Week 1 (January 11-17) The Math Leader's Domain of Reponsibility

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  • 10 Jan 2013 7:57 PM
    Message # 1177039
    Anonymous member (Administrator)
    • Introduction  vi-viii
    • pp 1-8  Chapter 1- The Math Leader's Domains of Responsibility
    Many of us have been involved in mathematics education for a long time, while some of us are relatively new to the profession.  With a starting point of the publication of the NCTM Curriculum and Evaluation Standards for Mathematics in 1989 and ending with 2013, how has math teaching /math education changed for you personally over the years?  How much has remained the same?

  • 11 Jan 2013 10:53 AM
    Reply # 1177453 on 1177039

    When I started teaching, the math textbooks at the high school level had a great variety of problems to do, from the easy to the challenging (some were even hard for me as the teacher!).  The books were laid out so everyone could easily see where the "easy" questions were and where the cut off was to the more challenging then the third cut off to the most challenging.  I miss those books.  They offered lots of fodder to help students practice at their level of ability.  One way they lacked was in asking students to explain their thinking (at least it did not formally get asked, it was an implied expectation).  Most, if not all, teachers expected students to show their work to justify their answers which is a great way to know the thought process used.  The criticism was that the answers became about the algorithm and not the thinking that may have been used to get the answer.

    As I continue to work with the new textbooks and support materials, I struggle to find many, varied challenge questions.  A recent review of a text intended to meet the Secondary Math I (SM1) that was written “from the ground up” not just an older text reworked to fit the CCSS, was limited to maybe 15 questions per section and 10 of those questions were multiple choice with only 5 open-response problems to solve.  There were some great examples for students to read through and try to understand what the concept was, but it was mostly examples.  Why do we not use “key concept” boxes or “concept summary” boxes to highlight the formal math along with the examples?  I am not convinced that exploratory learning is the only way we should be delivering material.  I believe that exploratory learning is one way to deliver concepts, but there are many, varied ways to help students understand topics.

    Perhaps my rant is based on my work as an advocate for the gifted & talented.  G/T math students tend to pick up on concepts quickly.  They do not always want to stop and explain what makes great sense to them.  I believe we need to work with them to do such explanations (as simple as showing their thought process).  At the same time, asking them to “discover” the right process can be very frustrating for them.  Why not tell them the formal definition or algorithm and, when needed, also give them the time to explore these definitions and algorithms?

    One other frustration I have as a math teacher is how we have to all use the same textbook for all levels of students.  Perhaps this is not the case in your school district, but in mine (and I’d hazard a guess in many) the idea of one teacher using one resource and another teacher using a different resource is not acceptable.  Just as students need different ways to understand the concepts, so do teachers need different ways to deliver the content.  My g/t students would do well with a more wordy book and higher level questions, but the middle or SPED students could use more manipulatives and mid-level problem solving (like using whole numbers instead of fractions when discussing geometry topics).

    The one constant in my teaching has been the basic topics.  All students should know how to manipulate numbers and variable quantities with all the operations.  All students should know how to find the perimeter, area, and volume of objects in the real world.  All students should be exposed to real world situations and how the math they are learning helps them to determine a solution.  These ideas have remained the same over the course of my career.  I dare say my approach has changed somewhat in that now I encourage students to approach the problem in any way that will make them successful, but to try and do it whatever way is currently being presented.  I have learned new ways to think about solutions and I am more accepting of alternate solutions than I would have been back in the 80’s.




  • 12 Jan 2013 6:04 AM
    Reply # 1178041 on 1177039
    Maggie Griswold
    The biggest changes for me happened with the 2000 NCTM Focal Points and Process Standards and new classroom curriculum [math programs funded by NCLB]
    • Focal Points provided a clearer structure of math concepts over grade spans.
    • Process standards provided guidance for a change in instruction: make connections, use models, communicate [ask questions, Why?, Show me how?], use real-life contexts [also other disciplines], reason and prove and focus on problem solving.
    • New math programs: These programs attempted to support the process standards: e.g., Terc's Investigations, Univ of Chicago's Every Day Math.
    Since then, standards and related focal points have evolved to the now CCSS with clear domain progressions. Process standards have evolved into the 8 Mathematical Practices of the CCSS.

