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Watch
Building Blocks towards Computational Fluency
Discuss
- How would you define computational fluency?
- What resonated with you from Craig's description of computational fluency? What would you add or adjust?
- How might you have seen the building block image (discussed in the video) reflected in your experiences with students?
Record your thinking Section 2.2a of your digital handout.
Watch
Task
Consider the following developmental flow of efficiency with basic facts.
The "Flow" of Basic Facts
Direct Modelling and Counting
Students can model the facts directly by using fingers or objects to count to determine the answer.
Counting More Efficiently and Tracking
Students can use strategies like counting on and use objects and tools to keep track of counts rather than to represent the problem.
Working with Numbers Alone
Students can split numbers flexibly and rearrange the parts to create 'easier' numbers to work with.
Automatic Retrieval
Students can recall any number facts (and number to 20) within 1 or 2 seconds.
Discuss
- Where in your own teaching practice, have you seen this "flow" in action?
- What challenges have emerged for you as you've moved from one stage to the next?
- What strategies, games or tasks have you used to develop basic facts to 20?
Read the section in A Guide to Effective Instruction in Mathematics K-6, Vol 5: Teaching Basic Facts and Multidigit Computations, pages 17-20) where it provides strong advice around such topics as: worksheets, flash cards, timed tests and models to build understanding.
- In what ways might this advice differ from the way basic facts were practised when you were a young student?
- What do you see as some of the advantages of rethinking the way we help students acquire automaticity with basic facts?
Want to dig deeper?
To learn more about this flow, check out monograph, The Mathematical Territory Between Direct Modelling and Proficiency by Dr. Alex Lawson (Lakehead University).
Watch
Task
Students need to have quick recall (ie, automaticity) with their basic facts. This means that they will need time to consolidate their strategies through practice.
A Guide to Effective Instruction in Mathematics: K-6, Vol 5: Teaching Basic Facts and Multidigit Computations (pages 69-112) includes a number of strategy-based games and activities to build both understanding and fluency.
Browse through these pages and notice games and activities that you find promising. Also talk about any other ideas you've used to develop fluency with basic facts. Record your recommendations in Section 2.2b of your digital handout.
If you have access to a printer -- and have time -- you may want to print out the instructions for one game and its related materials and give it a try.
Discuss
The use of calculators can be a very contentious topic for many parents - and educators! - even though the use of calculators is encouraged throughout the Ontario Curriculum.
First, read this excerpt from the Ontario Mathematics Curriculum: Grades 1-8 that describes the role of calculators in classrooms.
Discuss:
- What are your thoughts on the use of calculators in the classroom?
- In what situations and for what learning goals could you see calculators being an important tool for promoting learning?
- What might you not have students use a calculator?
- How might distinguishing between operation sense and computations add a helpful nuance to conversations on this topic?
- How would you respond to a parent of colleague who had concerns about the use of calculators in math classrooms? Consider specific examples of tasks that would clarify your position and illustrate your point.
Record your thinking in Section 2.2c of your digital handout.
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