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

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  • 15 Feb 2013 4:52 PM
    Message # 1209701
    Reading:  The remainder of chapter 4, pages 52-62.


    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?

  • 17 Feb 2013 12:01 PM
    Reply # 1210704 on 1209701
    Maggie Griswold
    As I am currently teaching a 4-graduate course mathematics series at UMF for math leaders, I zeroed in on the statement on p. 60:
       "In other words, a coherent program supports effective teaching as well as higher
         levels of student learning."
    In co-developing these graduate courses, I have been reading about mathematical content knowledge. Below I have included a few articles by two names in the field, Heather Hill and Deborah Ball:
    • ·      Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development initiative. Journal for Research in Mathematics Education, 35 (5), 330-351.
    • ·      Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
    • ·      Hill, H. C., & Ball, D. L. & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students.  Journal for Research in Mathematics Education, 39, (4), 372-400.
    This work listed above mirrors the readings this week that discuss the NCTM Professional Standards: communication, reasoning & proof, representations, connections/integration and problem solving in real situations.
    What math content knowledge does a teacher need to teach math effectively.

    This is my favorite section of the book so far, probably because I am currently so steeped in the content Leinwald presents here. In so few pages he has hit so many high points:
    • skills vs concepts
    • exercises vs problems; characteristics of tasks: rich opportunities for student to be active and to perform as they STRUGGLE to grasp important mathematical ideas.
    • coherence: learning progressions, logical structures, focus on connections & making sense of...

  • 17 Feb 2013 1:54 PM
    Reply # 1210780 on 1209701
    I found myself nodding through this section of reading.  Leinwand takes everything that teachers know and puts it into plain simple print.  However, the true question has bee stated here: How do we work in our buildings, departments and districts to make this happen?

    Within my building the struggle is time. One way to overcome this lack of time, would be asking teachers to create, share and/or brainstorm individually.  As a group we could then bring individual ideas to the table to enhance the task. This would give a focus to the limited common time and also help us to fulfill our common assessment initiatives.

    A 21st learning idea, would be teachers sharing their ideas or inspirations via a blog or online platform. Asking teachers to post mathematical starters or ideas which they need help in developing would allow collaboration that would exceed the one teacher working alone. I see how Dan Meyers has posted simple thought provoking images 101 questions, and think how can we use this same idea to develop sensible mathematics in the classroom.

  • 17 Feb 2013 2:44 PM
    Reply # 1210798 on 1209701
    Sally Bennett
    The only way to develop a meaningful curriculum is for teachers to have enough time for quiet creative collaborative reflection. 

    I do not believe we need to channel most math teachers' "thinking to issues of access, alternatives, skills, concepts," etc.  We know what we should focus on and it is singularly frustrating that the time we are given to meet with our colleagues must have some sort of a product to show for it. What Leinwand proposes may not directly result in any product immediately and without tangible evidence of its efficacy, it is a hard sell to school administration who must take the investment of time on good faith that it will ultimately result in better student learning.

  • 18 Feb 2013 10:03 PM
    Reply # 1211960 on 1209701
    Bobbie P

    Speaking from the perspective of the struggling student, comprehending language intense math curriculum is difficult, multi-step problem solving is difficult, stamina to stick with and / or focus on a complicated problem is very difficult, and transference of learning to novel problems is very difficult. As I stated in my Week 5 post, many districts around the country are developing resources to assist general educators to align to the Common Core, but the resources are not yet showing up for students with special needs, yet the requirements to meet grade level Common Core Standards are already there.

    On page 56, Leinwand states, “In fact it is nearly impossible to teach mathematics to students who cannot read, and it is extremely difficult to assess the mathematical understanding of students who cannot speak or write.” I have taught math to students who could not either read or write in English and barely spoke it. It is not impossible. Math is actually universal and not dependent on a student's ability to function in the dominant language of the instructor. This is not so far from the special needs student who struggles with reading and writing. A 'language rich' classroom is not mutually exclusive to teaching the ELL student or the student who struggles.

    What ever happened to validity in that we need to be sure we are actually testing the content we are teaching. Computerized testing as the only alternative from Smarter Balance is an obstacle to most of my students being able to demonstrate their knowledge. Why should a student with reading or writing difficulty be penalized when being assessed in math?

  • 19 Feb 2013 7:42 PM
    Reply # 1212668 on 1209701
    Jenny Jorgensen
    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. 
    As the Math Lead Teacher, I help keep teachers informed about the current thinking in mathematics education.  We look at student work together and discuss teaching practices that might improve student learning.  The principal reads and comments o the weekly notes that are on a google doc. In this way, I know he's invested in the work that we are doing together to help provide students with quality instruction.
    Discussions about math instruction, the CCSS Practices, and our students' progress take place during scheduled Math Learning Area meetings.  I wish these meetings happened more frequently (we have four throughout the school year).
    Sally's comment about needing time to meet to have rich, engaging conversations about our teaching practice and about student learning is definitely heard by me.  I value every moment that I have to talk with teachers, look at student work, discuss specific lessons observed, plan future lessons, etc.  There never seems to be enough time to do this. I am reminded by something that I picked up at a session presented by the DuFours which was basically to use the time we have wisely.  There's so much that goes on in school that keeping focused during the little time we do have is often difficult. So often other issues that arise during any given moment of the school day can usurp the allotted time; knowing how to address a valid concern and then guide the conversation back to math takes skill. 
  • 21 Feb 2013 3:36 PM
    Reply # 1223469 on 1209701
    Bill Shardlow

         At the expense of sounding repetitious, I would completely agree with what Jenny posted before and probably have very little to add. I have had the pleasure and the opportunity to work with her for many years and I completely agree with what she stated.

