Category: Module C

Investigating m-learning, mobile apps and embodied knowledge – Mobiles – Customising for exploration, interactivity and independent learning

How is  embodied learning facilitated by portable, hand held, and virtual reality technologies?

Embodied learning considers integration of mind and body in the process of learning. Developments in technology integration in math and science education show development from calculators to computer assisted instruction to mobile and hand held technology (Drjivers et al.,  2010). Within these developments the level of use and engagement of the body has increased to improve interactivity and individual work and active relationship with content. The mathematician Papert looked at learning activities of younger children and how the computer could enhance such learning activities. He promoted “putting children in a better position to domathematics rather than merely learn about it” (Drjivers et al 2010, 91).

Mobile apps assist in extending classrooms, and providing anytime, anywhere access (Bayaa & Daher, 2009). There are many apps that are presented in a number of formats and each has its benefits. I looked at three mobile Apps: Mathscard (all mobiles), Math Fact master (ipad et al.)  and Math Ref (itunes, app store). Math Fact offers drills and practice, progress reports, challenges (to test what they have learnt). Like Mathscard, Math Ref is more of a reference for formulas, with good tips but there are no opportunities for detailed explanations or exploration with the content/concept.

To facilitate embodied learning I would focus on making mobile apps with the ability to allow students to perform calculations and get feedback et al and apply learnt concepts rather than  just review content (as seen in the Mobile Math App Mathscard). Howson and Kahane, review this philosophy in looking at how computers could play in the learning of mathematics based on the use of computer graphics and on software design that encourage discovery and exploration of concepts (Drjivers et al 2010, 91). These are the two areas I would focus on in customising mobile technologies.

I would therefore customise apps such as Mathscard and Math Ref by including graphics that allow for input, interaction and manipulation of formulas et al., perhaps a mobile app that enables whiteboard interactivity and visualisations such as Classic Whiteboard (this would include benefits of whiteboard exploration and clarification of ambiguities as revealed in my interview process). Enabling exploration and discovery are essential. I would also include challenges as seen in Math Fact and the use of hints as methods of scaffolding and as guidance as seen in WISE platforms. Enabling interaction and the ability to save work and share for discussion, thought tracking and discussion for modification and clarification are also features I would customize.

References

Mathscard – http://www.mathscard.co.uk/

Math Ref – http://itunes.apple.com/us/app/math-ref/id301384057?mt=8

Bayaa, N. & Daher, W. (2009). Learning mathematics in an authentically mobile environment: The perceptions of students. International Journal of Interactive Mobile Technologies, 3, 6-14.

Drijvers, P., Kieran, C., Mariotti, M-A., Ainley, J., Andresen, M., Chan, Y., Dana-Picard, T-D., Gueudet,G., Kidron, I., Leun, A., Meagher, M., & Leung, A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J-B LaGrange (Eds.) Mathematics Education and Technology-Rethinking the Terrain, 89-132, Springer.

Second Life and Virtual Field Trips – Second Life and Virtual field trips: facilitating math/science knowledge/skills

How is knowledge relevant to math and science possibly generated in these networked communities?

In looking at the question of how knowledge relevant to math and science in networked communities I am drawn to an earlier portfolio entry of my concept and definition of math and science skills/knowledge with the latter identified primarily as: enquiry, concepts, exploration/procedures, observation and critical thinking and analysis and logical construction of hypotheses and testing. The generation of such knowledge is enabled within second life and virtual field trips primarily through interactive activities, interaction with concepts or organisms within virtually realistic simulations of real environments and through the creation of a collaborative and extended learning community.

Second Life

Second Life is a virtual environment in which learners can create an avatar and engage in a virtual world of learning. In Second Life learning communities can be created that offer interactives and simulations with games and experiments based on concepts and methodologies. Avatars are able to engage in self-directed activities and to explore independently. The virtual world explored in Second Life enables authoring and creating that involve mathematical and science skills for which they can have intellectual property  over creations [The Economist, 2006]. Exploration and Collaborative goal oriented processes are explored. Institutions such as Drexel University have utilized Second Life in creating a virtual learning space in which knowledge can be diffused and generated through virtual classroom settings in teaching (including lectures -PowerPoint presentations, assessments – quizzes and presentation) and in collaboration (through joining communities in a central pace) and research. Drexel even houses information on libraries and library access. http://drexelisland.wikispaces.com/

Virtual Field Trips and Web-Based Science Expeditions

For me the greatest affordance of virtual field trips and web-based science expeditions is the ability for students to participate in virtual scientific explorations, particularly of geographically remote places. Learning is real and relevant as members of the community participate in real images and expeditions through field trips. Virtual field trips are an essential aspect of scientific knowledge through development of concepts and phenomena and on skills in observation, and interpretation and analysis of observed organism or phenomena in a real environment/context. Knowledge is further diffused through the availability of and interaction with real scientists conducting real experiments with whom students can interact act with and ask questions. For example, in Field Trip Earth http://www.fieldtripearth.org/index.xml students are able to view video tapes of the organisms in their natural habitat and to interact with researchers who are actively involved in the research and if not then to view their notes.

Virtual versus Real

Of the two I believe that Virtual field trips offer an advantage in adding expert and real life contact for students, which is important in clarifying misconceptions and evaluating observations et al. as well as in contextualising, clarification and modification of knowledge.

Opportunity for Pedagogical Models

Both models allow for some level of GEM (Generate Evaluate Modify) and POE (predict observe evaluate) models. The opportunities to evaluate and modify/ clarify knowledge and/or observations are increased in Virtual field trips with the ability to interact with experts and actual researchers and/or view their notes. Levels of reflection and scaffolding are not readily seen but can be directed through defiined tasks although that may reduce the levels of open endedness and fun to the activities/process.

References

Drexel Island on Second Life (2007). Drexel University http://drexelisland.wikispaces.com/
http://slurl.com/secondlife/Drexel/216/209/24

Virtual Field Trips – Field Trip Earth
http://www.fieldtripearth.org/index.xml

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