#MondayMathBite: The Case for Praising Perseverance
Wow! Over 2,000 readers on last week's blog, and countless meaningful discussions started both face-to-face and on Facebook tell me that I'm on the right track with my #MondayMathBite! For the next few weeks, I am going to focus on the Standards for Mathematical Practice (SMP). The what!? you say? Read on.
There are two types of math standards in the Common Core State Standards for Mathematics: Content Standards and the Standards for Math Practice. The content standards vary by grade level and conceptual category. They describe what students should know, understand, and be able to do at a particular grade level. These are the kind of standards we are familiar with from our previous state standards. In my experience, a teacher knows the content standards for his/her grade level inside and out... it's what defines their world as a 1st grade teacher or 8th grade teacher. An example of a content standard would be for students to understand a fraction as a number on the number line, [and] represent fractions on a number line diagram (3.NF.A.2), which is specific to 3rd grade. The Standards for Math Practice, however, are common to all grade levels, K-12. There are eight SMPs that "describe varieties of expertise that mathematics educators at all levels should seek to develop in their students" (corestandards.org). They capture mathematical processes and "habits of mind" and thinking skills specific to math. Here are the eight Standards for Mathematical Practice:
This week I want to focus on SMP 1: Make sense of problems and persevere in solving them, and I want to try to start a grassroots movement to start praising perseverance. All of the SMPs begin with, "Mathematically proficient students...", and that is the goal: for all students to be mathematically proficient. To be proficient, students must be able to "explain to themselves the meaning of a problem and look for entry points to its solution". In our technology infused world, instant gratification has taken on a whole new meaning. Students have answers to literally everything at their fingertips at all times. Even my almost-5 year old knows that an answer is just a click away... but it's not always about the answer.
There are two types of math standards in the Common Core State Standards for Mathematics: Content Standards and the Standards for Math Practice. The content standards vary by grade level and conceptual category. They describe what students should know, understand, and be able to do at a particular grade level. These are the kind of standards we are familiar with from our previous state standards. In my experience, a teacher knows the content standards for his/her grade level inside and out... it's what defines their world as a 1st grade teacher or 8th grade teacher. An example of a content standard would be for students to understand a fraction as a number on the number line, [and] represent fractions on a number line diagram (3.NF.A.2), which is specific to 3rd grade. The Standards for Math Practice, however, are common to all grade levels, K-12. There are eight SMPs that "describe varieties of expertise that mathematics educators at all levels should seek to develop in their students" (corestandards.org). They capture mathematical processes and "habits of mind" and thinking skills specific to math. Here are the eight Standards for Mathematical Practice:
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| from http://www.bitingintothecore.com/ |
Embedded in our mathematics instruction, we want to foster students' ability to analyze problems, make conjectures (hypotheses) and connections, and answer the very simple but very important question, "Does this make sense?" The language of the SMPs is complex, and to really get into the nitty gritty of them you'll need a glass of wine or two, but for me, SMP 1 comes down to the adages "Always look before you leap," and "If at first you don't succeed, try, try again." These two ideas attend to our entire student population, from the ones that jump in with both feet before you've even finished giving directions or posing the question, to the ones that have struggled for so long in mathematics, that they give up before they even begin. Both "types" of students (and notice that I am deliberately not using the fixed ability terms "high" and "low") are going to have to persevere, and as teachers, we must promote and praise this effort... because it IS effort! When one way doesn't work, students must be motivated to seek another way, and the power of the math is in the path that they take to arrive at a conclusion, not in the conclusion itself.
Teachers and parents can develop mathematical thinking in their kiddos by asking questions like:
- How would you describe the problem in your own words?
- What do you notice about...?
- What information is given in the problem?
- Describe the relationship between the quantities.
- Describe what you've already tried. What might you change?
- What steps in the process are you most confident about?
- What are some other problems that are similar to this one?
- How else might you organize... represent... show...?
Embedded in this questioning is the academic language that we are trying to build in students. In addition to asking these language rich problems, I would suggest giving sentence stems to guide students' responses... "I notice...", "I've already tried...", "This reminds me of...", "Another way to think of this would be..."
While students are processing and grappling (struggling has such a negative connotation... let's say grappling), teachers and parents can acknowledge their perseverance by saying things like, "I really like the way you are not giving up", or "Wow, way to stick to it!" When they're on the right track, we can give them encouragement with a simple, "Your effort is paying off!" or if they're grappling and reaching a point of frustration, a reminder to "Look how far you've come!" Let's not kid ourselves - there will be resistance, from students as well as parents. Most of us are not used to explaining our thinking or thinking of problems in more than one way... in the past, getting an answer has been "good enough" for most of us, but I don't buy the "my boss doesn't care how I solved the problem as long as I solved it" argument against this new level of rigor. Learning is based on growth, and growth can not happen unless new strategies are accessed and attempted. We learn from others, and I promise that even the kid in the class who "gets it" without a whole lot of cognitive demand can learn from other students who think a different way.
At the heart of the Standards for Mathematical Practice is the need for building a classroom culture where "sharing your knowledge" is safe, and chances are always given for students to "revise their thinking" as the task evolves. After all, as adults, we revise our thinking continuously as we receive new information, so why wouldn't we afford our students the same courtesy? These questions, while seemingly specific to mathematics, can be easily applied to everyday tasks. Cooking, cleaning, playing with legos, etc; I challenge you to get through a day where you don't have to make sense of a problem and persevere in solving it. Let's get our kids thinking! SMP 1 is just the beginning. And remember...
While students are processing and grappling (struggling has such a negative connotation... let's say grappling), teachers and parents can acknowledge their perseverance by saying things like, "I really like the way you are not giving up", or "Wow, way to stick to it!" When they're on the right track, we can give them encouragement with a simple, "Your effort is paying off!" or if they're grappling and reaching a point of frustration, a reminder to "Look how far you've come!" Let's not kid ourselves - there will be resistance, from students as well as parents. Most of us are not used to explaining our thinking or thinking of problems in more than one way... in the past, getting an answer has been "good enough" for most of us, but I don't buy the "my boss doesn't care how I solved the problem as long as I solved it" argument against this new level of rigor. Learning is based on growth, and growth can not happen unless new strategies are accessed and attempted. We learn from others, and I promise that even the kid in the class who "gets it" without a whole lot of cognitive demand can learn from other students who think a different way.
At the heart of the Standards for Mathematical Practice is the need for building a classroom culture where "sharing your knowledge" is safe, and chances are always given for students to "revise their thinking" as the task evolves. After all, as adults, we revise our thinking continuously as we receive new information, so why wouldn't we afford our students the same courtesy? These questions, while seemingly specific to mathematics, can be easily applied to everyday tasks. Cooking, cleaning, playing with legos, etc; I challenge you to get through a day where you don't have to make sense of a problem and persevere in solving it. Let's get our kids thinking! SMP 1 is just the beginning. And remember...
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