         We do need much more time to discuss our instructional practices. It would be a huge advantage if our math learning area could meet more than four times a year. The discussions that we have during this time are invaluable and allow us to look at each other's practices, what we are doing each grade level, and how we plan on coordinating our efforts. Change is difficult and can only be maintained if we are allowed the opportunity to discuss what we do, evaluate our successes and failures, and learn from our peers. Every day at school is always busy but we do need to find more time where we can sit down and discuss what we do, how we do it, and the best ways to continue to move forward.

         As I type this post, I am at Michigan State University attending the CMP3 Users' Conference. I am looking forward to having some time to talk with Shawn Towle about what is ahead, attending the various presentations, and then sharing it via a Google doc with the other math teachers in the building. But, we need more time to discuss and determine how we are gong to implement the changes. Time, time, time...

  • 21 Feb 2013 4:40 PM
    Reply # 1223516 on 1209701
    Kate St.Denis
    My role/contribution to that discussion?
    Simply put, my role is to have those discussions. I push to ask of teachers what I ask of students as stated in the CCSS and repeated by Leinwand on page 61, "reason abstractly and quantitatively" and "construct viable arguments and critique the reasoning of others." I will fail my colleagues as the math specialist if I fail to ask them "why?" or "can you explain what you did and why you did it?" Of course the "what you did" piece is different for teachers and more likely to be about:
    what evidence led you to group your students in this way?
    what led you to believe that their knowledge was sufficient enough to skip said chapter or deficient enough to supplement in the way you did?
    what tasks will your students be engaged in during this unit?
    how will you connect the task to other areas of study?
    and so on....
    Several people have commented on a lack of time. These questions can be very quick interactions. Most importantly, they build a culture. The time I lack is my own as a leader. I need to advocate for increased value of instructional leaders so that we have the time to interact at all grade levels without so many other responsibilities tugging at us.
  • 21 Feb 2013 5:10 PM
    Reply # 1223538 on 1209701
    Suzanne Carbonneau
    I love this chapter but for a different reason. The author, Leinwand describes how different math and math teaching is to humanity curricula. Math is skill base: there is no getting around that fundamental point. But then if we agree that after the initial skill is introduced it is our advantage to take that skill and apply it to real context or higher leveling thinking activities. Lastly to use physical materials to give hands on experience then I am all for it.  That is so true.
     I use to teach this way ALL the time. The library was full of dream house built to a scale ratio and bridges made out of toothpicks that use angles and trig to get size and proportion. Taught reflections and translations using Escher.  I taught % by having students actually save money and buy presents for the needy at Christmas time. The group with the best deals got to get the most present for their money.  I had a cool activity about making candy boxes at after valentines day ( when candy was 50% off) the students had to calculate boxes that did not exceed a limit for volume or surface area. All these lesson were taken away so I could teach like every one else in the building from page to page of Connected Math. Now I am excited to say that these projects will be developed back in my math program. I will look at the common core and some of these ideas will be the project assessment. I am so happy that nothing in education stays the same  for very long.  Thank you Steven Leinwand for bringing back good teaching and good lessons. YEAH

  • 23 Feb 2013 10:10 AM
    Reply # 1224659 on 1209701
    Nancy Sirois
    I agree with everything that has been said above.  Math does need to be meaningful and relate to the students we teach.  We do have to to have those difficult discussions about what is truly quality math instruction and how can we make sure we are doing the best job teaching math to our students.

    What resonates with me is the issue of time.  We hear it every day...not enough time for this....not enough time for that.  It's true, there isn't enough time in the day to get everything done and there isn't even enough time in the day to teach what we have to teach.  As an elementary level teacher, when we get a new program or the district tells us what has to be implemented or targeted for the year, I think administrators forget that we don't only teach a subject, we teach children.  If we only had to teach subjects during the day, I think we could get it all done, but we have to work with students on emotional issues, bullying, study skills, note-taking, differentiating the instruction and taking the time to slow things down so they can master the work.

    Time will always be an issue.  What administrators need to do is respect that time.  It's not as easy as taking more time before and after school to do this type of work.  It's about administrators knowing that time spent on important curriculum and instructional work takes time away from other things we need to do.  It's about making professional development time meaningful and focused so that everyone buys in to the process and the change is deep and everyone takes ownership of it.  We should take the time to visit classrooms where a teacher is known to be a great math teacher.  I know I never have the time to do that.  If we want true change in how to teach our students, we need to focus in on what is truly important to teach and work on that.  I'm hoping the CCSS are a step in that direction.
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