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

  • 13 Feb 2013 12:22 PM
    Reply # 1207708 on 1203886
    Deleted user
    Shawn Towle wrote:

    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?
    Yes, I do agree with his "non-negotiables," but I can't help but think that he is missing some other critical skills. One such skill I wonder about is being able to find areas and volumes. It would seem to me that this is another basic concept that all students should be able to know in order to complete day to day tasks such as painting a room or filling a pool. One would need to be able to estimate the cost to do tasks of this nature. This example is only one of which I think is a much longer list.
    I also find it interesting that his list begins very specific and then as it continues, one may wonder exactly what he is referring to. For example, "evaluating and using formulas." Which formulas is he referring to exactly. I would imagine some formulas like those I mentioned above would be included, but what about the quadratic formula or the double angle formulas in trig? I think this list leaves way too much for interpretation.
  • 13 Feb 2013 7:43 PM
    Reply # 1208077 on 1203886
    Jenny Jorgensen
    I definitely agree with Steve's list of non-negotiables. I am happy to read that there continues to be the agreement that we need students to know their one-digit facts.  I noticed that the word, estimate, appears several times in his list. First when referencing answers to problems with the four operations and again when students are working with percents and proportions.  There is a time when students need to be able to estimate the answer and then use the calculator if an exact answer is needed.  I wonder about the topic of probability.  I didn't see that in his list and I think it's an applicable topic to our daily lives.
    I was reminded of Randall Charles' Twenty-one Big Ideas of Mathematics K-8 when I read about Steve's incomplete (as he put it) list of big ideas. I wonder how he'd respond to Randall Charles' (2005, 12-21) list.
    I appreciate Steve's attitude about "banishing the vestiges of yesteryear" and that it's time to move on to engaging mathematics that includes the use of available technology in a thoughtful way and empowering students.
  • 13 Feb 2013 10:55 PM
    Reply # 1208185 on 1203886
    Kate St.Denis
    In reading these posts I see the proverbial computation skill bandwagon being confused with number sense. When we desire for children to make sense of problems, to estimate, and to analyze, we don't ask them to memorize a procedure for doing so.
    If my student divides 468 by 0.9 and gets 4446 then I know that I need to work with them to build understanding of rounding, estimating, dividing, or sensemaking and not teach them where to put a decimal point which is obviously meaningless to them at this point.

  • 14 Feb 2013 3:34 PM
    Reply # 1208848 on 1203886
    Angela Marzilli
    I appreciate anything that continues to make me think about what skills are necessary for students to have and what they should have a deep understanding of while relying on a computer or calculator for the actual skills involved.  If you haven't watched this TED talk by Conrad Wolfram, enjoy!  He discusses much the same thing:


    For me, the crux of the matter is the number of students who are turned off of the ideas and creativity of mathematics because of the skills we say are necessary for "doing math."  Page 105 sums up my feelings quite nicely: "Today there are alternatives and there is no honest way to justify the psychic toll it takes."
  • 14 Feb 2013 10:47 PM
    Reply # 1209120 on 1203886
    Lisa Russell
    I also believe the list of "non-negotiable basic skills" is a great list. What we have to remember is that the goal is to ensure the ALL students possess these skills. As Maggie stated this list is comprised of a list of "sensible mathematics" that are included in the NCTM Process Standards and they are included in the 8 Mathematical Practices of the CCSS.

    In a college level class, one day we were in groups comprised of K-12 math teachers and were discussing fractions. Within the discussion it was recognized that at the elementary and middle school levels fraction skills are sometimes given up on, because it's just to hard for some students. As a high school teacher I had the opportunity to share with the others why a solid foundation in fraction skills are critical to high school mathematics. Not only do they need the background knowledge of fractions for slope, proportions, and reasoning processes, they also need them for upper level coursework as well. Without a solid foundation of number sense, algebraic processes are much more difficult for students.

    I do think teachers need more professional development to allow us to bring changing practices into our classrooms. We need support from each other and administration. We need to develop reasoning, communication, and a common vocabulary throughout our K-16 curriculum.

  • 14 Feb 2013 11:21 PM
    Reply # 1209149 on 1203886
    Pam Meader

    I also agree with the previous posts and with Steve’s non-negotiables.  I agree that the formula one is a little vague and I would like to see create formulas added along with evaluate and use. I have my algebra students derive many of the the  area , volume and surface area formulas through hands on activities.  This helps them to understand what the formula is stating rather than just mindlessly plugging in numbers.  And I also agree on the need for developing algebraic thinking as an important building block for algebra.  In terms of the fraction discussion, I truly believe we must step back and make sure our students “understand” the operations before teaching the algorithms.  I have developed a course called Arithmetic Skills for the Accuplacer where I have my adults work with fraction strips, fraction tiles, etc. before ever introducing the algorithm.  What I have also found is that many students don’t even understand what a fraction is.  We use some wonderful materials from TERC in Cambridge, Massachusetts called Empower Math that develop skills conceptually using benchmark fractions, decimals and percents. We are finding our students not only understand the concepts but remember them for future math classes.

