Week 6 (February 15-28) Chapter 4: Building Sensible Sense Making Mathematics

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  • 04 Mar 2013 5:02 PM
    Reply # 1233538 on 1209701
    Evelyn Krahn
    I agree with Steve’s thinking. This year the school department has been very active in providing information and professional development to its staff. My role this year has been part of a group of educators trying to see how well our present math program aligns with the CCSS. We have had many discussions on how to channel the information to our grade level partners. One major concern is whether teachers will be given more time to meet, discuss and plan our lessons according to the CCSS.

  • 04 Mar 2013 7:02 PM
    Reply # 1233664 on 1209701
    Wayne Dorr
    This discussion was rich in both ideas to forward sensible math and some of the pitfalls that get in the way.  I was struck by the fact that at least seven of you (Katrina, Sally, Jen, Bill, Kate, Nancy and Robyn) commented on the vital issue of time in the pursuit of improved and relevant math instruction.  And, for me, that speaks quite directly to leadership's role (as Leinwand suggests).  I won't elaborate here, but will note that in my own trying to deal with this huge issue (as both a supt. and assist. supt.), I created scheduling on a quarterly basis for each grade level team (K-8) to come together for a full day of discussion on particular topics with an expectation of certain products at the end of the day.  The teams would (dependent on the goals for day) attempt the lesson changes/additions/modifications and bring student work to their next all day session to review and discuss results.  These day were in addition to late starts once each week -where grade levels picked up and continued those discussions or work.  And, we often tied that content together with the 2 or 3 full PD days during the year.  One of the points made by Rhonda Fortin was that some work on math curriculum was initiated by a math committee, but ran into one of the most destructive causes of failure of initiatives - no follow-up.  If I had a dollar for every time I've heard that from teachers over many years, I'd be a kazillionaire!  As Jen Jorgenson pointed out, Rick & Becky DuFour always council schools to "use their time wisely"; and it's my opinion that this is exactly where leadership comes in.  Principals, curriculum directors, and superintendents must be responsive to this issue.  Leiwand says several times that if we keep doing the same things that have failed in the past, we'll get the same results.  Nancy Sirois argues for administrative advocacy for the time for teachers to get the work done, and I couldn't agree more.  I'm not in any way suggesting that it's easy, but I believe there are ways to deliver the resource.
    I do want to comment on Leinwand's urging that principals, and others, help channel teachers' energies and interest to the necessary changes he discusses throughout the book, because there's a certain inherent problem there - many elementary principals
    do not have deep mathematics backgrounds.  I'm thinking that they will need to add to their own knowledge of mathematics in order to lead that direction - so it becomes some what of a training issue for them as well.  On pages 60 & 61, Leinwand lists a number of the components of a coherent program, and a careful look at those implies training for both teachers and principals.  Not infrequently in our business, when new ideas arrive for implementation, the necessary training (and follow-up) gets little consideration.  This is a point that I am  hopeful that Leinwand will speak to this at the conference in April.
  • 06 Mar 2013 6:38 AM
    Reply # 1235016 on 1209701
    Kathryn Elkins
    This chapter was rich with 9 components of making a math program focused, coherent, rigorous and promoting conceptual understanding.  Our "volunteer" K-12 math transition team is piloting instruction by utilizing many of these 9 components through study from a variety of sources.  

    We have utilized numerous resources.  The following two resources were most helpful K-12 to establish a base of understanding:
    www.achievethecore.org/steal-these-tools/professional-development-modules/introduction-to-the-math-shifts/   
    North Carolina's unpacking the math CCSS by grade level  

    Embedded in all of this discussion is a focus on the math practices which gets at the application and conceptual understanding.  Our math coach examined our K-6 programs and aligned the type of problems our program has with the type of problems that CCSS and Smarter Balance expects.

    We also have a "volunteer" K-12 STEM study group which is studying the new Science Framework and the Next Generation Science Standards.  There is a new document, "Exploring the Science Framework: Making connections in math with the common core state standards" by Robert Mayes and Thomas R. Koballa, Jr. (PDF), which describes the alignment of math with recommended science grade span standards.  This is a very useful tool to integrate the math and science.  Four of the math practices are similar to the dimensions expected in science.

    SAD 17 will be offering our administrators the study of this text next year.

