Developing Mathematical Proficiency in Guided Math Groups
Mathematical Proficiency consists of 5 components or strands. The National Research Council published a report in 2001 called Adding It Up: Helping Children Learn Mathematics. In this report they define the 5 key components to learning math successfully as
1) Conceptual Understanding – Students with conceptual understanding know what they are doing on a conceptual level. They have knowledge and comprehension of the big ideas that they are exploring. So for example, David knows how to explain multiplication as 4 groups of 7. He also understands that if he skip counts by 7 four times he will get the answer. He can discuss the many different representations of multiplication.
2) Procedural Fluency –Students with procedural fluency are able to do the math (although sometimes they can do the math and not understand it at all). So for example, Stew can regroup but doesn’t understand place value, he only knows to “carry the one” as he mistakenly explains.
3) Strategic Competence – Students with strategic competence have flexibility with numbers. Sue can tell you that 8 +7 is a doubles plus one fact (7 +7+1) or a doubles minus one fact (8+8 -1). She has various ways of thinking about the numbers.
4) Adaptive Reasoning – Students with adaptive reasoning can think logically about the math and they can explain and justify what they are doing. So for example, students talk about math by saying things like “I know this is the answer because…” They ask questions like “How did you get that, because I got a different answer?” They can justify their answer with mathematical talk.
5) Professional Disposition – Students with a solid professional disposition know how to persevere when the going gets rough. They have a confident math outlook and know they are capable of doing the math, if they just keep trying. So for example, Tyrone might say, “This is the tricky part for me. I’m going to have to try it a different way.” He might also say, “Right now, it’s still fuzzy for me, keep explaining…”
When all 5 of these components work together, children become proficient in math. As noted in the report, “These strands are not independent; they represent different aspects of a complex whole. … the five strands are interwoven and interdependent in the development of proficiency in mathematics” (p.116) I am going to spend the next five posts writing about how we develop these in our students in small guided math groups. Guided math groups are the perfect setting to hone in on these 5 elements and help all children to become proficient mathematicians!