## Nano for Elementary and Middle School

### nano Model-Eliciting Activities (nano MEAs)

__nano Model-Eliciting Activities__

This page consists of links to activities that can be used to introduce middle school students to nanotechnology/nanoscience while reinforcing their mathematics skills. These MEAs (Model-Eliciting Activities) integrate science, technology, engineering and mathematics and are aligned with math and science standards.

These resources complement the MEA resources that have been developed for undergraduates. Users may find the MEA resources that have been developed for undergraduates may be helpful too.

__Nano-Roughness MEA__

The Nano-Roughness MEA is a model-eliciting activity that was originally developed for undergraduate students and then modified for use with middle school students. The middle school version of the MEA has been mapped to math and science standards and has been tested and researched in many classrooms to ensure that it is appropriate for middle school students. The Nano-Roughness MEA challenges students to define what roughness is on the nanoscale and then determine the roughness of sample materials based on data collected through an Atomic-Force Microscopy (AFM).

The materials for this MEA can be found here: http://docs.lib.purdue.edu/enewp/

The version of the MEA that was developed for college students can be found in the higher education section of nanoHUB. It is also further described by Zawojewski, Diefes-Dux, and Bowman (2008) throughout their book about mathematical models in engineering education. More content about the undergraduate version of this MEA can also be found on the following group page.

__Aluminum Bat MEA__

The Aluminum Bat MEA is a model-eliciting activity that was originally developed for undergraduate students and then modified for use with middle school students. The middle school version of the MEA has been mapped to math and science standards and has been tested and researched in many classrooms to ensure that it is appropriate for middle school students. In this MEA, students learn that engineers use the size of crystals to determine the strength of the material found in an aluminum bat. Students consider how to measure the average crystal size of aluminum crystal images of three different samples in order to determine which sample is the strongest.

More information about this MEA including the materials for this MEA can be found here: http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/2013/Vol18/Issue6/Model-Eliciting-Activities_-A-Home-Run/

Magiera, M. T. (2013). Model eliciting activities: A home run. *Mathematics Teaching in the Middle School*, *18*(6), 349-355.

The version of the MEA that was developed for college students can be found in the higher education section of nanoHUB. It is also further described by Diefes-Dux, Bowman, Zawojewski and Hjalmarson (2006) in their article in the Journal of STEM Education and Research.

__Impact on nanoHUB users__

Mathematical modeling is a fundamental concept that science, technology, engineering, and mathematics (STEM) students need to learn. As students learn mathematical modeling skills they can learn science, engineering and mathematics concepts that align with Common Core and Next Generation Science Standards, and learn how mathematics and science concepts apply to real-world situations.

### What is an MEA?

Model-Eliciting Activities (MEAs) are open-ended modeling problems that help students develop conceptual foundations for deeper and higher order ideas in mathematics, science, engineering, and other disciplines. Students complete pre-readings and individual activities and then work in teams to solve complex problems with realistic applications (Diefes-Dux, Hjalmarson, Miller, & Lesh, 2008).

Lesh and his mathematics education colleagues spearheaded the development of the Models and Modeling Perspective (M&MP) (Briggs, 2007) and the six design principles that guide the development and implementation of MEAs (Lesh, Hoover, & Kelly, 1993; Lesh, Hoover, Hole, Kelly, & Post, 2000). These principles ensure problems are set in realistic contexts that elicit mathematical model development and require students to communicate what they did and how they made decisions. These activities expose students’ internal thought processes and conceptual understandings via their approach to solving a given problem (Briggs, 2007) because teams of students are producing a description, procedure, or method (instead of a one-word or one-number answer).

These principles, when paired with engineering practices, are the foundation for the design, implementation, and assessment of MEAs in Purdue University’s First-Year Engineering program (Diefes-Dux, Zawojewski, & Hjalmarson, 2010) and are increasingly used in integrated-STEM K-12 curricula and teacher training (e.g. Moore 2008).

References:

Briggs, M. “Chapter 4: Models and Modeling: A Theory of Learning” In Bodner, G. M. and Orgill, M. K. (ed.) 2007. Theoretical Frameworks for Research in Chemistry/Science Education. Prentice Hill, pp. 72-85.

Diefes-Dux, Heidi A., Keith Bowman, Judith Zawojewski, and Margret Hjalmarson. 2006. “Quantifying Aluminum Crystal Size Part 1: The Model-Eliciting Activity.” Journal of STEM Education and Research 7 (1 and 2): 51-63

Diefes-Dux, H. A., Hjalmarson, M. A., Miller, T. K., & Lesh, R. (2008). Chapter 2: model-eliciting activities for engineering education. In J. S. Zawojewski,, H.A. Diefes-Dux, & K. J. Bowman. (Eds.), Models and modeling in engineering education: designing experiences for all students (pp. 17-35). Rotterdam, the Netherlands: Sense Publishers.

Diefes-Dux, H.A., Zawojewski, J.S., and Hjalmarson, M. (2010). Using Educational Research in the Design of Evaluation Tools for Open-Ended Problems. International Journal of Engineering Education. Vol. 26 (4), pp. 807-819.

Lesh, R., Hoover, M., and Kelly, A. “Equity, assessment, and thinking mathematically: Principles for the design of model eliciting activities.” In I. Wirszup and Streit (ed.). 1993. Developments in school mathematics education around the world. Vol. 3. Reston, VA: National Council of Teachers of Mathematics.

Lesh, R, Hoover, M., Hole, B., Kelly, A., and Post, T. “Principles for developing thought-revealing activities for students and teachers.” In A.E. Kelly and R.A. Lesh (ed.). 2000. Handbook of Research Design in Mathematics and Science Education. Mahwah, NJ: Lawrence Erlbaum. pp. 591-645.

Moore, T. “Moore, T.J. (2008). Model-Eliciting Activities: A case-based approach for getting students interested in material science and engineering. Journal of Materials Education, 30(5-6), 295 - 310.