Integrating internet-based mathematical manipulatives within a learning environment

1. Integrating internet-based mathematical manipulatives within a learning environment Presenters: Wei-Chih Hsu Professor : Ming-Puu Chen Date : 12/29/2008 Crawford, C. & Brown, E. (2003). Integrating internet-based mathematical manipulatives within a learning environment.Journal of Computers in Mathematics and Science Teaching, 22(2), 169-180.

2. Introduction(1/2) • This article explores necessaryrationale elements • to create a successful “student-centered”learning environment involving digital manipulatives. • The use of manipulatives within a mathematical classroomenvironment has traditionally been offered • Manufactured manipulatives. • Teacher-created concrete objects. • Manufacturedmanipulatives and teacher-created concreteobjects are usedto • provide tactile-kinesthetic learning activities • enhancemathematics conceptualization.

3. Introduction(2/2) • The primary purpose of the manipulative • offer a concrete visualization of mathematical concepts. • The appropriate integration of manipulatives within the learning environment ensures • the learner’s conceptualization of mathematical theories • tasks at a level appropriate to the learner by providing stimulating visual and concrete representations.

4. Literature review (1/4) Manipulatives • Manipulatives have been integrated into learning opportunities for years. • One of the first advocates of ‘hands-on learning’ was the Swiss educator Johann Heinrich Pestalozzi (1746-1827). • Students need to learn through their senses and through physical activity” • “things before words, concrete before abstract” (Pestalozzi, 1803).

5. Literature review(2/4) Numerous positive attributes can be associated with manipulatives(Burns, 2001) : 1. Manipulatives help make abstract ideas concrete. 2. Manipulatives lift math off textbook pages. 3. Manipulatives build students’ confidence by giving them a way to test and confirm their reasoning. 4. Manipulatives are useful tools for solving problems. 5. Manipulatives make learning math interesting and enjoyable. 5

6. Literature review(3/4) Burns (2001b) described several specific “musts” that need to occur to facilitate positive correlations when manipulatives are used. 1. The instructor conducts ongoing dialogue with students about why manipulatives help them learn math. 2. Ground rules are set and consistently communicated as students work with manipulatives. 3. Students are encouraged to develop a system for using and storing materials in the classroom under the teacher’s direction. 4. Time given to students for free exploration provides for more “ontime” behavioral applications as necessary. 5. Manipulatives are a natural for writing assignments, giving students’ a writing focus. 6. Parents are given opportunities to gain hands-on experiences using the manipulatives. 6

7. Literature review(4/4) Mathematical manipulatives have been integrated into the learning environments to expand the learner’s conceptual framework of understanding. to develop a link between theory and concrete explanations of mathematical concepts. The use of digital manipulatives provides an interactive environment with immediate feedback. to explore indepth mathematical theories that would be difficult to simulate with concrete models. 7

8. Methodology(1/2) An action research framework. A chart outlining “Elements of a Rationale for Using Technology in Education” delineated by Roblyer and Edwards. Elements of a rationale for using technology in education(Roblyer & Edwards, 2000) 1. Motivation 2. Unique instructional capabilities 3. Support for new instructional approaches 4. Increased teacher productivity 5. Required skills for an information age 8

9. Methodology(2/2) All participants were female with a large range of teaching service, one year to more than 25 years. First, a computer-generated survey. Second, participants were provided ample opportunity and resources to visit the web-based National Library of virtual manipulatives (2002) to independently select, view, and critique virtual manipulatives. Third, after visiting several sites during a four hour timeframe, participants were to respond appropriately to the computer-generated survey. 9

10. A major component of the action research led to vigorous discussion concerning “Why choose one manipulative over the other?” “Will virtual manipulatives do this better than concrete manipulatives?” Participants in this study indicated their willingness to incorporate digital manipulatives. Discussion (1/2) 91%

11. Discussion (2/2) 11

12. Conclusions (1/2) Thoughtful consideration must be given the instructional design of the course the specific learning objectives for each module of instruction. Our primary goal is not to help users accomplish some task faster or more effectively, but rather to engage them in new ways of thinking. 12