Mathematical thinking tasks
See also: building-a-thinking-classroom, teaching-mathematics
Resources:
Liljedahl (2020)'s variation? on rich-mathematical-tasks
Thinking tasks create conditions where students:
- get stuck;
- experiment;
- might fail;
- apply knowledge in new ways (non-routine tasks)
- engage in a cross section of mathematics (or other curricular thinking)
Such tasks should have
- Highly engaging problems
- and low-floor-high-ceiling-wide-walls
Implementation and other types of task#
Liljedahl (2020) describes three types of lesson type
| Lesson type | Description |
|---|---|
| 1. Non-curricular | Highly engaging thinking tasks, card tricks, and numeracy tasks are used without concern for curriculum. Echoing: inquiry-learning, rich-mathematical-tasks etc |
| 2. Scripted curricular tasks | Curricular tasks are turned into problems, which are posed to students as building on previous work, but requiring additional learning. Echoing productive-failure |
| 3. As-is curricular tasks | Standard direct or explicit-teaching of routines directly linked to curriculum goals. An approach that tends to promote "mimicking, not thinking" (p. 26) |
Research suggests that students are more successful with the following sequence.
- Start with three to five thinking tasks (lessons?) - non-curricular
- Then shift to scripted curricular tasks
But both task types use a common process - teacher poses either task as a challenge
References#
Liljedahl, P. (2020). Pulling the 14 practices together to build a thinking classroom. In Building thinking classrooms in mathematics, grades k-12: 14 teaching practices to enhance learning. Corwin Press.