Message-ID: <105630504.2212.1573587363831.JavaMail.confluence@external-wiki.terc.edu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_2211_1230954024.1573587363831" ------=_Part_2211_1230954024.1573587363831 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Math Content

# Math Content

=20
=20
=20
=20

While the REVEAL study sought to understand staff facilitation in genera= l, it was carried out in the context of exhibits that focused on math. In o= rder to conduct a rigorous study, the team had to define the kind of mathem= atical reasoning we hoped to see and develop instruments to reliably measur= e it.

=20
=20
=20
=20
=20
=20

=20
=20
=20
=20

## Mathematical Reasoning in REVEAL

The REVEAL study used three components of the Design Zone exhibition, which was created to engage visi= tors in functional reasoning, a type of algebraic thinking.=C2=B9 Functiona= l reasoning deals with quantities that are predictably related, so that a c= hange in one quantity results in a change in the other. Set in real-world c= ontexts of creative problem solving through art, music, and engineering, ea= ch Design Zone exhibit focused on a specific relationship among two or more= quantities or variables. Through interaction with the exhibit, visitors we= re encouraged to explore the question: =E2=80=9CWhen <Quantity 1> cha= nges in a particular way, how does <Quantity 2> change?=E2=80=9D Once= they figured out the relationship, visitors were able to use their underst= anding to accomplish a task, such as creating a balanced, esthetic mobile o= r collaboratively completing an Etch-A-Sketch drawing.

For example, at the Balancing Art exhibit used during REVEAL (pictured o= n the left), visitors hang pieces of different weights on either side of a = pivoting rod in order to create a balanced mobile. Since each piece is mark= ed with its weight and the positions on the rod are labeled with their dist= ance from the center, the exhibit engages visitors with the mathematical re= lationship among weight, distance, and force that underlies all mobiles: th= e force that an object exerts is the product of its weight and its distance= from the point, or fulcrum, from which the rod is suspended.

=20
=20
=20
=20
=20
=20

## Measuring Functional Reasonin= g, Math Awareness, and Math Enjoyment

The REVEAL team created an overall framework for investigating visitors= =E2=80=99 functional reasoning, consisting of four dimensions: (a) identify= ing mathematical quantities, (b) describing mathematical relationships, (c)= exploring mathematical relationships, and (d) achieving mathematical goals= . The rubrics for each exhibit=  were based on this framework and were used to code = videos of families at the exhibits. The team also developed survey instrume= nts to measure families=E2=80=99 enjoyment of the mathematics and awareness of the= mathematics in the exhibit.

=C2=B9 Greenes, C. E., & Rubenstein, R. (Eds.). (2008). Alg= ebra and algebraic thinking in school mathematics: Seventieth yearbook= . Reston, VA: National Council of Teachers of Mathematics. Kaput, J. J., Ca= rraher, D. W., & Blanton, M. L. (2008). Algebra in the early g= rades. New York: Lawrence Erlbaum Associates/National Council of Teach= ers of Mathematics. <= /p>

=20
=20
=20