Video 1 – Learning Environment 6 with Teacher G (Post-secondary Applied Science)
Observation
• Personal Response systems through the use of Clickers (each person had their own). Anonymous response.
• Very large class with only one teacher
• Technology use on three levels: to deliver content, to enable interactivity and participation and to evaluate learning (provide information on students’ level of understanding).
• Collaboration

Questions
I wondered why anonymity, because although reducing fear limits the opportunity for personal remediation.

Good technology and good technology use?
Good:
i) interactive and
ii) allowed individual choice.
iii) Provide feedback on results.

Questions
Process did not allow for divergent options and further investigations. However, this was supplemented with post discussions with the lecturer when reviewing student choices and also through collaboration with peers during problem solving. Is this enough?

Issues
Large classes with decreased ability to measure students’ level of understanding – The technology was chosen and used to address this specific issue as well as to increase interactivity and participation at the individual level. It was therefore well chosen.

However, I would increase the opportunity created here by assigning anonymous ids that could still give them a feeling of protection but enable me to also offer increased individual feedback or remediation design.

Students responded that the technology increased interest, concentration and active thinking, as well as participation. However, I wondered how to incorporate more technology in allowing students to act work through actual processes that were more inherent of the subject: exploration, problem-solving, divergent options, analysis, testing and real world applications.

The latter was more evident in the second video, Learning Environment 1 with Teacher F (Mathematics Graphing Calculators)

Observations
• Technology was used in: i) delivering content ii) enabling interactivity and participation and iii) presenting students’ work for discussion and feedback.
• Open ended questions were given that created the need for the technology and choosing tools.
• Students worked on individual projects that they designed.
• The technology gave them a comfort level and support that empowered them to take the course and/or activity to other levels.
• Some students used the calculator as a last step, saying it was better to start on paper because it increases understanding of the process and what they were doing,
• Others opted for the calculator right away. Those students commented on the fact that they missed out on the ‘mathematical part’ and kept having to start over. This in itself was a valuable lesson. Emphasis being on the process and not just the technology which they would not have had were it not for this personal exploration and choice.
• Students also commented that they were able to spend a longer time with the material, which became second nature, having a better knowledge of what to do rather than if they were just given a few questions to complete. The graphing calculator will not graph the image if a mistake is made.

Good technology or good technology use?
Good:
i) was interactive
ii) allowed for self-direction and choice
iii) provided support for self-directed activities
iv) enabled problem solving, particularly synthesizing and application with a real world problem
v) Created conditions of use or for use of technologies, and was
vi) open ended – allowing for divergent options and/or further investigation.
vii) The technology use also allowed for an experience inherent of Mathematics, namely: exploration, problem-solving, divergent options, analysis, testing and real world applications.

Question
I wonder if there could be any way to increase the real-world nature of the problem or its applicability or link to personal, societal and global situations/experiences

Issues
Limited access to computer labs that were overwhelmed with demand was an issue. Graphing calculators gave students the ability to have individual access to technology. This was also cited as a good financial choice within the reference of alternative models, as the cost of two hand held computers equates to the cost of a desktop device.

The lecturer noted that one issue was asking appropriate level questions that get the ‘Math out’ and not just the calculations. This also meant knowing the technology and its opportunities and/or limitations within the question and how to address that.

Gender issues also came up. Boys played more with the technology at home rather than completing assignments whereas girls complete homework assignments more diligently. In this case I would place a lot more emphasis on in-class assignments and presentations along with assignments that are geared more towards design. The assignment chosen for this class had a strong design element that I think would appeal to boys.

Commonalities (across videos):
i) The need for questions/activities that lead to the use of the technology to support processes rather than just calculations
ii) Technology increases capabilities and increases options that would not have been explored by the student had they not interacted with the technology
iii) The use of the technology increased interactivity and engagement, which increased interest and individual work.
iv) The focus is still on strong pedagogy and not just technology use

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

Technology Enhanced Learning Environment –  WISE, MYWORLD, JASPER and CHEMLAND

Strengthening pedagogical structures

The National Centre for Excellence in the Teaching of Mathematics (NCETM) in their 2010 report and in the 2011 report by the Joint Mathematical Council of the United Kingdom report that expected increases in enhanced learning using digital technologies have not been realised. Both highlighted potential problems in the pedagogy, a lack of opportunities for meaningful interaction, and too few opportunities for the use and application of concepts across subject areas. Sutherland et al. (2011) elaborate this point to define a major need for student-led mathematical models with high problem solving content using computer programming and digital technologies that are widely used in society and the workplace.  The use of pedagogy and models that are centred on presentation and exercises were also highlighted as weaknesses.