    I do wish to respond to Steve's comment about the fact that it is nearly impossible to teach math to students who cannot read.  I agree with that statement because for students to really understand math, it has to be in context. Unfortunately, for students to demonstrate their understanding in context, language rich problems are part of the process.  Deep comprehension of problems and students answering orally or in written form requires complex thinking and expression.  Having to read a complex problem to a non-reader is very difficult.  Not impossible, but nearly.  Implication: if we want our students to be higher achievers in math, we need to continually support their reading as a number one priority.
  • 07 Mar 2013 7:21 PM
    Reply # 1236605 on 1228431
    Robyn Graziano
    Ruth Neagle wrote:I really do enjoy reading everyone's comments, so thank you for posting.  

    Instead of reflecting generally on the reading, I am going to take this opportunity to try and apply the reading specifically and directly to selections from the CCSS.  

    1.  Copied from the standards for high school geometry (G-SRT #2):
    Given two figures, use the definition of similarity in terms of similarity
    transformations to decide if they are similar; explain using similarity
    transformations the meaning of similarity for triangles as the equality
    of all corresponding pairs of angles and the proportionality of all
    corresponding pairs of sides.


    If our goal is to make math sensible and accessible, then this is not the way.  Making sense of this statement is more challenging than doing the actual math.  The grammar is terrible and the meaning is nearly indecipherable yet we are expected to use such "standards" as the basis of our curriculum!  

    Here's another one.

    2.  Copied from the standards for high school algebra, Reasoning with Equations and Inequalities (A-REI #4a):
    Use the method of completing the square to transform any
    quadratic equation in x into an equation of the form (x – p)^2= q
    that has the same solutions. Derive the quadratic formula from
    this form.

    Really?  Are they kidding?  Have you tried having students derive the quadratic formula?  I have, and it's not pretty.  Every year I give it a try with my most math-literate students.  I happen to think it's fun, and I've had the pleasure of working with two or three students who agree, but I fail to see how proving the quadratic formula is an important life skill nor do I agree that it is a core skill or concept .

    Much of the math CCSS  are clear, concise, sensible, and well-written, and I believe that having consistency in curriculum and instruction is important.  But I just can't wholeheartedly and without reservation support the document as it is currently written.

    I welcome your feedback.
    Oh, my! This was awesome! I just had to chuckle. Because here we are trying for 'sense making' and #1 is pretty funny to read with that in mind. Your comment about #2 has even been around since the Maine Learning Results. I, too, have seen kids try to complete the square and I'm not sure why every student needs to now how to do this. There are other standards, where I just don't see why.
  • 12 Mar 2013 8:58 PM
    Reply # 1241121 on 1209701
    Michele Mailhot

    I have to say Steve's statement on page 59, "A coherent program is based on well-established learning progressions from grade to grade and/or course to course." is one of my favorites.

     

    I really feel the CCSSM has done a great job of providing this coherence to mathematics through the progression of the standards. The progression documents that are provided by Bill McCallum and his team (http://math.arizona.edu/~ime/progressions/) will be very helpful as we work to implement these new standards.

     

    It would be lovely to create a PLC around the study of these progression documents!

  • 27 Mar 2013 10:02 PM
    Reply # 1253415 on 1209701
    Maureen Brown
    Since our school is steeped in "proficiency" or "standard" based learning our teachers have concentrated on ensuring that our students can progress at their own rate through the standards. Many of our teachers have overlooked the importance of alternatives, thinking and reasoning, and performance tasks. I have been looking for a tactful way to remind our math teachers of the importance of including the "critical characteristics of sensible, sense making mathematics" and I think that if I can make suggestions and then give examples of figures 4-1, 4-2, and 4-3 on page 46/47 (traditional lessons vs Alternative lessons). These examples may spark some ideas that will lead to a resurgence in problem solving as well as thought provoking lessons that include higher level thinking. Performance activities need to be brought into the class room and after reading this chapter I see myself researching ideas and offering lesson plans and/or modeling lessons. I am thinking that a weekly e-mail with a quote from this chapter may spark discussion, questions, and action. At least it is worth a try.


  • 27 Mar 2013 10:05 PM
    Reply # 1253418 on 1241121
    Maureen Brown
    Michele Mailhot wrote:

    I have to say Steve's statement on page 59, "A coherent program is based on well-established learning progressions from grade to grade and/or course to course." is one of my favorites.

     

    I really feel the CCSSM has done a great job of providing this coherence to mathematics through the progression of the standards. The progression documents that are provided by Bill McCallum and his team (http://math.arizona.edu/~ime/progressions/) will be very helpful as we work to implement these new standards.

     

    It would be lovely to create a PLC around the study of these progression documents!

    Michelle - these progression documents are very helpful - I've been trying to put something together for my teachers but now I don't have to reinvent the wheel. Thanks
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