Often parents and teachers aren’t clear about what students of math should know and understand. Well the National Academies has put together a concise synthesis of almost-current research that helps to I understand the ‘what’ and ‘why’ of K-12 mathematics education. And, you can download a copy free at the link below.
Adding It Up: Helping Children Learn Mathematics
Jeremy Kilpatrick, Jane Swafford, Bradford Findell, Editors; Mathematics Learning Study Committee, National Research Council
ISBN: 0-309-50524-0, 480 pages, 7 x 10, (2001)
This PDF is available from the National Academies Press at:
The Committee reviewed and synthesized relevant research on mathematics learning from pre-kindergarten through grade 8.
Mathematical proficiency, as we see it, has five strands:
•conceptual understanding—comprehension of mathematical concepts, operations, and relations
•procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
•strategic competence—ability to formulate, represent, and solve mathematical problems •adaptive reasoning—capacity for logical thought, reflection, explanation, and justification
•productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
(Exec. Summary p. 5)
Students need to learn to make and interpret measurements and to engage in geometric reasoning. They also need to gather, describe, analyze, and interpret data and to use elementary concepts from probability. Instruction that emphasizes more than a single strand of proficiency has been shown to enhance students’ learning about space and measure and shows considerable promise for helping students learn about data and chance.
(Exec. Summary p. 8)