Four substantive projects with foundational technology-enhanced learning environments (WISE, MYWorld, Jasper and Chemland) were explored, compared and contrasted for   learning goals and theory and found to include elements designed to create a deeper relationship/integration of pedagogy and technology with the hope of increasing the perceived benefits on technology integration.

Below is a synopsis of each project, their learning goals and learning theories, a comparison of each and the potential for inclusion/impact teaching, learning and integration of technology within the mathematics and science classroom.

Learning Goals and Theories

WISE

WISE is a web delivered project designed based on the principle of Scaffolded Knowledge Integration and to support the design of curriculum projects in which students investigate problems, critique solutions and debate with their peers (Slotta & Linn, 2009). The Web delivery mechanism means there is no software, all content and functionality can be accessed within the Web browser. The interface and working space are designed for and promote collaboration for students and teachers to work on combined lessons and projects. Teachers can create, share and modify lessons using WISE software online.

WISE looks at knowledge integration on three levels: i) understanding content, ii) knowledge and development of skills within the course (scientific inquiry skills) and iii) epistemic knowledge (understanding the nature of the course) based on learning theories of: Scaffolding (content delivery and tools to support learning including embedded hints, guides and reflection activities) and Distributed congnition (online discussions).

The key difference in WISE is the Knowledge integration on all levels in one learning environment using technology, web delivery (Snyder et al., 2002). In this way WISE differs from all other processes as it is all web based which creates limitations for use if there is not internet access. However, pedagogical approaches and theoretical frameworks could still be employed.

MyWorld

MyWorld is a GIS software integrated in Life Sciences explorations and lesson delivery. It is based on learning goals of facilitating the integration of content studies with the inquiry process and for inquiry to play a more significant role in scientific learning. The primary theories of learning within MyWorld are based on four premises:

‘1. Learning takes place through the construction and modification of knowledge structures.

2. Knowledge construction is a goal-directed process that is guided by a combination of conscious and unconscious understanding goals.

3. The circumstances in which knowledge is constructed and subsequently used determine its accessibility for future use.

4. Knowledge must be constructed in a form that supports use before it can be applied’ p. 357

MyWorld offers the tools and support that enable students to compute necessary information, construct knowledge and to create, analyse and test data. It is interactive, customisable and allows for visualisation of data with affordances of allowing students to enter or create new data. It therefore offers independence and capabilities that are not possible without the technology such as computational skills (real scientific tools). The software is not as user friendly as the others and can be more interactive in both the input of and manipulation of data. Unlike T-Gem and Chemland and WISE elements a prior learning module and/or thought tracking and discussion are not enabled within the environment.

Jasper

Jasper is a learning series based on anchored learning in which instruction is anchored on solving a complex problem. This makes it distinctive from the other models. Instruction must be anchored and presented in small chunks. It is a constructivist approach in which students have a meaningful experience. In this experience problem setting is essential and forms the basis of that meaningful experience. Understanding how people think is an essential element to the foundation for the Jasper model (Pellegrino & Brophy, 2008). The Jasper technology is a series of interactive movies with defined problems. The technology provides anchors for the instruction, content, and defining problem, as well as provides the structure for independent and collaborative work.

The Jasper series supports:

• Scaffolding
• Practice
• Feedback
• Revision
• Reflection
• Community learning (distributive cognition)
• Divergent thinking/ instruction (The what if scenario)
• The inquiry process/discover learning.

Materials supported are context specific, activity oriented, and developed in levels, with increasing independence. It supports independent learning, all information required are presented in the question, as well as collaborative learning.

Chemland and T-Gem

Chemland is a digital software used in simulations and explorations of scientific processes in Chemistry. It was investigated here within the T-Gem methodology. The underlying learning goals and theories are the use of technology to strengthen students’ mental modes of knowledge.

TheT-gem approach has three components: Generate, Evaluate and Modify with specific teacher and student activities. Prior to the three step process the teacher provides background content. This differs from the Jasper series in that provision of background content is not a necessary precursor. The teacher’s role is to provide prompts to elicit desired outcomes within the three areas, likened to the scaffolding prompts in WISE.

Teacher’s/Designer’s use of projects

WISE

To create a WISE project teachers can create, use and/or modify an online lesson. The task should be inquiry-based with scaffolding features such as cognitive hints, embedded reflection, embedded notes and embedded assessments. These should be sequentially organised within the lesson in a step by step approach in which the progressions occur naturally through clicks (automatically goes to the next step/activity/task). The experience should promote autonomous learning and so should include: scaffolding, student self-monitoring through collaborative reflection, activities and teacher feedback. WISE software has embedded features to support each of these areas.

