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At an event during NCSM last week, Sue O’Connell, author of Putting the Practices Into Action, said, “Teachers have to truly understand the Standards for Mathematical Practice before they can move from theory only and into practice.”
June Mark, coauthor of Making Sense of Algebra, reinforced this by saying, “The ideas of the Standards for Mathematical Practice aren’t new, but getting them to work in all classrooms is.”
This has been the goal of the Standards for Mathematical Practice blog series: supporting true understanding and effective practice. Hopefully you have gained a clearer understanding of what each SMP communicates and how it can be woven into your instructional practice.
Consider some of the highlights from the series for understanding and bringing each Mathematical Practice into your classroom:
SMP 1: Make Sense of Problems and Persevere in Solving Them
“Pose problems that encourage perseverance…problems with multiple steps or with multiple answers. Discuss ways students may have gotten ‘stuck’ when solving a problem and how they got ‘unstuck.’ Praise patience, reflection, and perseverance.” —Sue O’Connell (@SueOConnellMath)
SMP 2: Reason Abstractly and Quantitatively
“How can we as teachers encourage the flexibility and generalized use of strategies so that students can reason abstractly and quantitatively? One way is to have students solve questions where the numbers are the same even though the situations suggest different thinking…The teacher can purposefully have students share strategies to solve the different problems and help the students make connections between the solutions.” —Pamela Weber Harris (@pwharris)
SMP 3: Construct Viable Arguments and Critique the Reasoning of Others
“A classroom culture that values critique rather than the one right way to get the one right answer is a culture in which students are far more actively engaged in their learning…In place of a single approach or justification, many approaches and justifications surface, thereby strengthening everyone’s learning.” —Steve Leinwand (@steve_leinwand)
“Students too often view what happens in the math classroom as completely removed from and irrelevant to the real world. Modeling bridges this gap and allows students to understand that situations occurring around them in daily life involve and require mathematics.” —Nancy Butler Wolf (@drnanbut)
SMP 5: Use Appropriate Tools Strategically
“We play a critical role in the development of strategic use of tools. First, we make tools available to our students. We encourage their strategic use. We model using them. We don’t admonish students who choose to use them. Instead, we ask them to share their reasoning for using a tool. We identify how tools connect to the ideas of mathematics.” —John SanGiovanni (@JohnSanGiovanni)
“Use familiar vocabulary to help specify which object(s) are being discussed—which number or symbol, which feature of a geometric object—using specific attributes, if necessary, to clarify meaning. Pointing at a rectangle from far away and saying, ‘No, no, that line, the long one, there,’ is less clear than saying ‘The vertical line on the right side of the rectangle.’” —June Mark, Paul Goldenberg, and Jane Kang (@EDCtweets)
SMP 7: Look for and Make Use of Structure
“Students do need to know arithmetic facts, but random-order fact drills rely on memory alone, where patterned practice can develop a sense for structure as well. Learning to add 9 to anything—not just to single digit numbers—by thinking of it as adding 10 and subtracting 1 can develop just as fast recall of the facts as random-order practice, but it also allows students quickly to generalize and add 19 or 29 to anything mentally.” —Paul Goldenberg, June Mark, and Jane Kang (@EDCtweets)
SMP 8: Look for and Express Regularity in Repeated Reasoning
“Sometimes being painstaking on the path to understanding or solving, putting in the effort even though it is hard, is necessary. But getting stuck doing the same inefficient methods every time is not what being a mathematician is all about either. We also want to look for efficient and elegant solutions. We want our methods to be powerful and generalizable. We want to use what we know and what we’ve done to become faster, more powerful problem solvers.” —Max Ray (@maxmathforum)
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SPECIAL OFFER: Read more from many of the authors who contributed to this series. From now until the end of 2015, use the promo code 8SMP15 at online checkout to take 30% off the list price of professional books by Sue O’Connell, Steve Leinwand, Pamela Weber Harris, Nancy Butler Wolf, John SanGiovanni, June Mark, Paul Goldenberg, Jane Kang, and Max Ray.
If you enjoyed the SMP series, come back each Monday for new math content. You can also check out Heinemann.com/Math to see more math resources from all our expert authors.
