Effective Mental Computation

Whereas KCM Community members are passionate about helping teachers and students develop number knowledge, this page is a place to post and consider challenges encountered while working to influence practice for assessment and advancement of mathematical fluency (defined by the Kentucky Committee for Mathematics Achievement as: “a deep understanding of mathematical concepts, which results in facility to efficiently and accurately access, compare, and apply strategies, knowledge, and skills”). KCM Community members are encouraged to reply or add to the topics shown here. We hope you will find these community reflections and resources supportive of your important leadership activities for improving mathematics education beyond your own classroom.

Effective Mental Computation

Everyone agrees that students need to learn basic facts, but sometimes that learning is shallow and does not support students' ability to reason quantitatively. Consider with colleagues best practice for assessment and instruction to support students in prolonged learning experiences over several years leading to the development of profound understanding of and skill with number operations. Below are some readings and a video that can further the conversation. Please feel free to reply with additional comments and resources.

For questions 1 and 2, see the Common Core Progressions for Counting and Cardinality and Operations and Algebraic Thinking:
http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf.

1) Page 6 of the Common Core Progressions document above shows the trajectory for, "Methods used for solving single-digit addition and subtraction problems," culminating with "Level 3. Convert to an Easier Problem. Decompose an addend and compose a part with another addend."
Discuss with colleagues why you think these methods are suggested instead of memorizing basic facts. And, consider how converting, decomposing and composing can internalize the understanding and application of arithmetic properties, essential for later algebraic reasoning.

Talk with colleagues about how to best ensure students develop fluency so they know basic facts and can successfully strategize, decompose and compose number.

3) View this ten-minute video in which Professor Alistair McIntosh, Honorary Research Associate, University of Tasmania, reflects on the importance of and suggestions for developing in our students the ability to effectively compute mentally. http://www.nlnw.nsw.edu.au/videos10/7583_2010_mcintosh/vid7583.htm. Discuss with colleagues how your school does or does not support the development of mental computation.
Alice Gabbard

Posts: 341
Joined: Wed Feb 27, 2008 4:26 pm
Location: Highland Heights, KY

Re: Effective Mental Computation

Want to know more?

Here is a five-page handout with a nice summary of important considerations for mental estimation, facts about mental calculation, principles of instruction, mental computation and written algorithms, and mental calculation and calculators:

See Valuing Mental Computation Online--defining mental computation, reasons to teach it and how to teach it:
http://www.curriculumsupport.education.nsw.gov.au/vmco/index.html
Alice Gabbard

Posts: 341
Joined: Wed Feb 27, 2008 4:26 pm
Location: Highland Heights, KY

Re: Effective Mental Computation

Alice Gabbard

Posts: 341
Joined: Wed Feb 27, 2008 4:26 pm
Location: Highland Heights, KY

Re: Effective Mental Computation

Enjoyed reading the article that Belle found. I have shared it with some teachers in my building and we discussed it during a PLC meeting. A real eye opener to some teachers.
jbingham

Posts: 60
Joined: Fri Aug 22, 2008 4:06 pm
Location: Central Elem., Barbourville, KY 40906

Re: Effective Mental Computation

The empty number line was the topic of our latest PLC/PD training. It is being used with great success by our 3rd graders. Most teachers have made a conscious effort to encourage students to find their own methods of solving problems. Most of their strategies are very efficient.
Angela Miller

Posts: 7
Joined: Fri Aug 22, 2008 3:44 pm