    The road map for math concepts is much clearer now. Instructional changes have been more difficult to accomplish. The advent of math leaders in schools, to address lack of adequate student performance, in the form of math coaches, often funded by Title I is encouraging. A math specialist certification, to mirror the literacy specialist certification, would support the preparation of these math leaders.
  • 12 Jan 2013 10:17 AM
    Reply # 1178124 on 1177039
    Math teaching for me over 30+ years has become an exercise in frustration in many ways.  The basic skills that students come with to the high school are greatly diminished.  I believe this is largely because the students are never held to mastery along the way.  We have also discussed in my district that calculators were readily being used in the middle school and I think they have now stopped that.  Basic math facts and manipulation of fractions is such a problem, it makes it more challenging for kids to be successful in algebra.  I agree that high schools could benefit from a math lab or tutor to work with kids to get them up to speed.  But what would be even more beneficial if kids would be expected to achieve mastery in the lower grades, and those who aren't get the extra support there until they do.
    I also believe that there has been a huge shift in society that has contributed to many lazy students who are happy to pass and not really understand.  I have many more students today than in my early years of teaching who do not do the homework.  They excuses are numerous, and many times parents have said they can't their child to do their homework and want suggestions.  I am guessing the time spent on facebook and computer games trumps homework time in each of these situtations.There are still the motivated math students who will be successful engineers, business people etc., but the majority want to know "how do I do it?" and don't want to do the thinking that leads to understanding and internalizing.  
    As to the idea that our text books are not adequate, I don't teach by a book.  I teach the topics in the curriculum and pull practice and application from a variety of sources.  I suppose if there was one text that provided everything I might use it.  I am happy to see newer texts providing SAT prep problems the way they are presented on the SAT, so students are becoming more familiar with the test format.
  • 12 Jan 2013 6:49 PM
    Reply # 1178394 on 1177039
    Deleted user
    Shawn Towle wrote:Reading: 
    • Introduction  vi-viii
    • pp 1-8  Chapter 1- The Math Leader's Domains of Responsibility
    Many of us have been involved in mathematics education for a long time, while some of us are relatively new to the profession.  With a starting point of the publication of the NCTM Curriculum and Evaluation Standards for Mathematics in 1989 and ending with 2013, how has math teaching /math education changed for you personally over the years?  How much has remained the same?

    I began my teaching career in 2000, right out of college at the high school I graduated from. At that time, I was assigned a mentor teacher from the math department who helped me with various issues that would arise from day to day planning, curriculum questions. She was also responsible for giving me the curriculum for each course I taught, all organized by chapter with any materials I might need from daily assignments to assessments. This opportunity that she offered me allowed me to really focus on my teaching strategies instead of figuring out the content or what particular activities I would give the students. I think this experience runs parallel to the creation of the Common Core now as it addresses "the what" we should teach. On page 2 and 3 in the reading this is discussed specifically and I appreciate the Common Core because of the ability of leaders to focus on teaching strategies as we move forward. 
    Another important aspect discussed in this portion of the reading on pages 5 and 6 is professional development. Upon earning my first job, I was also required to be trained in the specific program that I would be teaching, Math Connections. This particular program required many teachers to transition from the more traditional approach to teaching mathematics to a more discovery based approach. My district had made a commitment to providing all teachers at the high school level with the appropriate training in the program to ensure it was delivered as it had been intended. We are no longer teaching this particular program, but we are very much rooted in its philosophy that math education is best understood when students are able to discover as much of the math as possible with support from the teacher. The classroom should provide students to the space and time to explore new concepts, while determining which prior knowledge is needed to move forward. The teacher prods students along with questioning techniques aimed at pushing students to think about the situation in front of them. All of which is done while collaborating with their classmates.
    As time has gone on, we have not provided teachers with the adequate time necessary to collaborate with other teachers nor have we given the much needed professional development to continue to grow as effective teachers, though. Often, we have expected teachers to simply find the time to collaborate with one another, adapt to changing student needs, and take on more responsibilities and duties. All of this will less time, funding, and teachers.

