Forest Glen
A collaborative inquiry in math in a grade 3 classroom
Exploring the comparison of solutions to authentic word problems in order to support student communication and ownership of learning in mathematics.
Theory of Action
If we provide opportunities for students to justify and compare their solutions when solving authentic word problems, then students will improve their ability to communicate their thinking.
Our Starting Point
How Relevant is the Question?
SWST: Do you eat turkey?
Student: No
The classroom has only 3 students who had ever eaten turkey.
Student: No
The classroom has only 3 students who had ever eaten turkey.
Examining Student Work
Initially students pictures were 'detailed'. What does detail mean to a student? The student has drawn the turkey both dead and alive.
Moderating the math
Collaboration between the SWST and the Classroom Teacher focused on the next steps for student learning. How do we have students pay attention to the mathematics of word problems and communicate that math?
Using Success Criteria and Learning Goals
Reading Word Problems
These success criteria were used with the students. They are taken from Krpan's math expressions Developing Student Thinking and Problem Solving Through Communication
Mathematize the Situation
"Verschaffel, Greer and de Corte argue for an 'open' approach in which students draw on several sources of information to tackle problems in a more realistic way"
Word Problems Connecting Language math and life
Word Problems Connecting Language math and life
Success Criteria
Students and teachers discussed the success criteria for making their thinking visible in mathematical writing and pictures. Learning goals related to the mathematical process of communication.
Reflecting on Comparing Solutions
Comparing Solutions by blog
A solution to a word problem was posted on the class blog. Students were asked to reflect upon the solution using the success criteria to justify the answer.
Transparent
Perhaps some students reflected on the mathematical concepts, or process of communication with their parents at home.
Deepening Conceptual Knowledge
Acceptance of various strategies
Anchor charts consolidated the various strategies students could use for procedural processes.
Building Conceptual Knowledge
An emphasis was placed on students using strategies that made sense to them rather than using the standard algorithm without understanding.
"The four themes supporting authentic learning are:
1. An activity that involves real-world problems and that mimics the work of professionals; the activity involves presentation of findings to audiences beyond the classroom.
2. Use of open-ended inquiry, thinking skills and metacognition.
3. Students engage in discourse and social learning in a community of learners.
4. Students direct their own learning in project work. source" = ernweb.com
Typhoon Haiyan Relief
Integrated Learning
Students were learning about natural forces. Science, math and literacy were integrated when students wrote commercials to raise funds for relief.
Cooperative group work
Students counted the total money raised. They worked in groups. Students were using genuine math thinking tools to determine the total funds raised!
Presenting the methods
Students presented their strategies for the methods used to total the money and explained how they presented the information
Drinking Box Blow Up Word Problem
Interview
After interviewing the student she shared that she had intentionally changed her answer from an odd number to an even number to facilitate a way to determine half. This revealed her comprehension of the math concept.
Strategy Sharing
This student shared his strategy with the whole class. As he explains his thinking, he deepens his conceptual understanding. Other students may follow his strategy. See Hintz article on Strengthening Discussions, (2014)
Next Steps
As students represent their mathematical thinking, teachers and students can assess their work. They can discuss mistakes, share strategies and listen to classmates' solutions. Hintz (2014)
Transition Time Tension Word Problem
Students communicated their mathematical thinking through a variety of representations. Each student followed their own reasoning when applying strategies. Evidence of knowledge, understanding and application is demonstrated.
Student Voice
Documentation
Videos of students were taken as students compared strategies, insights into their thinking were revealed.
Transcript
Conversations and observations are as valuable as products.
Key Learnings and Next Steps
- "If students are given the opportunity to grapple with complex tasks, to observe good models of thinking, reasoning, and to justify their solutions they will develop a view of math as meaningful and as something that they personally can engage with and understand." (Smith, Stein, 2011)
- A mathematical climate that supports focusing on the process of arriving at the solution instead of determining the right answer leads to risk taking on the part of the students.
- When students are sharing their solutions, they are comparing and contrasting. Comparing and contrasting is a way for students to make connections in their learning.
- Connecting the Learning goal to a mathematical concept/idea can help to push the thinking forward and prevent strategy sharing into a show and tell type situation.
- Students' engagement with problem solving activities is increased when students find the task relevant and meaningful, and when they feel they have background knowledge to access the question.
Click on the Resources and Research title to view a Haiku Deck of resources that supported our learning.
Student Work Study Initiative 2013/14 at Forest Glen P.S.
A collaborative inquiry in using strategy sharing by students to compare and justify solutions to authentic word problems, conducted by Marie Stephenson (grade 3 teacher) and Janet D'Silva (Student Work Study Teacher).
@PDSBSWSTs. @janetdsilva
Email: Janet.dsilva@peelsb.com
Location: Peel District School Board