Use of Technology in Teaching and Learning Mathematics

1. Use of Technology in Teaching and Learning Mathematics January 30, 2014 Melchor Espanola

2. Technology is an essential tool for teaching and learning mathematics effectively; it extends the mathematics that can be taught and enhances students' learning.

3. Calculators, computer software tools, and other technologies assist in the collection, recording, organization, and analysis of data. They also enhance computational power and provide convenient, accurate, and dynamic drawing, graphing, and computational tools. With such devices, students can extend the range and quality of their mathematical investigations and encounter mathematical ideas in more realistic settings.

4. In the context of a well-articulated mathematics program, technology increases both the scope of the mathematical content and the range of the problem situations that are within students' reach. Powerful tools for computation, construction, and visual representation offer students access to mathematical content and contexts that would otherwise be too complex for them to explore. Using the tools of technology to work in interesting problem contexts can facilitate students' achievement of a variety of higher-order learning outcomes, such as reflection, reasoning, problem posing, problem solving, and decision making.

5. Technologies are essential tools within a balanced mathematics program. Teachers must be prepared to serve as knowledgeable decision makers in determining when and how their students can use these tools most effectively.

6. RECOMMENDATIONS • Every school mathematics program should provide students and teachers with access to tools of instructional technology, including appropriate calculators, computers with mathematical software, Internet connectivity, handheld data-collection devices, and sensing probes.

7. Teachers of mathematics at all levels should be provided with appropriate professional development in the use of instructional technology, the development of mathematics lessons that take advantage of technology-rich environments, and the integration of technology into day-to-day instruction.

8. Curricula and courses of study at all levels should incorporate appropriate instructional technology in objectives, lessons, and assessment of learning outcomes.

9. Programs of preservice teacher preparation and in-service professional development should strive to instill dispositions of openness to experimentation with ever-evolving technological tools and their pervasive impact on mathematics education.

10. Teachers should make informed decisions about the appropriate implementation of technologies in a coherent instructional program

11. The use of technology cannot replace conceptual understanding, computational fluency, or problem-solving skills. In a balanced mathematics program, the strategic use of technology enhances mathematics teaching and learning. nctm.org

12. Why should a teacher use technology in his or her mathematics classroom?

13. It supports computation. • It presents a tangible image of mathematics, which helps students understand difficult concepts.

18. In primary school classrooms, many teachers use concrete manipulatives, Geoboards (allowing children to make geometric figures by stretching rubber bands over a grid of nails) DienesBlocks (providing children with a physical model of the place-value system in which “473” means four hundreds, seven tens and 3 ones).

19. In secondary school, researchers have found that more advanced tools are necessary. These advanced tools help students learn by supporting computation and by giving abstract ideas a more tangible form.

20. Researchers have found that whereas physical manipulatives are the right tangible form for elementary school, ICT-based tools are the right tangible form for secondary school (Kaput, 1992; Kaput 2007). Researchers have found that ICT can support learning when appropriately integrated with teaching techniques, curriculum, and assessments (Means & Haertel, 2004).

21. Technology can reduce the effort devoted to tedious computations and increase students focus on more important mathematics. • Equally importantly, technology can represent maths in ways that help students understand concepts. • In combination, these features can enable teachers to improve both how and what students learn.

22. Technology can reduce the effort devoted to tedious computations and increase students focus on more important mathematics. FOCUSING STUDENT THINKING Technology can represent math in ways that help students understand concepts. Making Ideas Tangible

23. FOCUSING STUDENT THINKING Teachers should minimize load that is unimportant to the current learning goal and direct student activity to thinking that is germane to what they should be learning (Sweller, 1988).

24. What is important or germane depends on the math topic and age of the student. In primary school, it is important to learn to do arithmetic fluently. Using technology to do this thinking for the student would be inappropriate. In secondary school, however, students have mastered arithmetic and should be focused on more advanced skills and concepts.

25. For example, researchers have found that when calculators are available to offload details computations, teachers can better focus on (Burrill et al., 2002; Ellington, 2003): • ƒ More realistic or important problems. • ƒ Exploration and sense-making with multiple representations. • ƒ Development of flexible strategies. • ƒ Mathematical meaning and concepts

26. Piaget discovered that children first develop ideas concretely and later progress to abstractions (Piaget, 1970). In designing learning environments, it is often helpful to apply this principle in reverse: to help students learn an abstract idea, provide them with more tangible visualizations. For example, it is easier to see how the variable m in f(x) = mx + c represents a rate of change when the function is graphed and students can explore the connection between m and the gradient (slope) of the line (Roschelle et al., 2007).

27. Although drawings on paper or on the teacher’s board can make ideas tangible, static drawings often fail to convey math principles. For example, many students think a triangle is an isosceles triangle if it looks like one and do not understand how to establish the property formally. With an ICT-based geometry tool, students can grab and drag a corner of a geometric construction of a triangle and see how it behaves under transformations. Playing with this tangible image can prepare students to understand the formal proof, which is much more abstract.

28. Researchers have found that when technology makes abstract ideas tangible, teachers can more • easily (Bransford, Brown, & Cocking, 1999; Roschelle et al., 2001;diSessa, 2001): • ƒ Build upon students’ prior knowledge and skills. • ƒ Emphasize the connections among mathematical concepts. • ƒ Connect abstractions to real-world settings. • ƒ Address common misunderstandings. • ƒ Introduce more advanced ideas.

29. Online Instructional Videos Khan Academy https://www.khanacademy.org/ Ace My Math Course http://acemymathcourse.com/ How to download Online Instructional Videos KeepVid http://keepvid.com/ Video Downloader (Firefox)

30. Online Math Manipulatives Math Play Ground http://www.mathplayground.com/index.html Glencoe Virtual Manipulatives http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html Houghton Miffin Math Manipulatives http://www.eduplace.com/kids/mw/manip/mn_1.html

31. Math Software Geogebra Geometer’s Sketchpad BagatrixSoftwares Geometry Blaster Algebra Blaster

32. Math Add-ins Mathematics (MS Excel) Data Analysis (MS Excel) Phstat (MS Excel)