Week 3 (January 25-31) Chapter 3 - Responding to These Changes: What to Expect and Advocate

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  • 25 Jan 2013 5:22 PM
    Message # 1189563
    Anonymous member (Administrator)
    Reading:

    Pages 25-39 (you may stop on page 39 at "Professional Development Shifts")

    Discussion Prompt:

    The reading, this week, focuses on shifts in Curriculum, Instruction and Assessment.  On page 37 are some examples of assessment items/tasks that are taken to the "alternative."  This week, take a task or item you would typically use with your students and "take it to the alternative."  What did you learn?  
    Last modified: 25 Jan 2013 5:23 PM | Anonymous member (Administrator)
  • 26 Jan 2013 10:19 AM
    Reply # 1190019 on 1189563
    Mark Campbell
    My apologies for the late entry to the discussions...I shall begin with a brief summary of thoughts on the prior prompts.  First of all I currently serve as an Assistant Principal at Lawrence HS overseeing both the Mathematics and Science Departments.  I began my career in the early 1980's teaching both Computer Literacy and 9th grade HS Math classes (Algebra I and General Math).  After 14 years in the classroom I accepted a position as a JH Principal where I stayed until I joined the staff here at LHS in 2005.

    It is ironic that one of the prompts inquired about the changes in education since we began because I had that very same conversation with a Social Studies teacher in this building just yesterday in response to his call for a change in our daily schedule to better meet the needs of the students.  I shared with this teacher that we needed to look in our classrooms to see what and how we are teaching students because of the changes in their surroundings outside of school; their responsibilities outside of the classroom as it has changed the way our kids learn.  Furthermore what they need to be able to do with this information/knowledge has and is continuously changing as technology changes.  The question I have... can we do a better job of keeping up?

    In the mid-80's leaders in mathematics recognized the need and began the process of calling for change.  I remember the initial discussions with Vern Byers at UMF about the changes being called for by NCTM.  I was excited to do away with the Dolciani texts (with Copyright dates listed before I began my own journey through public education in the mid 1960's!).  I embraced the MLR standards which outlined the ideas of the NCTM Standards to specific performance indicators and began my journey of incorporating data analysis of student assessment results to assess my curriculum and my instructional practices.  I am blessed in that I am working with a group of math educators here at Lawrence that embrace many of the same beliefs that I have operated under.

    So having made that last statement, I shall find a teacher who will be willing to work with me so we can attempt the task outlined in this weeks agenda.

    One last thing...what do I fear?...incompetence and politicians.
  • 27 Jan 2013 1:18 PM
    Reply # 1190661 on 1189563
    Suzanne Carbonneau
    I  try not to teach in isolation. So this week I will start by telling you what are my lesson plans... and then follow up with how did the thinking shift. My (never do any practice on their own group) is working on the 6th grade assessment on geometry. This is area and surface area. Last week was skills based. This week we will take that knowledge and apply it to real problems with surface area.  We also will use clay to model the surface of several shapes.  I am hopeful that there has been enough practice that students will be able to leap over from remembering formulas to understanding and applying concepts. 
    More to come on Friday!!!
  • 27 Jan 2013 9:11 PM
    Reply # 1190915 on 1189563
    Nola Urban

    I will endeavor to “take a task or item you would typically use with your students and "take it to the alternative."  What did you learn?”

     

    Meanwhile, I am writing now because I have an issue with the second example on page 37.  I believe the store clerk correctly computed the amount that you would be charged in any store with the same advertisement.  I am confused by how the example given shows the additional 10% based on the original price, not based on the adjusted sale price.  In my experience, stores always give the “additional discount” on the lower price.  Perhaps a better example would be to have students explain why the excerpt on the top of page 29 (jet lag recovery) has used the wrong math and how to correct the mistake.

