Using a Journal Article as a Professional Development Experience
Title: Learning about Students’ Mathematical Literacy from PISA 2003
Authors: Sharon M. Soucy McCrone, John A. Dossey, Ross Turner, and Mary Montgomery Lindquist
Journal: Mathematics Teacher
Issue: August 2008, Volume 102, Issue 1, pp. 34-39
Rationale for Use
The Program for International Student Assessment (PISA) is an international program focusing on the assessment of the mathematical literacy of fifteen-year-olds. The article provides several examples of assessment items that require students to apply their mathematical knowledge. In this session, participants will consider the connection between how our students perform on PISA assessment items and the implications for their practice. Particularly, they will consider the connection to the Learning Principle, which states, “Being proficient in a complex domain such as mathematics entails the ability to use knowledge flexibly, applying what is learned in one setting appropriately in another. One of the most robust findings of research is that conceptual understanding is an important component of proficiency…”
Goal: Participants will consider using student work to inform instruction.
- Write the following quote from the Learning Principle on a piece of chart paper, “In the twenty-first century, all students should be expected to understand and be able to apply mathematics.” Ask the question, “Where do you think students in your classes/school are related to this 21st century goal and how do you know (or how might you find out)?” Allow some private think time and ask participants to respond by writing down their ideas. 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 1-2 thoughts they would like to share with the whole group. Do a go-around and get at least one idea from each pair – chart these. The purpose here is to assess what participants are already thinking about the Learning Principle and to heighten awareness that we need to find ways to determine the level of student understanding and ability to apply mathematics in problem situations.
- Allow time (about 5 minutes) for participants to read the beginning of the article pp. 34-35 (through the section on “Mathematical Literacy”). Ask participants to turn and talk to their partner to process what they read and determine what questions they might have about Mathematical Literacy. Briefly discuss any questions. Note: Don’t get bogged down here in discussions about the pros and cons of assessments like the PISA – keep the conversation focused on mathematical literacy and table other discussions for later.
- Number Cubes Problem:
Repeat the process in #3 with the other two problems, “The Exchange Rate” problem on page 37 and the “Test Scores” problem on page 38. Note that these items include sample responses. If possible, remove the sample responses when copying these for teachers to use. Allow ample time for participants to do the math and discuss the core mathematics with their partner and/or group, but limit discussion about student results until they finish the article (see #5).
Return to the article and ask participants to read the final sections on pp 38-39 (“Usefulness of PISA Results” and “PISA-like Problems for the Classroom”). Ask participants to reflect privately on the question, “What are the implications for our practice?” and keep a record of their thoughts.
Before facilitating a whole group discussion of the article, ask participants to read “The Learning Principle” and to reflect (again in writing) on the question, “What are the implications for our practice?” and also on the question, “What are the implications of the Learning Principle in the light of the PISA results?”
Preparation for follow up – Divide participants into three small groups and assign each group one of the three problems from the article. Ask them to consider some possible student misconceptions related to that problem. Ask each group to share their predictions on chart paper and keep these for the next session.
- Do the math: Allow time for participants to do the problem on page 36 privately.
- Encourage them to keep track of their thinking so they can explain how they arrived at their answer, not just record the answer. Remind them to journal and be prepared to share their thinking with others.
- Ask them to respond to the question, “What is the core mathematics in this problem and where would you use the problem in your curriculum?”
- Share with a partner: Allow time for participants to share with their partner (using the dyad described in #1) how they solved the problem and their thinking about the core mathematics in the problem.
- Present solutions: While participants are sharing, select 1-2 to present their thinking to the group. If a document camera is available, ask them to put the record of their thinking under the document camera so others can follow their explanation. Encourage others who might have thought about the problem in different ways to share their thinking.
- Return to the article: Allow participants a little time to return to the article to read the section on how students in the US, Canada, Mexico did on the Number Cubes Problem (pp. 35 – first few lines at the top of 37) compared to the OECD average. Point out the chart in figure 2. Allow a brief opportunity for them to process what they read with their partner. Ask if there are questions about the interpretation of the chart. Hold discussion of how students performed until all three problems have been discussed. (Note to facilitator: Again, participants may want to discuss possible biases of the assessment items. Table these discussions for later so as not to derail the conversation away from teaching and learning.)
Ask participants to give the three PISA assessment items to at least one class of students (suggested 15-year olds or older). Bring back the student work (un-scored) to the next meeting.
Goal: Participants analyze data to support inferences about how students are applying mathematics (see #1 above).
- At this meeting, divide the group into three sub-groups so that each sub-group is scoring one of the three problems. (These may be the same groups that predicted student misconceptions at the end of the last session.) The group should agree on criteria for scoring, score a few of the student papers and determine if their criteria is working, then edit or revise as needed. They should also keep track of student misconceptions as they score the papers. Each group should revise the chart prepared in the previous session to indicate misconceptions they actually observed.
- Re-group participants so there are 1-2 people (the “expert(s)”) from each of the question sub-groups. Allow time for each group to rotate through the three poster sets and for each “expert” to share their groups’ findings. Compare these findings to their predictions about possible student misconceptions at the end of the first session.
- Facilitate a whole group discussion around the question, “What did we learn about how our students are applying their mathematics?” “What are the implications for our practice?”
- Consider reading the article, “Action Research: A Tool for Exploring Change” by Thomas A. Evitts (Mathematics Teacher, May 2004, vol. 97, No. 5, pp. 366-370) as reading for homework and developing a plan for the members of the group to conduct their own action research as they implement some change in practice.
Connections to Other NCTM Publications
- Allsopp, D., Lovin, L., Green, G., & Savage-Davis, E. (2003, February). Why students with special needs have difficulty learning mathematics and what teachers can do to help. Mathematics Teaching in the Middle School, 8, 308-314.
- Boyer, K. R. (2002, September). Using active learning strategies to motivate students. Mathematics Teaching in the Middle School, 8, 48-51.
- Chissick, N. (2004, January). Promoting learning through inquiry. Mathematics Teacher, 97, 6-11.
- Ellis, M. W. (2003, November). Constructing a personal understanding of mathematics: Making the pieces fit. Mathematics Teacher, 96, 538-542.
- Hodge, L. L. (2009, April). Learning from students’ thinking. Mathematics Teacher, 102, 586-591.
- Manouchehri, A. (2007, November). Inquiry-discourse mathematics instruction. Mathematics Teacher, 101, 290-300.