  • 12 Jan 2013 8:17 PM
    Reply # 1178429 on 1177039
    Susan Hillman
    Great, prompt!

    I teach K-8 pre-service teachers in math methods, so a huge shift has occurred to incorporate peer teaching emphasizing leading with questions and focusing on the children's understanding of math.  It is a behavior change that one cannot do by just reading a textbook or being lectured to or even doing many problems in which the pre-service teachers must show their understanding.  Thus they peer teach two lessons with both being video-taped, so they can reflect on what they are doing and how they need to push themselves.  I believe pre-service teachers must experience this way of teaching to get it to "click."  Thus a tremendous focal change has occurred...and I will say for me as well.  As a professor, I have to fight the urge to "tell," to "show."  My questioning skills have improved, but I still feel I am learning and need to remind myself to do so, for example, about providing wait time, about volleying questions to someone else rather than back and forth between me and the student, about even when the answer is "correct" following up and having them explain why.  I feel I am so much a learner still as I try to cast off old ways.
  • 12 Jan 2013 8:45 PM
    Reply # 1178440 on 1177039
    Tracey Hartnett
    As a literacy ed. tech. at Songo Locks School in 1992-93, I gathered my 3rd graders at the end of their math class.  Impressed by their ability to reason and problem solve, I asked their teacher, Jeannie Martin, to recommend professional development.  That summer, I took part in a Marilyn Burns institute and learned that, unlike my experience as a student, mathematics could be learned with understanding.  I have been continually involved in mathematics professional development since then.  It took a couple of years to relearn all that had been learned without understanding (example: flip and multiply to divide fractions) but for many years, my teaching was relatively consistent- embedded in context, focusing on conceptual understanding first, fluency with procedures last.  The last two years, I participated in a formative assessment course provided by EDC.  As a result of this p.d., I still focus on teaching for understanding.  However, my students are now aware of learning intentions and success criteria.  They are learning to assess their own progress and utilize formative feedback.  My instruction has been greatly affected by this experience learning to implement the critical aspects of formative assessment.
  • 12 Jan 2013 11:25 PM
    Reply # 1178531 on 1177039
    Maureen Brown
    This is my 40th year in education - When I graduated from college and took my first gr 5-8 math teaching job in NH,  the buzz word was "INDIVIDUALIZATION"...every student was to be on his/her own pace...and individualization was interpreted as worksheet, drill, worksheet. (on mimeographed sheets - I still smell the fluid!) When my 5th graders got to 7th grade and still didn't "know" math I realized something was wrong - and I couldn't blame it on their previous teacher - so I read, went to some conferences and figured out that there had to be a different/better way. After working as a math consultant in Portland, teaching adult ed in a school setting as well as in different companies, teaching in the Maine Apprenticeship Program (which was well before it's time!), working with the Career Center at the "Training Resource Center" and now as the "math specialist" at GNGMS I still feel that we need to involve the students in active learning in math. The math practices need to become the first standards that we unpack. I am terrified that those schools that are heading toward a standards or proficiency based model will interpret those concepts as worksheets, test, put away, and start another worksheet. I am afraid that the children will not have the wonderful opportunity of discovery, discussion, playing and talking math. It is the one time I do not want to see math education come "full circle."
  • 13 Jan 2013 7:26 AM
    Reply # 1178644 on 1177039
    Kimberly Smallidge
    To be honest, I don’t think all that much has changed in classrooms since 1989. When I started teaching in 1992, I had taken one math methods course. Sure, it focused on the NCTM Standards, we talked a lot about them, but it didn’t really focus on how to TEACH them for student understanding. There were suggestions, sure. But, when I stepped into my first classroom I, like so many others, fell back on what I knew, which was my experience as a math student. I had done ok with that method of teaching so I knew it worked, right? I still see lots of classrooms where the teacher teaches the algorithm early on and students do a page of practice problems that simply require them to employ that algorithm repeatedly. I know that sounds a bit simplistic, but I think it is basically true...and it is much neater and easier than teaching for deeper understanding. In my opinion, the emphasis has been, and continues to be, on “getting the right answer”. I agree that “getting the right answer” is important, but I think that uncovering the thinking that leads you there is key to uncovering student understanding, or misunderstanding as the case may be.My classroom experience is primarily as a middle school math teacher. In my middle school classroom, I remember seeing students using partial sums, partial products, lattice multiplication, partial quotients, and other “non-traditional” methods, and I remember thinking those methods were clunky and inefficient and wondering what on earth my elementary colleagues were doing down there. Little did I know that those methods I was questioning in middle school were the very ones (with the exception of lattice multiplication!) that I would be encouraging colleagues to use five years later in my role as “Math Interventionist/Math Specialist” to help our kids discuss and develop number sense. To be honest, I have discovered that I had very little understanding of how kids develop mathematically...and this after having taught math for well over 10 years! I don’t think I am the only one in this boat. Professional Development needs to be a priority if change is really going to happen.In the last few years I have been our school’s “Math Interventionist/Specialist”. This has been an incredibly eye opening opportunity simply because it has given me portholes into the math classrooms of grades K-8. One change that I do see, especially at the elementary age (at least at my school), is that some teachers work hard to encourage students to use varying strategies to reach the right answer. I see students being encouraged to actually THINK about the numbers before doing a calculation in an effort to use the most efficient strategy, not just the standard algorithm which, in many cases, is the least efficient strategy to use. In classrooms that encourage this, it is amazing to hear the reasoning and understanding of numbers that students really do bring to the table. Likewise, it is often amazing to me to realize how little understanding students who are able to get the right answer using the traditional algorithm really DON’T understand. What a conundrum! It appears that we all still have much to learn.
  • 13 Jan 2013 8:52 AM
    Reply # 1178684 on 1177039
    Sally Bennett

