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

  • 23 Feb 2013 7:44 PM
    Reply # 1224965 on 1209701
    Tom Light
    "Steve says that principals and other school leaders “should channel people’s thinking to these issues of access, alternatives, skills, concepts and big ideas, tasks, language, integration and connections, alignment, coherence, and thinking and reasoning” in ALL discussions about the mathematics program."

     
    I like the concepts that these words represent, but I think it is not realistic to include all of these in all discussions.  They are big ideas and deserve to be understood in a visceral way.  I don't think I'm a particularly slow learner, and I believe I can explain most (if not all) of these ideas, but they are not yet "part of me."  As a matter of fact, I'm wondering now if I can compare and contrast "concepts and big ideas" and "thinking and reasoning" in a way that satisfies me.

    I decided there are two audiences who need to have some understanding of these ideas.  One is the teachers and administrators who are involved with math instruction and the other are other school community members who are not directly involved in mathematics instruction.  It is important for the greater school community to understand the direction the common core is going, and an overview of these ideas is important for parents, school boards, and perhaps especially students.  Looking at ways to translate the ideas that each word in this list represents into words and examples that will be accessible to non-practitioners is something that should happen.

    I believe that each idea represented deserves to have time set aside for teachers and other educational leaders to consider closely.  What is happening in our school/classroom to see that all students have access to the big ideas behind the math?  What is the appropriate learning progression that can be followed to help our students grasp the mathematical idea?  How can we/do we design our instruction so it is preparing students for the mathematical tasks that they will be faced with in their lives? 
  • 24 Feb 2013 5:43 PM
    Reply # 1225341 on 1209701
    Robyn Graziano
    I think it is important to include all of the characteristics in our creation of a math program. I loved the examples in the 'ACCESS' section that showed a traditional versus alternative tasks. I wish I had the time to look for the data that would be the basis for these tasks. I would love the time to make math more human. I wish I were more creative to be able to think of these thoughtful tasks. I would love to meet with my co-workers and create lessons that were meaningful and include all of Steve's characteristics. In other countries, teachers get part of their day to work together. We get once a month in departmental meetings. It is so difficult to get anything done once a month.
  • 25 Feb 2013 3:56 PM
    Reply # 1226071 on 1209701
    Anonymous

    I think that the beginning of this work will have to start at the grade levels and school leaders need to be instrumental in encouraging those in teaching positions to embrace the concepts of “sensible math” within their classrooms.   The Common Core State Standards provide guidelines for educators, but without clearly envisioning how to embrace and implement those standards, some educators may not be on board with the task of aligning assessments and creating the reality of the Common Core State Standards in math or in any other subjects.

     

    I do believe that this can happen in schools and districts.  We are leaning in the direction of Mass Customized Learning, as other countries have approached learning with great success for many decades.  If this does become a reality in our Maine schools, the chance for encouraging a shift in our approaches to teaching and learning of mathematics will most definitely be closer achieved.  Sense making rather than memorization would have to be demonstrated in aligned assessments in a standard based curriculum.  All in all, it would be a much better way to approach math as a teacher and a much better way to learn math as a student learning.

  • 26 Feb 2013 8:26 PM
    Reply # 1228431 on 1209701
    Ruth Neagle
    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.
  • 27 Feb 2013 11:30 AM
    Reply # 1228960 on 1209701
    Susan Hillman
    I believe this is essential and I would include teacher certification programs in this effort.  All of us as teacher educators MUST be preparing our future teachers in the fundamental importance of what the author is calling "sensible mathematics." 

    I also feel that alignment is needed with our assessments. The author speaks quickly about this yet this is an essential component.  Teachers are under incredible pressure with their evaluations being linked to student achievement growth.  Alignment of the large standardized assessments is of fundamental importance since these assessments will be the louder voice regardless of our commitment to make the shift.

