-emphasize long paper and pencil computations, and to emphasize teaching and learning skills in context, but I believe that adding, subtracting, multiplying, and dividing fractions and decimals is a paper and pencil skill that needs to be included in this list
  • 01 Mar 2013 11:08 AM
    Reply # 1230773 on 1228888
    Tracey Hartnett
    Susan Hillman wrote:
    Personally, as I teach my pre-service teachers--for right or wrong--they must be attuned to the CCSS-M period.  So what I think is much more important than the list are the three bullet items that follow this list:
    • solve everyday problems
    • communicate their understanding
    • represent and use mathematical ideas

    In working with future teachers the most difficult thing to get through is the emphasis on those three pieces regardless of the content while also getting kids to enjoy math.

    Thank you, Susan.  I look forward to potentially working with "your" math teachers in the future.  I, too, am thankful that folks organized this book study...
  • 03 Mar 2013 8:20 AM
    Reply # 1232017 on 1203886
    Peggy Brown
    My lens for interpreting the list came from my work with the students who daily struggle with the basics.  They are at least 2 years below grade level in math and often also in reading. They have language and processing isssues.  (When we were discussing a perimeter problem about a "goat pen", there were students in the room who needed clarification that the pen in question was not something you write with.)  So having a list of "non-negotiables" is helpful.  I think that when we are looking at this list we also need to include the words below it on page 51:  "But the key here is not having basic skills for the sake of completing decontextualized exercises.  Rather, the goal is ensuring that all students possess these basic skills so that they can:  Solve everyday problems, communicate their understanding, represent and use mathematical ideas.
  • 12 Mar 2013 8:26 PM
    Reply # 1241100 on 1203886
    Michele Mailhot

    I agree with Steve's non-negotiable list! As I read through the various posts I can't help but see how the curriculum in mathematics has gotten to be a mile wide and an inch deep!


    As we all add to what we feel should be part of the non-negotiable list...I wonder if we can make the connections from the very basic skills of the non-nogotiable list to the additions we are asking to make?


    For example, having students learn to read/measure with a ruler. This can be connected to students working with fractions on a number line and seeing fractions as true numbers and not just something to fear. If students can work with fractions on a number line, they will be able to use a ruler (which is just a number line with fractions)!



  • 24 Mar 2013 5:03 PM
    Reply # 1250744 on 1203886
    I know this is very late but enjoyed reading all the posts. They made me go back and look at the list over and over. I do agree with the list and find that having a great concern for fractions shared by others, have come to understand that once the three that do deal with fractions are accomplished the concerns vanish because they are so basic.

    I can't say enough for estimation, number sense (including fraction and operation sense), and the need to daily refresh the basics with quick easy interesting compelling techniques.
  • 26 Mar 2013 10:46 PM
    Reply # 1252531 on 1206627
    Maureen Brown
    Anonymous wrote:
    Mary Belisle wrote:One of the big bugaboos that we have is understanding fractions and decimals. He mentions some basic computation of them and equivalent fractions. I find that fractions cause a lot of trouble for students because they can't quite get their head around them in number sense and later in algebra. I think Leinwand alludes to this but does not seem to see it the problem that I have seen it to be.

    I agree with you, Mary!  Why not throw their relationship with percents in as well as many students view them as a whole different animal?  Students often get so caught up in (or afraid of) the algorithms for computing with fractions, they do not see the forest for the trees and many result to conversion to decimals so they can use a calculator.
    Interestingly, I had a conversation with a colleague today about a student not understanding the concept of scale factor as a fraction - getting smaller....tomorrow I will sit with the child to see if I can identify whether it is the entire idea of scale factor that the child doesn't "get" or is it the fraction basics that he is missing. I think I may find that this child simply doesn't understand "one third of"....and the whole concept of a part. ..I do see this in the 9th statement in representations...I agree with most of this list as long as it is in context with the three goals at the bottom of the page... I also see the years long debate on calculators...where do "we" draw the line? I love them....but many disagree. 
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