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Standards for High School Mathematics: Why, What, How?

Using a Journal Article as a Professional Development Experience


Title:           Standards for High School Mathematics: Why, What, How?
Author:       Eric W. Hart and W. Gary Martin
Journal:      Mathematics Teacher
Issue:         December 2008/January 2009, Volume 102, Issue 5, pp. 377-382

Title:            Transition to a Problem-Solving Curriculum
Author:        Carmel Schettino
Journal:       Mathematics Teacher
Issue:          November 2003, Volume 96, Issue 8, pp. 534-537

Rationale for Use  

Because the topic of curriculum at the high school level raises so many concerns and is such an issue in conversations of reform vs. traditional, the first article is a nice way to frame the conversation about the Curriculum Principle. It sets the stage for a meaningful, sense-making and problem solving curriculum at the high school level.  The second article answers some questions about how we might begin to move toward a problem-solving curriculum. By using these articles as a lens to focus on the Curriculum Principle, participants will consider the importance of a coherent curriculum and how that differs from a set of activities drawn from multiple sources that may or may not be well connected.
In the second session, participants consider curriculum from two points of view - both agreeing on the importance of a problem-centered curriculum. One article is written by a faculty that has developed it’s own problem-centered curriculum and the second article is about the implementation of one of the reform NSF curricula. Both articles reiterate that “A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.” Teachers are then asked to consider the implications for their own practice.

Procedures/Discussion Questions 

Goal: Participants will consider the importance of a coherent curriculum and how that differs from a set of activities drawn from multiple sources that may or may not be well connected.

  1. Allow some private think time and ask participants to write some ideas, issues and/or questions they have regarding the curriculum at the high school level. Suggest that they consider these in terms of their school, their district, their state and nationally. Ask participants to pair up and allow a few minutes for one partner to share; call time and allow a few minutes for the second person to share (dyad); call time again and announce that the pair should come to consensus on two to three things they would like to share with the whole group. Do a go-around and get at least one idea from each pair – chart these (possibly under categories of school, district, state, national). The purpose here is to assess what participants already think about the curriculum and to find issues/ideas/questions that are important to the group.
  2. Read “Standards for High School Mathematics: Why, What, How?” individually. Ask them to mark three ideas that are important to student learning; two quotes that are critical or relevant to you; and form one question you still have after reading the article.
  3. Have participants form two parallel lines so they are facing a partner (or form concentric circles facing each other or just ask participants to find a different partner for each of the opportunities to share listed below. If in parallel lines or concentric circles, participants will move to a different partner for each share listed below.) The purpose is to debrief and process what they have read and to hear from several different people as they process the information.
    • Find a partner and do a dyad about… What is one idea that seems especially relevant to student learning? What is your reasoning?
    • Find a different partner and repeat for another idea. (Note: You can do a share with the third idea, but the intention was to have three ideas in case others have the same idea.  To keep the sharing from going too long, only share two of the three).
    • Find a different partner and dyad about… What is one quote that seems especially critical or relevant to you?  What is your reasoning?
    • Find a different partner… Repeat for the second quote with a new partner.
    • Find a different partner and dyad about… What question is prompted by the article?
  4. Sample Discussion Questions for the whole group. Also consider any questions/issues that arose from the pre-thinking and are charted as a result of the discussion in #1.
    • What are the current developments with regard to high school mathematics standards?
    • How do/will national standards for high school mathematics effect your work at the school and district level?
    • How will you proactively confront the issues and advocate that all students receive a high quality mathematics education?
  5. Ask participants to read the second article, “Transition to a Problem-Solving Curriculum” and highlight three ideas that are particularly useful for them and their students/work in the classroom.
  6. In groups of four, do a go-round timed protocol (each person is given a set amount of time to share their ideas from the reading – about 5-7 minutes each) It’s important that each person use their allotted time and that the next person not begin sharing until their turn is called. This protocol assures equitable time for all participants and encourages those who may not often share to deepen the conversation.
  7. At the end of the go-around, ask each table to come to consensus on five big ideas they have for moving toward a more problem-centered curriculum and to put these on a piece of chart paper.
  8. Display the charts and ask participants to gather around the charts and look for similarities and differences in the ideas, also look for ideas about which they have questions or would like more explanation from a group.
  9. Distribute copies of The Curriculum Principle and allow time for participants to read and highlight at least two ideas that stood out for them. Ask participants to turn and talk to a partner to process what they read and share what they highlighted.
  10. Close this session by asking participants to reflect on what they have read and discussed and to respond in writing to the following prompts.
    • What is your professional learning from today’s reading and discussion?
    • How has your thinking about The Curriculum Principle changed or been confirmed?
    • In what specific ways do you intend to change/refine your practice as a result of today’s collaboration?
    • What will be specific student-based evidence of your success with these refinements/changes?