    I used to teach the way I was taught.  I figured that if it was good enough for me, it would be good enough for my students.  In class, I would model how to do a problem (to show how super intelligent I was) with minimal student input  and then assign 10 - 20 problems that were similar with different numbers (the more difficult problems probably used fractions rather than whole numbers).  We would waste a good portion of the next class period going over the homework (whether we needed to or not) and then I would demonstrate a new concept (masterfully, of course), assign the requisite homework, and the cycle would continue.

    I used to think the best classes were quiet classes where students sat in neat rows, raised their hands with alacrity, and waited patiently to be called on.  They would always give the correct answer (or at least the one I was looking for) and everyone else would nod their heads sagely in agreement.

    All that has changed.  The more research I do and the more I learn, the more mortified I am about by initial forays into teaching mathematics for understanding.  My classroom is messy (no more neat rows) and noisy as students discuss and critique each others' thinking.  I try never to say anything a student can say for him or herself.  I allow students to make mistakes and then I ask them questions so they can self-correct and achieve a sense of personal empowerment.  I listen for all answers - even if they are not the ones I had in mind and I find I learn a lot from my students.  I assign a lot less homework and through using ASSISTments, I can pinpoint the assignments I need to bring up in class to allay any confusion and save time for more hands-on mathematics.

    It is a lot harder to teach this way (I never quite know what to expect and I am a bit of a control freak) but I sense that the students who are willing to put in the effort learn, truly learn, the material as they make it their own.  I am still working on a strategy to motivate those students who would rather not put themselves at risk and try.

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