     

    More to follow…  :)

  • 28 Jan 2013 9:26 PM
    Reply # 1191955 on 1189563
    Susan Hillman
    I hope you do not mind that I must sidestep this question, since I am not a K-12 math teacher, but a math methods teacher.  I, instead will react to this chapter.  This chapter reflects the heart of what I am exploring with my K-8 pre-service teachers.  Last week we discussed the importance of having a problem such as the examples on page 37, but also the importance of discourse during a math lesson.  I provided them with several handouts that provide numerous questions that could be used to probe and prompt the students' thinking.  I wish I could attach some files here, since I could then show you the examples I provided the students. 

    One set of resource books that are phenomenal in terms of helping you to develop great problems are
    Schuster, L., & Anderson, N. C.  (2005).  Good questions for math teaching: Why ask
           them and what to ask, grades 5-8. 
    Sausalito, CA:  Math Solutions Publications.


    Sullivan, P., & Lilburn, P.  (2002).  Good questions for math teaching: Why ask them and what to ask, [K-6].  Sausalito, CA:  Math Solutions Publications.


    Susan


  • 29 Jan 2013 7:58 AM
    Reply # 1192294 on 1191955
    Anonymous member (Administrator)
    Susan Hillman wrote:  I wish I could attach some files here, since I could then show you the examples I provided the students. 
    Susan and others,

    Forum administrators are able to upload and link to files. I'm happy to do this if you email your file to me: pamela.rawson@gmail.com. Having examples to illustrate a point is well worth the two minutes it would take for me to post.

    Pam
  • 29 Jan 2013 1:20 PM
    Reply # 1192606 on 1189563
    Nancy Sirois
    As I am reading this book, I realized that I had read this book about 10 years ago when it first came out.  Ahhhh, that's why it's so familiar!

    When I read it then, and again today, it reminded me of how important it is to teach an inch wide and a mile deep.  I know, that's an expression we hear all the time but it's so important to keep this in mind when we look at the Common Core Standards and at our curriculum.

    This book, along with a few others and some classes I have taken in the past, changed how I teach and assess students.  My students have a math journal with a weekly problem that is much like the alternative problems in the book.  The problems are multi-step and usually have a writing component where they need to explain their thinking or defend their work.  Over the past 10 years it has changed how my students think about and "do" math. 

    The math journal problems usually relate to real life like saving money to purchase something or figuring out how much they will need of something to do a project.  They have to answer the question correctly, of course, but I make sure there are many ways to solve a problem so that there are different entry points for different abilities.  If they use repeated addition instead of multiplication to solve one part of the problem, then it tells me something.

    I remember doing problem after problem after problem as a kid.  Today, I believe that if they can show their learning in five problems (or even one meaty one), why should they do 20 or more.  It's about being able to solve the problem, explain their reasoning, defend their decision and use different strategies to solve a problem.
  • 29 Jan 2013 3:12 PM
    Reply # 1192692 on 1189563
    Ruth Neagle
    As an introduction to exponential functions and equations, instead of jumping right to the algebraic form, I used an "alternative" activity based on population growth.  I will e-mail the document to Pam Rawson and ask her to post it here for those interested.  As I expected, students struggled with setting up the graph (units, scale) and reading large numbers expressed as scientific notation on their calculators.  These students are college prep juniors and have done lots of graphing and calculator work, but still without specific detailed step-by-step instructions they flounder.  I was surprised however by their extreme reluctance to estimate, from the given data, future population.  A few even refused to answer the question until I told them how to do it.  Over and over I emphasized that there was no right or wrong answer, that there was not an equation or formula, that their answer depended on how they interpreted the data, and that whatever their estimate they needed to have some explanation of their reasoning.  I tried to relate the situation to a job -- that the boss has asked for a prediction and their job depends on a well thought out response.  Reluctantly they did find a way through to an answer.  Interesting class experience for me and the students both.  

    I was also surprised that there were so very many questions -- I thought I had written instructions with such clarity there could be no confusion, and I had my ed tech complete the activity before class to double check.  She agreed that the activity was quite clear, but still students did not understand many of the questions.  For example when asked to find the average growth -- and even with a hint to divide by the number of years -- students needed more direction.