Software tools for activities include: Drawing, Concept mapping, Diagramming, and graphing with additives/potential affordances for interactive simulations and models. The teacher’s role is as a facilitator/guide primarily encouraging discussion.

MyWorld

The design strategies suggest a three step process: Motivation – to acquire specific skills or knowledge within a real life context or setting; Knowledge Construction – Goal directed and involves the use of and facilitation of incremental constructs organised in a way to allow for linking to memory banks and experiences (prior learning) and for making connections and Knowledge refinement – the application of knowledge and how to access that knowledge.

MyWorld offers interactive components but I did not find it very user friendly enough to enable a level of ease of use with the software that enabled students to act as independently as desired in the motivation and goal directed stages described in the LFU model. In using LFU and or a MyWorld based technology and model for mathematics I would utilise activities within the three steps as highlighted and emphasise the digital technology. However, I would make the technology more interactive in both the input of and manipulation of data and I would also include a prior learning module before the motivation stage to identify or clarify misconceptions.

Jasper

The Jasper series is based on the premise that effective learning environments are: Knowledge centred (concept of understanding rather than just mastery of skills), Learner centred  (with a need to understand attitude and skills that students take to the classroom, preconceptions and misconceptions), Assessment centred ( gage where students are and develop accordingly) and Community centred (sharing and arriving at an answer etc).

The Jasper series is therefore designed to be an adventure series to provide motivation as in MyWorld but differs in that content is not taught directly but encourages students to find information. The Jasper series can therefore be used either as a motivation/ introduction to or culminating activity (application of concepts) depending on the pedagogical desires. In my programme, for example, in college mathematics with at risk learners I can use Jasper to provide context, a real world problem and creating more meaningful problems for students to solve rather than completing questions devoid of context and/or only practicing through drills and practice. The medium also caters to multiple intelligences and diverse learning styles (Gardner, 1983). Also, the SMART and STAR structures enable the tracking of thought patterns, progress and direction setting for both students and teachers (Pellegrino & Brophy, 2008). Jasper can also be used to assist students in structuring problems into manageable and separate and more approachable sections while distinguishing between relevant and not needed data (Vye et al., 2009). KWL charts can be used alongside Jasper to support metacognition and independent, self-paced learning by helping students to organise what they need to research.

 A Reflective/Synthesised framework

Independent use and Exploration

I am in agreement that in instances independent use and exploration of technology may not result in significant gains in learning. But I believe it is dependent on how and when that independent learning is introduced into the lesson and the support given to reflection of that independent learning process.
The kind of independent use and exploration I refer to is that placed within scaffolding strategies where the process is demonstrated and modeled, students are guided in the process, students then attempt the process themselves, and further explored in a way that they can test their theories/concepts.

However, potential missing elements, which if included will fill gaps in independent work, are: reflection, presentation, discussion, debate and analysis.

While working independently students can reflect on their process and present how and what conclusions they arrived, this can then be discussed whether verbally or asynchronously (discussion posts or chat room). In the latter an online medium should enable viewing of results and posting comments.The above are based on my current teaching experience, my interview and my exploration with  four substantive projects with foundational technology-enhanced learning environments (WISE, MYWorld, Jasper and Chemland).

Social affordances, Cognition and metacognition – Activities for success

“factors that might facilitate participation and interaction in CSCL environments are promoting alternative views for students to discuss, anchoring discussions to students’ personal experiences, option to make anonymous contributions, offering interesting and timely topics, making online discussion a part of legitimate classroom activity, and alternating face to face and electronic discussions.” Lipponen, L. et al. (2003).

Lippoen’s discourse reflects benefits seen in my practical teaching experiences. I instituted a primarily asynchronous (chats, blogs and discussion post) means of discussion set questions in two of my courses. Both offered independent learning and links to web resources that provided background content and examples. The two deliveries were slightly different in how materials and activities were organised to introduce or support discussions. The delivery model that worked better was the one that had fewer activities with one or two clear goals, with supporting materials that did not require having to use too many external links. In the latter experience also aiding success was that content was organised in one space and presented in small chunks.

Prompts suggested in Lippoen (2003) and resonated in Anderson (2004), are integral in my experience. Although some believe that the discussion environment should be a space for more student-centred and driven discussion I have found that it depends on the level as some students feel neglected and do not want to return to the discussion as much as if the teacher responds regularly to their comments (even if students are responding).

