Powerful Mathematics Practices: Overview
Lesson Objective: Create a deep understanding of mathematics through powerful practices
All Grades / Math / SREB

Thought starters

  1. To what extent is a balanced approach to mathematics evident?
  2. To what extent do assignments advance mathematical reasoning with grade-level or above content?
  3. To what extent is questioning and feedback used to deepen student understanding?
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Transcripts

  • Powerful Mathematics Practices: Overview Transcript
    Speaker 1: Good morning, good morning. Please find your seats. The seating chart's up here.

    Powerful Mathematics Practices: Overview Transcript
    Speaker 1: Good morning, good morning. Please find your seats. The seating chart's up here.
    Speaker 2: All right. Good morning boys and girls.
    Speaker 1: Y'all ready? Okay. What I want you to do, on your white board is I want you to write me an example of [crosstalk 00:00:16]
    Speaker 3: SREB Powerful Mathematics Practices include five major indicators. Each indicator, when applied to planning, instruction and assessment, can ensure a mathematics classroom built on deep student understanding, rather than coverage of material. These indicators include: ensuring a balanced approach to mathematics, engaging students in assignments that matter, utilizing questioning and feedback for deeper understanding, using formative assessment data, and fostering a classroom environment that supports student ownership of learning.
    Speaker 3: Let's take a closer look at each of these.
    Speaker 2: In math, we know, we have to have some evidence for what we say.
    Speaker 3: A balanced approach to mathematics places emphasis on student understanding of mathematics facts and procedures, which are generated from applying mathematics to real world or non-routine scenarios.
    Speaker 2: Can we confirm or deny the author's claims?
    Speaker 3: Students not only have fluency with math procedures, but there is a confidence in selecting appropriate tools and strategies for a given situation.
    Speaker 4: The question is measure or estimate about 1500 hundred meters. What can you see from that distance? So you got to think about that far up there, we would be in an airplane. We could barely see houses like [crosstalk 00:01:32]
    Speaker 3: A balanced approach uses conceptual knowledge to build procedural fluency.
    Speaker 5: We should divide this by five, because it says that the eagle sees five times more, and if the eagle sees 1,500 meters, we should divide it by five.
    Speaker 2: Have y'all possibly researched how far or how high an eagle could fly?
    Speaker 5: Mr. Foster makes us use vocabulary, or the facts, to understand what he's asking in a problem, and apply it. We could see most things from 1,500 meters if we had eagle vision.
    Speaker 1: What are all of these a form of?
    Speaker 7: Perfect squares.
    Speaker 1: Perfect squares.
    Speaker 3: Selecting and framing quality assignments is the backbone of a powerful mathematics classroom.
    Speaker 1: Here's your pattern cards, and here is your polynomials that you're going to write with them.
    Speaker 3: Quality assignments require students to engage in problem solving and reasoning to complete.
    Speaker 8: M plus?
    Speaker 9: M plus one squared.
    Speaker 3: Students engaged in productive struggle should work collaboratively with one another while sharing and critiquing their reasoning and understanding of acquired mathematical concepts. Enactment of quality assignments places the students at the forefront of completing the task, with the teacher providing appropriate support. The mathematical purpose must be clear, and reflected upon frequently, as students complete complex assignments.
    Speaker 8: It would be M1, and there's two. When we first started, I was like, "Whoa, how are we supposed to solve this?" You know, but the whole thing was to build an understanding, and I think as we work on it more, and talk to each other more, we build [inaudible 00:03:13] Oh, I know what. Okay, so there's eight here. So, half of eight is four.
    Speaker 1: So, tell me how you illustrated that the angles were the same?
    Speaker 3: Teachers in powerful mathematics classrooms ask targeted questions that require students to analyze, synthesize, and predict in order to advance their sense-making for a deeper understanding of mathematical concepts.
    Speaker 1: Real quick, tell me why you moved that one.
    Speaker 3: They require all students to formulate and share responses to higher order questions.
    Speaker 1: Explain to me what your reasoning was for saying, "These two are similar."
    Speaker 3: Teacher feedback highlights student misunderstandings in a way that encourages thought and consideration by the student, rather than simply giving the answer.
    Speaker 10: I thought since those two were congruent, since that was the same one as that, that both of these would be 70, just like there, because that is the exact same triangle. Her coming around and not telling us the answer, not telling us yes or no, kind of helps. When she asks us questions, she pushes us to understand, and then she makes sure we understand, and it really helps.
    Speaker 1: Why are angles P and angle S congruent?
    Speaker 11: Because they're alternate interior angles.
    Speaker 1: Created by what kind of lines?
    Speaker 11: Parallel.
    Speaker 1: Parallel lines, and a, what do we call-
    Speaker 11: Transversal
    Speaker 1: Very good.
    Speaker 2: You can use one of these blank cards. What'd those cards do to match that?
    Speaker 3: The ability to adapt instruction minute to minute, and day by day, based on formative assessment information is a skill acquired by powerful mathematics teachers.
    Speaker 2: What could you do to check to see if that's right?
    Speaker 3: Effective use of formative assessment data includes the ability of the instructor to apply various formative assessment strategies throughout a lesson, identify and acknowledge misconceptions and student misunderstanding, and personalized teaching and learning to individual students by adjusting instruction.
    Speaker 2: As I was walking around, I heard some very interesting conversations. One thing that I noticed, is that most groups had an issue with card K. David, would you like to show what you had for card K?
    David: So, for K, every orange juice, there would be 1 1/3 fizzy juice. He wants us to show our answer, and if we don't actually write our answer down, he may think that we don't know it at all. So, he wants to know if we know it, or we don't, and if you're wrong, he'll know how to help you.
    Speaker 2: Can you explain a misconception that you had, and how David helped you out with that?
    Speaker 13: He wants to see everybody's answers, and he'll take people who had the same answer, and people who had different answers, and then he's gonna ask us why we did it.
    Speaker 2: Think about some misunderstandings that you had before, and then how those misunderstandings were cleared up based on what your classmate said.
    Speaker 13: I confer that this is similar.
    Speaker 3: Classrooms where student collaboration encompasses the sharing of ideas, justifying approaches, and critiquing others reasoning, result in more confident math students. These students take greater ownership of their own learning, as they are willing to take risks and persevere when presented with challenging assignments that require reasoning and problem solving.
    Speaker 13: I think it might not be determined.
    Speaker 14: Wait. It doesn't give you any information on this one, except for parallel lines. I don't necessarily want to say that it's similar, or-
    Speaker 13: Being in a team, asking each other steps and how this works out, and how to fix this, you persevere more with more people.
    Speaker 10: Two times two.
    Speaker 13: Would you distribute?
    Speaker 10: That's what I'm gonna go with right now. Being able to work with a partner also helps me understand it, and ask my partner, "What are you thinking? How did you come up with that, or find it?" It motivates me to continue. What we did for that, is we plugged what N equals for N [crosstalk 00:07:13]
    Speaker 3: As emphasis is placed on deeply understanding and implementing the concepts of ensuring a balanced approach to mathematics, engaging students in assignments that matter, utilizing questioning and feedback for deeper understanding, using formative assessment data, and fostering classroom environments that support student ownership of learning. Mathematical understanding and achievement by students will increase. SREB is committed to providing rich tools and professional development for schools and districts, committed to identifying, implementing, and enriching powerful mathematics practices.

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