    I'm not sure yet if the activity will have any carry-over as we proceed with the more abstract content of exponential functions and logarithms, but hopefully it will at least have provided a concrete point of reference.
    Last modified: 29 Jan 2013 5:51 PM | Anonymous member (Administrator)
  • 30 Jan 2013 11:30 AM
    Reply # 1193496 on 1192692
    Lisa Russell
    Ruth Neagle wrote:As an introduction to exponential functions and equations, instead of jumping right to the algebraic form, I used an "alternative" activity based on population growth.  I will e-mail the document to Pam Rawson and ask her to post it here for those interested.  As I expected, students struggled with setting up the graph (units, scale) and reading large numbers expressed as scientific notation on their calculators.  These students are college prep juniors and have done lots of graphing and calculator work, but still without specific detailed step-by-step instructions they flounder.  I was surprised however by their extreme reluctance to estimate, from the given data, future population.  A few even refused to answer the question until I told them how to do it.  Over and over I emphasized that there was no right or wrong answer, that there was not an equation or formula, that their answer depended on how they interpreted the data, and that whatever their estimate they needed to have some explanation of their reasoning.  I tried to relate the situation to a job -- that the boss has asked for a prediction and their job depends on a well thought out response.  Reluctantly they did find a way through to an answer.  Interesting class experience for me and the students both.  

    I was also surprised that there were so very many questions -- I thought I had written instructions with such clarity there could be no confusion, and I had my ed tech complete the activity before class to double check.  She agreed that the activity was quite clear, but still students did not understand many of the questions.  For example when asked to find the average growth -- and even with a hint to divide by the number of years -- students needed more direction.

    I'm not sure yet if the activity will have any carry-over as we proceed with the more abstract content of exponential functions and logarithms, but hopefully it will at least have provided a concrete point of reference.
    Ruth, I do like your alternate activity. It reminds me of the approach of Core Plus Mathematics. I have been looking for another activity to work with my RTI students and if you don't mind I would like to use yours and by your comments and consideration of my struggling students, I will break it up a little and probably lead them a little along the way with discussions. Thank you for sharing. I will let you know how it goes.
  • 30 Jan 2013 11:56 AM
    Reply # 1193521 on 1189563
    Lisa Russell
    I too am joining these discussions late and apologize.  I'm enjoying the book and it aligns nicely with the changes being initiated in RSU 10.  I know the math curriculum must shift and it became very clear to me as a teacher of high school mathematics when I had the opportunity to teach Core Plus Mathematics and Honors level classes at the same time.  What I mean by this is that I really felt that the investigative approach of the Core Program allowed students to gain a much richer understanding of the content being taught and the assessments confirmed that with the explain and justify questions, where the honors students wanted to memorize everything, just to score well on an assessment.  I have worked very hard to incorporate that change with the honors students. I have shifted the old curriculum to a new approach that has given students a deeper understanding. An example that I'm trying now... In my Honors Algebra II class the students can choose between a paper and pencil assessment or a project on Quadratics. In this class I'm dabbling a little in Mass Customized Learning (MCL) so not everyone is at the same place.  The project is that students must choose a quadratic in either art or architecture, do some research, create an equation in standard and vertex form, and find an additional point on the graph of their subject.  They are to use graphing calculators to confirm their calculated equation as correct or incorrect, after they have done their calculations by hand.  They have the choice to write a one page report, create a poster, or use technology to turn in for grading.  They must show all their work, but even more challenging is they have to determine where their errors are in their application and explain them.  What I have seen so far is that it is giving them a much richer understanding about quadratics in the real world and why precision in the equation is essential.  Not all students have completed the unit but all of them so far have chosen the project.
    The book confirms that "teachers need time and support to analyze these changes" and that a school leaders must support this movement, but the question is how do we get that support?  I do feel fortunate that I have a great department to work with and a supportive administration, but it is the time and financial piece that is a road blocker.
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