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

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  • 10 Feb 2013 5:57 AM
    Message # 1203886
    Anonymous member (Administrator)

    Pages 44-52 Chapter 4  (stop on page 52 with the "scrap heap.")
    Pages 104-106 "It's Time to Abandon Computational Drudgery (but not the computation)"

    Discussion Prompt:

    On page 51, Steve lists some "non-negotiables."  Do you agree?  Do you disagree?  Do you think there is something else that should be on this list?
    Last modified: 10 Feb 2013 5:59 AM | Anonymous member (Administrator)
  • 10 Feb 2013 12:50 PM
    Reply # 1204057 on 1203886
    Nancy Sirois
    I teach 4th grade and I love the math I get to teach.  It is really the first year where you get to really work with mental math and look at many strategies to solve problems.  I know there is some of that in primary grades but 4th grade takes so much of that wonderful foundation work that is done in K-3 and moves outward from there.

    The list of non-negotiables is a great one and I agree with so much of it.  I have been at meetings with teachers (and I have to say that many are middle and high school teachers) and they tell me that what kids are missing is their knowing their basic math facts.  I agree with some of that but they forget that we have to cover so many things in math and, although we work with math facts day in and day out, we can't always focus so much on them if we have to get everything else in.  It has become a mile wide and an inch deepp when it comes to math.  The new Common Core Standards take care of some of that but we have to recognize how important it is for students to know how to "think" about mathematics and to communicate their understanding.  I have students who may not know their math facts with authomaticity but if you give them 5 seconds, they'll solve it using a convenient math fact or other strategy.  The struggle with doing 30 multiplication facts in 1 minutes but give them 2 minutes and they will get them completely right.  I agree with math facts being as ingrained and automatic as possible but these other non-negotiables have so much weight as well.

    - more than one way to solve a problem
    - estimating
    - understanding what a problem is asking them to do
    - using appropriate measures
    - solving everyday problems

    All of these and more are so important in how we use math in everyday life.  I think I'd add is the ability to defend the solving of a problem and the answer and also to do mental math.
  • 10 Feb 2013 2:24 PM
    Reply # 1204109 on 1203886
    Nola Urban
    I am surprised he included the fourth item: "Having at least one effective method to add and subtract two two- or three-digit numbers or dollar amounts to $100.00 and to multiply and divide two- and three-digit numbers by one-digit factors or divisors."  Given his emphasis on knowing the basics ("zero to 10 addition, subtraction, multiplication, and division") and using estimation, I would have thought he would not have included these basic skills, or at least the multiplication and division portions of these skills.

    An area I think he does not have enough emphasis on is algebraic representations.  He included "evaluating and using formulas, " along with "creating and solving equations and inequalities for variable situations," but I am not sure those two alone are enough.  I know he is going after basic skills, but are these two the only basics needed to be ready for algebraic thinking and symbolic reasoning?  Perhaps, perhaps not...

  • 10 Feb 2013 3:59 PM
    Reply # 1204148 on 1203886
    Maggie Griswold
    There is beginning to be a consistency in the literature [Sensible Mathematics included] that is painting a picture of math content knowledge [MCK] that teachers need to teach "sensible mathematics". The characteristics of this MCK build upon the NCTM Process Standards:
    • Connections: math, to real situations and other disciplines,
    • Communication: the ability to "talk math" to students and understand what students are saying when they talk back to us,
    • Reasoning & Proof: why, how do you know, can you show me?,
    • Representation: use appropriate models,
    • Problem Solve: have math be in context.
    Now to change practices in classrooms and have resources that support this picture.

    The non-negotiable skills for the "language of math" is a very thorough and instructive list. It was great to see these skills listed.
  • 11 Feb 2013 7:38 AM
    Reply # 1204501 on 1203886
    Mary Belisle
    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.
  • 11 Feb 2013 7:34 PM
    Reply # 1206220 on 1203886
    Ruth Neagle
    At the bottom of page 51 Leinwand lists the goals of which his non-negotiable skills provide a foundation.  The goals are "solve everyday problems, communicate their understanding, and represent and use mathematical ideas."  He claims that anything beyond is "obsolete. . . and no longer valued by society."  Which society?   In U.S.  school settings, the holy grail of mathematics is calculus.  Statistics runs a close second.  One or the other is required by most college programs in science and business, and one needs a whole lot more mathematical literacy than just the basic skills as listed to succeed in calculus and stats.  He hasn't even mentioned irrational numbers (though that may be implied by "using and understanding the number line"), or logarithms (yes, sorry, still an important piece of calculus), or complex numbers, or the concept of infinity and division by zero.  I could go on and on, but what I'm trying to say is that I don't believe we can comment on the appropriateness of his list of non-negotiables without reference to the related goals.  His list is fine for his goals, but insufficient for the goals of many students, especially those headed to 4 year colleges.  

  • 12 Feb 2013 6:29 AM
    Reply # 1206627 on 1204501
    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.
  • 12 Feb 2013 6:35 AM
    Reply # 1206628 on 1203886
    Gail Stetson
    As I read through the list of "basics", I have two competing reactions.  On the one hand, I think that the list is too "basic", that these skills are not enough of a foundation for students.  On the other hand, I think about how beneficial it would be for my students' math success if they actually did have these skills and habits of mind in place.  It is frustrating for my students and for me to work through math workshop where so much of the deeper math is inaccessible because of these obstacles.  It is very difficult to think deeply about a math context when so much of the intermediate pieces are "stumbling blocks" rather than "steps" to the solution.  How best to address thee deficits?  What is the right balance of remediation to instruction? 
  • 12 Feb 2013 6:22 PM
    Reply # 1207133 on 1203886
    Why do we give computational skills such a bad rap. The building blocks of higher level math skills come from a strong understanding of the fundamental skills. Blooms states it is important to start with remember, understand THEN move to higher level concepts of application and compare and contrast.  We do such a dis service to our children by not ensuring their success in basic skill development. Non negotiable are Number Sense operations with factions decimals and percents as well as a laundry list of more topics that students should conquer and feel proud of their achievements.
    I do not care if they learn them on the laptop or through mad minutes or through role play...just as longs as they are able to hold on to this knowledge and retrieve it faster than pulling up an app on a smart phone
  • 13 Feb 2013 10:56 AM
    Reply # 1207636 on 1203886
    Bill Shardlow

    After reading the previous posts, I must admit that I would agree with much of what has been said already. Therefor, no sense in repeating any of what was written. As a middle school (7-9th grade math levels) teacher, I am not as aware of the specific concerns voiced by some of the other teachers at the different grade levels, but acknowledge their concerns.

    Although I agree with Steve's non-negotiable's in their purest sense, I believe that we must be a little bit more broad-minded when looking at what is necessary. I believe that algebraic reasoning, estimation, percents, and other areas as listed by the previous respondents need to be addressed as well. Sorry, I did repeat some of what was mentiond before. But, having said all this, I believe that he is on the right track. We must prepare our students for their future and not our past. This implies that they need to have a working knowledge of mathematics, and be able to apply it the most practical real-world situations. I believe the common core standards will help us move forward towards this goal.

    I am in great hopes that the new CMP3 materials will be more like the alternatives that were suggested in the reading rather than the traditional approach to problem-solving we have now. Right Shawn?  :-)

    In conclusion (cause I'm sick and at home), I believe that the nonnegotiable's need to be addressed in a real sense, that the practices of common core be emphasized on a daily basis, and computation fluency be reinforced. My simplistic, but practical, response. Back to bed!

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