Bridging STEM with

Mathematical Habits of Mind

MENA STEM SummitApril | 2016

Dr. Cory A. Bennett, Director

Albion Center for Education Innovation

benncor3@isu.edu

What is Mathematics?

1. What is mathematics?

2. Where is mathematics—where do we find it?

(be SPECIFIC on this one!!)

Math is Everywhere

Optimizing “Mathed” Potatoes

Mathematical Thinking & Habits of Mind

“Mathematical thinking is more than being able to do arithmetic or solve algebra problems. In fact, it is possible to think like a mathematician and do fairly poorly when it comes to balancing your checkbook.”

“Mathematical thinking is a whole way of looking at things, of stripping them down to their numerical, structural, or logical essentials, and of analyzing the underlying patterns. Moreover, it involves adopting the identity of a mathematical thinker.”

~Dr. Keith Devlin, Stanford University

Pirate’s Chest

You discover a secret cave with a three pirate chests; they are labeled Gold, Iron, and Mix. Just as you are approaching the chests the pirate finds you and says that if you can find the chest with the gold he will let you go otherwise you will walk the plank but he warns you that all of the labels are wrong. To give you a chance he will show you one piece from one chest.

Which chest will you choose to see a piece from and which one has the gold in it?

Bridging STEM

Practices in Mathematics, Science, and English Language Arts*Math Science English Language Arts

M1. Make sense of problems and persevere in solving them.

M2. Reason abstractly and quantitatively.

M3. Construct viable arguments and critique the reasoning of others.

M4. Model with mathematics.

M5. Use appropriate tools strategically.

M6. Attend to precision.

M7. Look for and make use of structure.

M8. Look for and express regularity in repeated reasoning.

S1. Asking questions (for science) and defining problems (for engineering).

S2. Developing and using models.

S3. Planning and carrying out investigations.

S4. Analyzing and interpreting data.

S5. Using mathematics, information and computer technology, and computational thinking.

S6. Constructing explanations (for science) and designing solutions (for engineering).

S7. Engaging in argument from evidence.

S8. Obtaining, evaluating, and communicating information.

E1. They demonstrate independence.

E2. They build strong content knowledge.

E3. They respond to the varying demands of audience, task, purpose, and discipline.

E4. They comprehend as well as critique.

E5. They value evidence.

E6. They use technology and digital media strategically and capably.

E7. They come to understanding other perspectives and cultures.

* The Common Core English Language Arts uses the term “student capacities” rather than the term “practices” used in Common Core Mathematics and the Next Generation Science Standards.

Practices in Math, Science, and ELA*

Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

8 Mathematical Practices

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated

reasoning

Science & Engineering Standards1. Asking questions (for science)

and defining problems (for engineering)

2. Developing and using models

3. Planning and carrying out investigations

4. Analyzing and interpreting data

5. Using mathematics and computational thinking

6. Constructing explanations (for science)

and designing solutions (for engineering)

7. Engaging in argument from evidence

8. Obtaining, evaluating, and communicating information

Pirate’s Chest

You discover a secret cave with a three pirate chests; they are labeled Gold, Iron, and Mix. Just as you are approaching the chests the pirate finds you and says that if you can find the chest with the gold he will let you go otherwise you will walk the plank but he warns you that all of the labels are wrong. To give you a chance he will show you one piece from one chest.

Which chest will you choose to see a piece from and which one has the gold in it?

Rethinking “Integration”

Bennett, C. A. & Ruchti, W. (2014). Bridging STEM with mathematical practices. Journal of STEM Teacher Education, 49(1), 17-28.

Make Sense of Problems and Persevere in Solving Them

• Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Make Sense of Problems and Persevere in Solving Them

• [STEM] proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

Ship a Chip

You notice that an open package of Pringles chips that appears to have a bacteria growing on it. You want to test it and decide to send it to a laboratory. However, the laboratory asks that you ship just one Pringle chip. How do you plan to do this in the most effective manner?

Which maths practices will be evident in this task?

What would you expect students to do in developing a solution to this problem? What would you see and/or hear?

How can we understand Earth on a global scale?

Does the Sun heat fairly?

“Which of these materials—pebbles, white sand, or black dirt—will absorb the most heat from the sun?”NCTM. (2005). Mission mathematics II grades 3-5: Linking aerospace and the NCTM standards. Reston, VA: NCTM.

Which maths practices will be evident in this task?

What would you expect students to do in developing a solution to this problem? What would you see and/or hear?

Rethinking Integration• What actions on teachers’ part is needed to

promote mathematical (and STEM) thinking in the classroom?

• What actions are needed school-wide to support teachers in their actions?

• What will mathematical (and STEM) thinking classroom look and sound like?

• What is one action you can take at the beginning of the year to make this kind of classroom come alive?

So…

• Focus on the Mathematical Practices

– Habits of mind that bridge STEM

• Choose a couple to (initially) develop deeply

• But take action! (Time is not on our side).

Reflection and Next Steps

What might you do differently for the next year?what can you do now to start this work?what will be developed over the year?With whom do you need to collaborate to make this happen?

How can you support more authentic STEM in your school & community?

How else can we help develop students mathematical understandings of science and engineering?

Dr. Cory A. Bennett

Albion Center for Education Innovation DirectorIdaho Regional Mathematics Center DirectorAssociate Professor, Mathematics EducationNBCT Mathematics, Early Adolescence

Email: benncor3@isu.edu

@AlohaCory

Albion Center for Education Innovationwww.ed.isu.edu/icee

Bridging STEM with

Mathematical Habits of Mind