The Common Core State Standards (CCSS) include eight “Mathematical Practices” that teachers and students are encouraged to use throughout their mathematical lives. These are different from the grade-level content standards in a few ways. Firstly, these Mathematical Practices are not grade-specific. Rather, they remain constant practices throughout the child’s education, with the hopes that they become habit. Further, as the words practice and habit imply, these are not mathematical procedures or rules, but are more akin to mindsets and broad strategies.
For a broad look at all eight Math Practices, check out the post What Are the Math Practices and What Do They Have to Do With Me? For a deeper dive into the other seven practices, check out the list at the bottom of this post.
The eight practice, Look for and express regularity in repeated reasoning, has students begin to abstract (observe and describe general patterns) from repeated mathematical actions.
We see in this standard, as in so many others, that the ideas overlap a lot with the other standards. This idea of repeated reasoning has already come up as pattern recognition in Standard 7 and repetitive practice to experience advantages and disadvantages of tools in Standard 5 and models in Standard 4, among others. We see the idea of abstracting these repeated observations in Standard 2. What Standard 8 adds to this discussion is the idea of moving a subconscious learning to a conscious recognition of the patterns with the ability to describe and abstract (observe and describe in general terms) that repetition.
This post was originally published at mathteacherbarbie.com. If you are viewing it somewhere else, you are viewing a stolen copy.
Repetition in early childhood
The good news is: you’ve been building this with your child since they were very young!
Though the statement of this standard gives examples starting in upper-elementary, I propose this activity starts as early as toddlerhood and preschool. We typically teach children to count by reapeating the number words of our native language (one…two…three… etc in English) while showing images or pointing/touching/moving items. The repetition here is the counting words and assigning each word to a different object. The objects themselves change, as does the location and context where we do the counting. Because the words and the act of assigning are the repetitive parts, children develop the idea of oneness, twoness, threeness, etc. They also begin to associate the final counting word as the “how many” of the group. As with so very much learning in early childhood, it is the repetition that is important in the learning.
How do parents support repetitive reasoning in early childhood?
In general, this comes absolutely, frustratingly, naturally to very young children. Indulge your child in doing same things over and over. They’re learning something new out of it each time. Make minor changes or vary the conversation slightly each time, both to develop their abstract reasoning as well as to maintain your own sanity.
Middle Elementary: Describing Repetition
Though they’ve been observing repetition throughout their lives, it’s middle elementary when teachers really begin expecting students to describe that repetition. Multiplication is many things, among them multiplication is repeated addition and students are expected to internalize this idea of multiplication around this time. Their math worksheets and number corners have been asking them to observe patterns since kindergarten, and in middle elementary the students begin to be expected to do this independently of their peers and make their own pattern observations and descriptions. This is where the rubber meets the road, if you will, in this practice.
How do parents support repetitive reasoning in middle elementary?
Children at this age tend to have a black-and-white, right-or-wrong, scientific, and less nuanced view of the world. It’s a great age for exploring ideas in the style of a science experiment. Questions such as “what would happen if we changed [this one small piece]” are great for brainstorming these kinds of explorations. (If you read any type of fan fiction, this is the “one thread pulled” style of fanfic writing, where just one element of the setting, plot, or characters is changed and the author explores what would happen as a result.) It’s extremely important at this age to keep working on those multiplication tables as well, which can fit right in with this standard. Modern research encourages learning these in ways that support the repeated reasoning and abstraction of multiplication facts rather than the “old-school” memorization such as static flashcards provide. My article How to Learn Multiplication Facts: A Roundup gives a lot of ideas that can help your student learn in this way and encourage developing these repetitive reasoning and abstraction skills at the same time.
Pre-Algebra and Algebra: The study of abstraction
As students move into the upper elementary and secondary years, they face pre-algebra and algebra. At its core, algebra IS the process of abstracting and describing patterns in numbers. Every single part of algebra I can think of as I write this is either
- writing and describing patterns that numbers follow, or
- using those descriptions to explore and discover new patterns
Thus the eighth mathematical practice is built in and at the core of this, as well as any future, stage of math learning.
Partly because of the way these subjects are taught, and partly just because it’s very often hard to see the bigger picture when one is stuck in the weeds, it can be very difficult to see this aspect of algebra and higher level math. However, if you can trust that this truly is both the point and nature of algebra, you’ll catch those glimpses of the larger picture and gain a greater appreciation of the purpose, if not the procedures.
How do parents support repetitive reasoning in secondary school?
Because of the nature of the subject, simply supporting your child as best you can through these math years is enough. It can be discouraging to be lost among the weeds and lose sight of this bigger picture. However, this is where the perseverance of Standard 1 comes in. Dig deep for the motivation that will get you and your student through these weeds and out the other side where you can both look back and see what you just came through.
You’ve Got This!
For a deeper dive into all eight practices, check out the following posts:
MP1: Sense Making and Perseverence
MP2: Abstract and Quantitative Reasoning
MP3: Constructing and Critiquing Arguments
