Embedded Files
Anticipating
Anticipating students’ solutions to a mathematics taskMonitoring students’ in-class work on the taskSelecting student strategies and students to share themSequencing students’ solutions purposefullyConnecting students’ approaches & the underlying math
Anticipating students' solutions to a math task.
Anticipating students' solutions to a math task.
What different strategies may students use to solve or work on this problem?
What mathematical thinking might emerge?
Which representations might students use?
This requires much more than deciding if the task is at the right level of difficulty or interest for the students or if students can show the "right" answer. Anticipating students' responses with an array of strategies (both correct and incorrect) and how students may be working with strategies within key ideas or mathematical concepts that they are learning will prepare the educator in being able to respond effectively as they work and in a meaningful consolidation.
Brainstorm the approaches that students might use as they work on the task, considering both correct and incorrect ideas.
- Educators might work individually or collaboratively to anticipate solutions
- Research may be useful to identify common misconceptions (e.g. Marian Small)
- Educators can analyze samples of student work from previous years
Consider what actions you will take when a student uses a particular approach. For example, what questions will be asked to elicit student thinking? How can you move the student's thinking forward without giving away the solution to the problem?
A Grade 4 class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?
A Grade 4 class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?
What might a student in grade 4 do? How may the multiplicative relationship between the quantities be worked out?
For our example above, if you are working in a group, please share some of the ways of solving or working through the problem. Discuss the following:
- What strategies and what misconceptions are you thinking about?
- Why might it be a good idea for teachers to first try the math problems themselves?
- What insights do you think could be gained from this process?
- What strategies may students use? Which are more efficient?
- What manipulatives might those gr. 4 students use? What models might be supportive?
Report abuse