Next Steps/ Extensions 

Goal: Participants will compare problem-centered curricula and consider implications for their practice.

As a follow up session, use the next two articles to consider how some faculties have begun to address the issue of a problem-centered curriculum.

* One article is from the perspective of a faculty that has written it’s own problem-centered curriculum that spirals (“Bugs, Planes, and Ferris Wheels: A Problem-Centered Curriculum”)  

Title:         Bugs, Planes, and Ferris Wheels: A Problem-Centered Curriculum
Author:     William E. Campbell, Joyce C. Kemp, and Joan H. Zia 
Journal:    Mathematics Teacher     
Issue:       February 2006, Volume 99, Issue 6, pp. 406-413

* The second article is from the perspective of the Reform Secondary Textbooks developed under NSF grants which are unit-based.  

Title:          How Reform Secondary Mathematics Textbooks Stack Up against NCTM’s Principles and Standards
Author:      Tami S. Martin, Cheryl A. Hunt, John Lannin, William Leonard Jr., Gerald L. Marshall, and Arsalan Wares
Journal:     Mathematics Teacher 
Issue:        October 2001, Volume 94, Issue 7, pp. 540-545,589

Divide the group into two sub-groups. One sub-group will work sample problems, read and debrief (become experts) on one article (Article #3) and the second sub-group will work sample problems, read, debrief, and become “experts” on the second article (Article #4). 

  1. Doing the Math: Distribute copies of the problems p. 407 from the “Bugs, Planes…" article to sub-group #1. Ask participants to work problems #2 and #10 and as many others as time allows. To sub-group #2, distribute copies of the Tri-Square Rug Games task page 543 or any one of the other problem samples from the other curricula. Allow sub-groups about 20 minutes to work on the problems from their article. They may not finish, but will have enough experience to be able to share. Some participants may want to work privately before beginning to share their work with others. The intention is for participants to have enough experience with the type of problem solving encountered to analyze the different approaches in the two articles.
  2. Make public records: Form smaller groups within each sub-group to share their work on chart paper. Note the prompt here would be to share your thinking about the mathematics so far – with the understanding that they may not be finished. If the work is charted, it may then be referenced as the articles are compared.
  3. Read: Allow some private think time for participants to read their assigned article. Again, allot a specific amount of time and point participants to the following pages if they don’t have time to read the entire article. Participants should highlight at least two ideas that align with or raise questions about the implementation of the Curriculum Principle.
    • In “Bugs, Planes…” read pp 406 - p. 410 first column; p. 412 second column - end 
    • In “How Reform…” read pp. 540 – 543 (to “Distinctive Features”); pp 544-end (“Conclusion”)
  4. Share in Expert Groups: Return to small groups to discuss the reading using a go-round protocol to share their two ideas. Each participant shares one idea – others respond to that idea; second participant shares their idea – others respond; etc. (The facilitator will need to time both the sharing of ideas and the time for responses to those ideas). The group then records 2-3 ideas to share when they share their poster (from #2). It’s important all participants record these ideas as they will be experts in the jigsaw groups in step 5.
  5. Share in Jigsaw Groups: Form groups of 4 so that 2 participants are experts on one article and two are experts on the other article. If you formed more than one group for each article in step 2, it would be good to re-organize so no one is with a person from their own “expert” group.  These jigsaw groups will now rotate between the posters to share the ideas of each ‘expert’. Allow about 5 minutes for the two ‘experts’ to share the ideas and the math from their article and then about 3 minutes for the others to ask questions and respond. Switch posters and have the other set of ‘experts’ share (5 min) with time (3 min) for responses and questions.
  6. Share whole group: Bring the group back together as a whole group and ask participants to take a few minutes to reflect and write about their own learning from the readings and discussions about curriculum and to consider what might be some next steps for the group to consider regarding the Curriculum Principle. Do a go-round one protocol so each participant shares one learning/idea for next steps; chart these; connect back to the original poster from the first session to consider the growth/ new ideas from the group.

Try some of the problems from either or both of the articles with students in your classrooms and bring back student work.

Connections to Other NCTM Publications 


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