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| Standards of Mathematical Practice |
I'm intrigued by the way that big ideas and overarching practices are woven into learning design. As I look at the charts above and think about the Math/STEAM program I'll teach next year, I wonder how I will integrate these skills, standards, and concepts.
Overall the practices lead us to inspire and develop inquisitive students who explore their world in logical, reasonable ways. We give students the opportunity to develop a keen, creative, and critical lens for looking at, interpreting, and interacting with the world. Helping students to see and interact with their world in this way creates both practical and creative thinkers--people who are confident and proactive about traversing their environment with understanding, problem solving skills, and intuition.
I've come up with a host of questions that will lead students' thinking and study in this regard. What would you add? How do you plan to embed the math and science practices, standards, and crosscutting concepts into your teaching/learning efforts next year and in the years to come?
Practices/Standards
- What is your question?
- Can you specify, identify, define, or describe the problem to me?
- What patterns, regularity, process, and structure do we notice in this situation?
- How can we create and conduct a process or investigation to gain understanding and/or solve a problem? What regularity, patterns, processes, and structure can we use to investigate, understand, and solve?
- How do you plan to persevere to solve this problem? What steps will you take?
- What tools and other resources will help us to solve this problem and/or answer this question?
- How can we use the tools and resources appropriately and strategically?
- Can you create a model of that to explain your thinking or what's happening?
- How can we use the model to simplify the problem in order to reason abstractly and/or quantitatively about what is happening or has happened?
- Are we able to determine a relationship(s) in this situation? How can we define that relationship
- What specific mathematics will help us to understand, prove, or present this better?
- How can we explain this in a step-by-step, logical, and explicit manner?
- Can we come up with a number of solutions to this problem, and then choose one that we think will be the best?
- How would you defend your idea in this situation?
- How can you critique the ideas of others?
- Is our thinking, process, efforts, and result precise? Did we check our work by our selves and with others?
- What is the best way to communicate these ideas, facts, and/or information to others? How can we help others to understand?
- Is our thinking reasonable? Why or why not?
Crosscutting Concepts
- What patterns do you see?
- How would you define your daily, weekly patterns?
- What caused this? What led up to this situation? What was the effect?
- What is the scale? How often does that happen? What are the actual statistics? Are we talking one, ten, a hundred, or a million? Is this a rare occurrence or an every day event?
- Where did the energy (ability to do work) come from? What obstacles slowed energy down, and what created more energy?
- Is the matter a liquid, solid, or gas? What properties define matter? How does the matter look and feel? How does the matter behave? How can we manipulate the matter?
- How is it structured? Does the structure lend itself to the results we're looking for? Can we change structure (form) to impact its function in more useful, efficient, beautiful, or desired ways?
- What is mostly stable in your life? What changes frequently? In nature, what can we typically expect? What changes happen over a long period of time; what changes often; and what kinds of unexpected changes occur?
- How would you compare the size, frequency, distance, or other measurements? What is the proportion? How often did this happen? How many? (quantity)
- Where does this lie in the system? How does the system work? What are the system parts and how do they work together to form an efficient, effective system? What system will you create?