    So my formula for making this shift includes not only our voices in the schools, but teacher educators in pre-service teaching programs + alignment with standardized assessments + alignment with what gets put into textbooks.  The latter two pieces, in particular, will provide a solid basis for the message from school leaders to take hold.
  • 27 Feb 2013 7:39 PM
    Reply # 1229322 on 1209701
    Deleted user
    Shawn Towle wrote:Reading:  The remainder of chapter 4, pages 52-62.

    Prompt:

    If we truly are seeking to implement sensible, sense-making mathematics programs like the ones described in chapter 4, Steve says that principals and other school leaders “should channel people’s thinking to these issues of access, alternatives, skills, concepts and big ideas, tasks, language, integration and connections, alignment, coherence, and thinking and reasoning” in ALL discussions about the mathematics program.  

    What do you think?  How do you see this being done in your department, school or community?  What do you see as your role/contribution to that discussion?

    I see my role as someone who is supporting our math teachers in our high school as we are transitioning to the Common Core. We are learning about it together and I am pushing my colleagues to take some risks with our teaching strategies to push our students to think before we move to give them the next step in a problem. I am working to change my ways so that I can share my experience with my colleagues to give them the strength to do the same. We as a department are regularly sharing what we have been doing with our students, how it is different, how the students performed, and challenges we have faced.
  • 01 Mar 2013 12:13 PM
    Reply # 1230810 on 1212668
    T. Hartnett
    Jenny Jorgensen wrote:In reading the last part of chapter four I am in full agreement with the statement: "... mathematics being taught is expected to make sense to students..." (p.60) I have often told my students to stop doing their homework if it doesn't make sense. I don't see any logic in having students complete an assignment if it doesn't make sense to them. I want students to understand mathematics; not have a set of memorized procedures. 
    Miles away, my students in central and now western ME have been hearing these same words from me, Jenny.  The three children with whom I live have heard similar words at home.  I told them as early as 2nd grade, "Never use a method in math that you don't understand." This advice served my oldest child well through elementary school.  She was absent on the day dividing fractions was introduced in 6th grade but, because her understanding of fractions and division was so strong, she was able to develop her own algorithm (completely unrelated to invert and multiply) for dividing fractions.  Because she understood it (She created it.), she has not and will not forget it.  In 7th grade, she was placed in a traditional (procedural) pre-algebra class and her favorite subject quickly became her least.  Fortunately, her teacher agreed to allow her to use Mathscape books to teach herself and, with very little help from me at home, she continued to learn with understanding.  Algebra 1 as an 8th grader is breaking the 8 year cycle of learning with understanding.  While successful, she is not making connections, and is not learning mathematics within a meaningful context.  She is not thinking and reasoning.  I'm certain that this is a Leinwand example (p.57) of "follow the textbook".  But, what is the alternative?  To paraphrase what Robin G. said, this all sounds good but, at the same time, daunting... Leinwand seems to be hopeful that the CCSM will result in better alignment between curriculum, instruction and assessment. If any of you come across curriculum materials that provide opportunities for students to learn topics in an integrated and connected manner, please share.
     
    To get back to this week's prompt...

    "What do you think? How do you see this being done in your department, school or community? What do you see as your role/contribution to that discussion?"

    I am pleased that our district's focus in terms of transitioning to the Common Core has been on the Standards for Mathematical Practice.  Unfortunately, participation on this "team" is voluntary and takes place after school.  I wonder how teachers and administrators who have not been involved in p.d. will implement/support the changes. My contribution to the discussion will be to continue to attempt to influence mathematics instruction that makes sense to students. 
  • 01 Mar 2013 2:39 PM
    Reply # 1230951 on 1209701
    Cecile Carlton

