Investigating Mathematics and the use of illuminations for Knowledge Representation and Information Visualization
Knowledge Representation and Information Visualization for Learning Math and Science: information visualization digital tools, such as animations, simulations, and modeling tools
Investigating Mathematics and the use of illuminations
Background
This activity focuses on Grade 7 mathematics skills development to enhance students understanding and ability to conceptualize fraction, decimals and percents in relation to each other. Observations from teaching this level reveal that students at this level often struggle with the relationship between these three concepts and creating accurate mental models. For example, improper fractions as mixed numbers, decimals, or percents beyond 100% prove challenging for many. Often students believe that memorization of steps will carry them to success in math rather than understanding what’s behind the number symbols. Their conceptual understanding, or lack thereof, becomes problematic when they need to apply this knowledge to a different context and adapt strategies to fit the new situation. As put forward by Whitehead (as cited in Edelson, 2001), this “focus on memorization leads to ‘inert knowledge’ that cannot be called upon when it’s useful” resulting in a poor or non-existent transfer of skills.
Illuminations applets
The Illuminations activities provide simulations that, if properly designed and used in the right context, will enhance and foster conceptual understanding (Finkelstein et al., 2005). When integrated within tasks designed to promote inquiry and understanding of Grade 7 mathematical outcomes, students are provided with an opportunity to enrich their thinking and improve their comprehension of abstract concepts.
British Columbia Grade 7 Learning Outcome (A7)
- compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using
- benchmarks
- place value
- equivalent fractions and/or decimals
Comparing percent to fractions and decimals is a Grade 6 outcome, but by Grade 7 this is consistently not understood well so it needs to be re-taught in preparation of Grade 8 expectations with percent (greater than 100% and between fractions of percent between 0 and 1) and the overriding relationship between all three values. In this activity, this Grade 6 learning outcome will be reinforced as an integral component of the task.
Grade 6 Math Learning Outcome (A6): demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially, and symbolically .
Incorporating principles of the Learning for Use and T-GEM models into the instructional design of this activity grounds it within an inquiry process. The constructivist tenets of LfU and GEM are supported well with the use of technology. In this scenario, motivation and curiosity are elicited through initial tasks designed to help students generate ideas and collect information. The second stage involves key observations by students and their construction of knowledge based around this to help them evaluate relationships between the variables. The third stage focuses on the refinement and application of new understandings to afford students the opportunity to modify their previous evaluation. In total, this activity runs through two GEM and two LfU cycles using a process of guidance and inquiry.
Supporting Math/Science instruction
Inquiry-based learning has the potential to enrich math and science classrooms encouraging students to develop a greater depth of understanding while promoting transfer. The process outlined for this fractions activity in math can be used as a foundation for further science inquiry as well. Grade 7 Processes of Science outcomes include generating and testing hypotheses, as well as creating models to help explain scientific concepts. These process skills can be observed in this mathematics activity. As students become more familiar with inquiry-based learning, they will be able to access these process skills for transfer in different contexts. Reflection, collaboration, and communication are key aspects of inquiry that have a significant impact on thinking and students’ reasoning allowing them to dissect previously held perspectives and seek out new truths and understandings.
The use of simulations within the lesson provides opportunities to provide concrete reference, connecting abstract concepts and offering more diversity: “simulations are designed to build explicit bridges between students’ everyday understanding of the world and its underlying physical principles, often by making these physical models such as current flow or electric field lines visible” (Finkelstein et al., 2005, 2). Using Illluminations, students are able to keep a record of data collected through the learning process that can be used to determine patterns in relationships as well as reflect on past activities or make future predictions.
Background/Content Knowledge needed
- Vocabulary & Concepts: numerator, denominator, common/proper fraction, improper fraction, mixed number, whole number, simplest form, equivalent fractions, multiple, factor, benchmark fractions/decimals/percents, addition equations equaling 1 whole, decimal place value (tenths, hundredths), parts of one, relating fractions to decimal place value, percent
- The initial activity therefore is a revision of fraction relationships, content and skills building to activate prior knowledge, which is essential within the scaffolded activities designed to meet students’ needs.
References
Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385. http://onlinelibrary.wiley.com/doi/10.1002/1098-2736%28200103%2938:3%3C355::AID-TEA1010%3E3.0.CO;2-M/abstract
Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., & Podolefsky, N. (2005). When learning about the real world is better done virtually: A study of substituting computer
simulations for laboratory equipment. Physics Education Research,1(1), 1-8. Retrieved April 02, 2006, from: http://phet.colorado.edu/web-pages/research.html
Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905.
Srinivasan, S., Perez, L., Palmer, R., Brooks, D., Wilson, K. & Fowler, D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15(2), 1-5