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.

2) From page 18 and 19 of the Common Core Progressions document above: "The word fluent is used in the Standards to mean “fast and accurate.” Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies. It is important to push sensitively and encouragingly toward fluency of the designated numbers at each grade level, recognizing that fluency will be a mixture of these kinds of thinking which may differ across students. The extensive work relating addition and subtraction means that subtraction can frequently be solved by thinking of the related addition, especially for smaller numbers. It is also important that these patterns, strategies and decompositions still be available in Grade 3 for use in multiplying and dividing and in distinguishing adding and subtracting from multiplying and dividing. So the important press toward fluency should also allow students to fall back on earlier strategies when needed. By the end of the K–2 grade span, students have sufficient experience with addition and subtraction to know single-digit sums from memory; as should be clear from the foregoing, this is not a matter of instilling facts divorced from their meanings, but rather as an outcome of a multi-year process that heavily involves the interplay of practice and 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.