    From the given prompt Steve’s strategy ‘ is that principals and other school leaders “should channel people’s thinking to these issues of access, alternatives, skills, concepts and big ideas, tasks, language, integration and connections, alignment, coherence, and thinking”’.  This is not a onetime discussion – but an on-going one in a district that asks its department to identify a vision, devise, implement and continuously review a mathematics program.  Within a district, there needs to be PK-12 representation and time devoted to the development and on-going implementation and review of an identified mathematics program.  Time at the end of school year and before the beginning of the next school year should incorporate such opportunities, as well as time for grade level teachers during the school year. (Each district needs to identify what works for them in this area – there are varied models).  So I would say another key school leader must be the district’s superintendent.  From my experience, it was the    the recommendations from such a committee (led by a Mathematics Supervisor) and endorsement by the superintendent that made for meaningful movement in the way mathematics instruction was to be delivered to students.  What Steve identifies above, becomes part of the committee’s (and eventually carried to each school by the representatives on that district committee) research, discussions and development of mathematics program elements that then becomes part of the interactions, discussions, implementations, continuous review at each building level.  (This also implies, principals are involved in the process as well.)

    It can be done if it is supported (annually) by the school leaders at the top, and teachers involved in the committee are supported in working with the teachers at their respective buildings. This is only a skeletal framework suggestion, the individual district/ school leader has much to do to set this into action – but again – it does need the support and resources.
  • 03 Mar 2013 11:59 AM
    Reply # 1232167 on 1209701
    Peggy Brown
    Shawn Towle wrote:Reading:  The remainder of chapter 4, pages 52-62.

    Prompt:

    If we truly are seeking to implement sensible, sense-making mathematics programs like the ones described in chapter 4, Steve says that principals and other school leaders “should channel people’s thinking to these issues of access, alternatives, skills, concepts and big ideas, tasks, language, integration and connections, alignment, coherence, and thinking and reasoning” in ALL discussions about the mathematics program.  

    What do you think?  How do you see this being done in your department, school or community?  What do you see as your role/contribution to that discussion?

    Over the last several years the focus has been completely on literacy in our district.  The professional development energy and money going to literacy have eclipsed math, if not completely then pretty close to it.  The result has been that we have seen growth in student achievement in reading - at least at the elementary level- but we have stayed pretty flat on the math side.  Those of us in math leadership positions have started to say um, hey, are we going to get around to math soon?  We did start a district wide Math Review Committee this year to assess where we are and what we need.  That's a start.  The coincidence of serving on this committee and reading this book has been a happy one.  I've been pulling from Leinwand liberally in bringing the "best practice" piece to the table.  
    My principal is on board.  He is all about clear and coherent learning progressions in every subject, not just math.  And he is also very clear on the relevance piece.   My role is to act as coach, cheer leader and keeping the focus during the limited time we have each week and month to work together as math teachers.
  • 04 Mar 2013 9:23 AM
    Reply # 1233089 on 1209701
    Deleted user
    Prompt:

    If we truly are seeking to implement sensible, sense-making mathematics programs like the ones described in chapter 4, Steve says that principals and other school leaders “should channel people’s thinking to these issues of access, alternatives, skills, concepts and big ideas, tasks, language, integration and connections, alignment, coherence, and thinking and reasoning” in ALL discussions about the mathematics program.  

    What do you think?  How do you see this being done in your department, school or community?  What do you see as your role/contribution to that discussion?

    In my district the focus has been on literacy for the past few years even with the CCSS. In the spring of 2011 a district-wide committee was formed to look at the math standards to see if how well they aligned with our current standards and how well our current resources aligned with the CCSSM. I believe the group met twice. We had a plan for moving forward but there was no follow through. In the fall of 2011 we were told the district was focusing on literacy and that possibly later in the year the math committee would get back together. We have not.

    This year the district did create the new position of math coach. I work every day with teachers in grades 5-12 discussing what the standards mean, what instructional strategies would be effective with particular standards, and how to assess certain standards. I am currently working with the Director of Teaching and Learning to reprise the district-wide committee. Currently, the K-4 teachers have little guidance or support for math instruction. The plan is to have a math coach next year for those grades as well, but right now those teachers need a venue to express the successes and challenges of implementing the CCSSM. A big part of what I do is just keeping math at the forefront of everyone's thinking.

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