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Expanding the TE in STEM Dave Burghardt Mike Hacker Hofstra University

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General Theme for 20 years is Interconnected STEM Interconnected STEM Learning--Content and Pedagogical Challenges The Double E--Using Engineering Design as a Pedagogical Strategy

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Interconnected STEM Learning MSTP--Math infusion in middle school science and engr/technology to improve student learning in mathematics Math Contextualized STEM Learning Communities

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MSTP STEM Learning Communities STEM University Faculty with middle school disciplinary teachers and an administrator. Lesson Plan development, implementation, and critique with student work.

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Proof of Concept Studies Engr/Tech Education (ETE) Enhanced math in existing lesson, Bedroom Design. 20 day lesson with virtual and physical modeling. Fall 2008 15 math infusion ETE teachers (500 students) 15 comparison teachers (300 students) Spring 2009 National sample. 20 math infusion Engr/Tech teachers (600 students)

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Proof of Concept Studies--Findings Results from science and engineering-technology education were similar Mathematical Content Knowledge Analyses of covariance revealed infusion students scored statistically significantly higher than comparison students on relevant content knowledge Greatest difference on students in bottom one- third of classes

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Proof of Concept Studies--Findings Attitudinal Differences Statistically positive differences between infusion and comparison students’ post scores dealing with enjoyment of math during science, interest in math, math not being a waste of time, and math not being boring.

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MSTP--What was Learned Math Infusion is possible within the regular school day Students recognize value of math for science and engr/technology Students are better able to solve math problems that are relevant to the science and engr/technolgy content they are learning

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MSTP--What was Learned Science and ETE teachers who infuse math in their lessons Report an increase in student engagement in math Find the math helped their content teaching At times, struggled teaching infused math concepts.

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Why Engineering/Technology Education? To think like an Engineer requires OPTIMISM CREATIVITY And other Habits of Mind, but these two provide insights as to why design pedagogy can be so powerful in engaging children in learning.

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K12 Engineering—Study of the Human-Made World Engineering Design ◦ Optimization/Trade-offs ◦ No Unique Solutions—focus on the process, searching for optimal solutions ◦ Modeling

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Engineering Design

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Informed Design Design under constraint with specifications and challenges No Gadgeteering, knowledge based, hence a connection to STEM content knowledge Influenced by Wiggins and McTigue, Understanding by Design Inherently Constructivist Project-based Learning

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Drying by Design Design, construct and test a dehydrator to efficiently dry fruit. The instructor will decide the dehydrating time. The dehydrator with the highest efficiency will be viewed the optimal design. efficiency = (initial weight – final weight)/time Drying area can be no greater than 196 square inches All slices must be from a single apple with the exception of end slices and core, before another apple can be used.

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Drying by Design--Math Analysis Imagine an apple— Think of it as a 3 inch sphere. Slice it! What is the total area of the slices? Apple weight over time is non-linear-- extrapolation of non-linear data.

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Why Engineering Design is an Effective Instructional Strategy Integrates Learning Pluralistic Thinking (e.g. visual, kinetic) Student Controlled Reflective Innovative The focus is on the process of learning, not the product!

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MSTP Bedroom Design Hybrid modeling ◦ Virtual and Physical Modeling Use of Google Sketch-Up Math includes area, perimeter, percent and ratio Physical modeling can be completed in computer lab or classroom.

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Hybrid Modeling Integrates screen-based 3-D simulation and real- world physical modeling

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Bedroom Design Challenge You are moving into a new home. You and your team mates have a challenge to design an optimally furnished bedroom. You have a budget of $27,500 to design it with as a rectangular bedroom with minimum dimensions of 120 square feet. However, if you wish to be really creative and design a non-rectangular bedroom of 120 square feet minimum, the budget increases to $30,000. You will construct virtual and actual scale models of your bedroom, with furnishings.

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Infusing Core Disciplinary Concepts into Bedroom Design Knowledge and Skill Builder 1: Geometric Shapes Knowledge and Skill Builder 2: Ratio and Proportion Knowledge and Skill Builder 3: Creating and Folding Nets Knowledge and Skill Builder 4. Aesthetics Knowledge and Skill Builder 5. Pricing Information: Creating Formulas in Spread Sheets

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KSB--Geometric Shapes It is important to understand different geometric shapes so you can use them in your design. In this KSB you will draw different geometric shapes and determine their areas and perimeters. Using 24 square tiles, arrange them to make rectangles that have an area of 24 square units and have whole number dimensions. Then draw them on the grid provided. Length in units Width in unitsArea in square units Perimeter in units

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KSB--Geometric Shapes 1. From a math perspective, what are the factors of 24? Indicate next to each figure its perimeter. (Show the whole numbers used for the dimensions.) 2. How do you know you have found all rectangles meeting the requirements ? 3. What is the relationship between a rectangle’s dimensions and its area? 4. What is the relationship between a rectangle’s dimensions and perimeter? 5. Which rectangle with an area of 24 square units has the greatest perimeter. 6. Which rectangle with an area of 24 square units has the least perimeter. 7. How can the cost of wall construction and wall covering be minimized?

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Math Infusion - Challenges Teacher Content and Pedagogical Content Knowledge Assessment Questions (did they really assess the infused math?) Scoring Rubric for open-ended questions Consistency of the teaching the bedroom design unit between teachers

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This is all about Expanding the TE in S TE M

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Shift Happens We are currently preparing students for jobs and technologies that don ’ t yet exist ….in order to solve problems we don ’ t even know are problems yet. “ We can ’ t solve problems by using the same kind of thinking we used when we created them. ” (Albert Einstein)

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The ETE Journey Continues… Thank You! Dave Burghardt Mike Hacker m.d.burghardt@hofstra.edu m.hacker@nycap.rr.com www.hofstra.edu/CTL

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