## Department of Mathematics and Philosophy

### Undergraduate Research - Mathematics Education

#### Faculty

##### Kim Hartweg

**Areas of Interest:** Elementary and Middle School Mathematics Education; Constructivist Learning, Problem-Based Learning, Brain-Based Research, the Integration of Computer Technology into the School Curriculum, and the Implications of these on the Teaching of Elementary and Middle School Mathematics.

**Description:** I am interested in assisting with undergraduate research projects that can provide insight into how elementary and middle school students learn and understand mathematics. Projects could be designed around the use of invented algorithms for all elementary and middle school math concepts, the use of problems to promote conceptual understanding, uses of computer technology in the mathematics classroom, and the use of conceptual activities to promote a better understanding of mathematical concepts.

##### Bob Mann

**Areas of Interest:** Mathematics education; the concept of function; technology in the classroom, guided discovery approaches to learning and teaching mathematics; interdisciplinary math and science courses.

**Description:** I am especially interested in how activities (science experiments, interactive games, technology simulations, open-ended problems) can be used in fostering and developing mathematical understanding. In particular, I am researching the role of ADAGE (activity, data, analysis, generalizations, and extensions) based lessons in the mathematics curriculum. I would invite interested undergraduate students to devise, research, and assess activity-based instructional materials and then comment on their effectiveness in the math classroom.

I am also interested in studying how students learn the concept of function and the importance of this concept in all branches of mathematics. This is a broad topic which could include research involving the development of the function concept and definition, the multiple representations or uses of functions, graphing techniques, rates of change, or concept maps.

##### Jim Olsen

**Areas of Interest:** Uses of technology to help students learn mathematics, student understanding of the function concept, using problem solving to teach mathematics, using Internet java applets to help students learn mathematics, other areas of mathematics education.

**Description:** Two of my areas of interest are problem solving and technology. In both cases, there now exists a large supply of non-routine problems and technology resources (I'm currently especially interested in java applets) which can be used to illuminate mathematics concepts for students. However, from a practical standpoint, using these in the classroom for instruction is easier-said-than-done. I'm interested in finding ways that non-routine problems and java applets can be connected to the *Illinois Learning Standards*, lesson plans, and practical strategies, so that they can be used effectively for mathematics instruction in the schools.

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