  • 15 Feb 2013 7:39 AM
    Reply # 1209283 on 1203886
    Amanda Dyer
    I too agree with the list of non-negotiable basic skills on page 51 but as he states, keeping it in mind with the list below it of why students need these skills..."so they can: solve everyday problems, communicate understanding, and represent and use mathematical ideas".  This section reminds me of those students who come into Kindergarten being able to read most books within the classroom but do not understand that the process of reading is not being able to look at words and say them, but to read and think and use that understanding.  We do a disservice to our students when we don't teach/show/let them discover that mathematics is about thinking and using numbers.

  • 15 Feb 2013 9:49 AM
    Reply # 1209352 on 1203886
    Rhonda Fortin
    I agree with most of Steve's list but I think a couple of things are missing. I agree with Lisa that students need to develop skills with fractions and decimals in the early grades because many ideas in high school math and beyond build on the fraction foundation. One of the skills I don't see in Steve's list is being able to use a ruler to measure. Many of the students in the vocational school come in not knowing how to measure....or how to use measurements once they are found. Students have a difficult time finding the center of a 23 foot board to cut it in half or the center of a 14 and 3/4 inch t-shirt in order to center the graphics. It is very disheartening to see. These are the people who will be in our homes installing lights, building additions, and working on our cars. Being in the middle of a big remodel at our house, I see the builders constantly using mathematics. I'm not sure as ten minutes goes by when they are not talking about math. All the math is done in their heads....no matter how messy the fractions are. I've heard them divide walls up into sections in order to get the windows in the right place and discuss how big a vent needed to be in order to have the correct volume for the stove fan. They say they don't have time to get a calculator out every time they do math...it is such a big part of what they constantly do. More importantly, they think mathematically and they communicate with each other about the math they are doing. The remodel has been a great experience for me to see how math is used in a trade.
  • 15 Feb 2013 3:18 PM
    Reply # 1209634 on 1203886
    Wayne Dorr
    I do agree with Steve's non-negotiable basic skills, and also most of the comments from you all that suggest there's more that needs to be considered.  A couple of things popped into my mind though, from a discussion I had several years ago with an ASCD book editor, that might explain some of the brevity, or lack of clarification, in Steve's list.  He pointed out that his job was to assure the essence of an author's intent/message at the same time he was seeking efficiency in the volume of what's written.  One of my thoughts about his list was that quite a bit of it seems mechanical, and not as process oriented/reflective as the NCSS envisions; and I too couldn't understand why algebraic fundamentals were absent.  Having said that though, Steve did term this list as "basic skills ... for all students", so my guess is that he could easily elaborate, i.e. "Evaluate and use formulas", etc.  However, can you imagine if all of our kids acquired all the skills on that list? 
    There is one small note he made on page 52, that I believe doesn't get enough notice  during math instruction, and frankly I'd love to hear from any of you on this matter (because it's a critical issue in the development of long term memory (and there is substantial neurological evidence of this).  Leinwand points out that ongoing practice is just as important as the basic skill being identified - "one of the most effective strategies for fostering retention and mastery is daily, cumulative review.
    And when he goes on in the next page about conceptual understanding of the big ideas, those basic skills need to be deeply embedded.  And lastly, I have to say, when he discusses computational drudgery, I couldn't agree more - the hours that I spent as a kid doing 20 examples of something that I had in the first two, were miserable; and it did have an impact on me in terms of avoiding math courses later in life. 

  • 16 Feb 2013 2:56 PM
    Reply # 1210238 on 1203886
    Kathryn Elkins
    Since I am only a curriculum director and not a math teacher, I acknowledge that my "deep" understanding of what skills should be essential may be limited.  However, I am reminded that Hong Kong considerably outperformed the US on the TIMMS test by not teaching 48% of what was covered vs the US which taught to all but 17% of the TIMMS content.  Lesson is "Less is More." 

    I believe Steve was referring to elementary focus when he listed his non-negotiables.  We do not want to be categorized as "schools ...equally powerful perpetuators of what they've always done" (p. 106).  By limiting the skills taught at elementary to a smaller list, allows teachers to go much deeper using a variety of alternative approaches.
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