Another discussion point is that of modality of interaction (asynchronous vs synchronous means). Asynchronous means such as online discussions (blogs, chats, and posts) serve to extend discourse beyond the classroom, deepen student-to student interaction and enabling teachers to keep more abreast of individual students’ thoughts, conceptions and misconceptions. However, the latter becomes difficult to manage with large classes and if the lecturer has many classes. This gives me a greater appreciation for the metacognitive, reflection and discussion capabilities embedded within WISE. The integration of such tools was central in my delivery of  Mathematics and the T-Gem methodology.

All the series we have viewed so far present instruction and anchored problems in small chunks. Jasper requires the learner to seek solutions that may require the teacher to use supported environments that simulate/ aid scaffolding activities. Of them all WISE is the most comprehensive in creating the one learning environment experience. In the Chemland experience I would have to create my learning space to include my simulations and such affordances for communication and social interaction to enable this meaningful interaction that would engage all students but I would make that learning space one such as WISE which incorporates all elements in one learning environment. A lesson from WISE is the inclusion of reflection and metacognitive elements within the tasks themselves. A lesson from Jasper is to use multimedia and presentation tools that motivate and present anchored problem solving using real experiences but also to give students enough motivation to seek out additional information. The use of Simulations as presented in MyWorld is also noteworthy in instructional design and delivery.

Regarding physical infrastructure and support I think smartphones with internet connectivity, which are increasing in prevalence, may become viable options for facilitating discussions. Also increasing is the potential for Mobile Apps for education technology alongside developments in ‘Social software and participatory learning: Pedagogical choices with technology affordances in the Web 2.0 era’  (Lee & McLoughlin, 2007). There are other programs such as the one lap top per child program that may also help with infrastructure to support digital technology integration.

Teachers can therefore support at-risk-learners by:

i) modeling the process
ii) guiding students through the process
iii) enable independent exploration through application of concepts
iv) include media for discussion of results (synchronous and asynchronous, and enable feedback)
v) structure presentations and discussions on understanding sources of misconceptions and on clarification, using collaborative structures and distributed cognition strategies.

References

Anderson, T. (2004). Toward a theory of online learning. In T. Anderson & F. Elloumi (Eds), Theory and practice of online learning (pp.33-60 ). Athabasca, AB: Athabasca University. http://cde.athabascau.ca/online_book/ch2.html Retrieved 21 February 2011

Cognition and Technology Group at Vanderbilt (1992a). The Jasper experiment: An exploration of issues in learning and instructional design. Educational Technology, Research and Development, 40(1), 65-80. http://ezproxy.library.ubc.ca/login?url=http://dx.doi.org/10.1007/BF02296707

Gobert, J., Snyder, J., & Houghton, C. (2002, April). The influence of students’ understanding of models on model-based reasoning. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), New Orleans, Louisiana.
Retrieved Saturday, October 29, 2005 from: http://mtv.concord.org/publications/epistimology_paper.pdf

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

Edelson, D. C., Salierno, C., Matese, G., Pitts, V., & Sherin, B. (2002, April). Learning-for-Use in Earth science: Kids as climate modelers. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, New Orleans, LA. http://www.worldwatcher.northwestern.edu/userdownloads/pdf/LFU_PF_NARST02.v3.doc

Joint Mathematical Council of the United Kingdom.(2011). A report from a working group of the Joint Mathematical Council of the United Kingdom. Chaired by Professor Rosamund Sutherland. Edited by Dr Alison Clark-Wilson, Professor Adrian Oldknow and Professor Rosamund Sutherland

Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905.

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.

Lee and C. McLoughlin. (2007) ‘Social software and participatory learning: Pedagogical choices with technology affordances in the Web 2.0 era’ http://www.ascilite.org.au/conferences/singapore07/procs/mcloughlin.pdf   Retrieved 29 February 2012

Linn, M., Clark, D., & Slotta, J. (2003). Wise design for knowledge integration. Science Education, 87(4), 517-538. http://onlinelibrary.wiley.com/doi/10.1002/sce.10086/abstract

Lipponen, L. et al. (2003).Patterns of participation and discourse in elementary students’ computer-supported collaborative learning. Learning and Instruction. 13 (5), 487-509.

National Centre for Excellence in the Teaching of Mathematics (NCETM). Mathematics and Digital Technologies -New Beginnings. A report Date: September 2010. https://www.ncetm.org.uk/public/files/3399763/NCETMDigitTechReport2010.pdf , Retrieved February 23, 2012

http://cme.open.ac.uk/cme/JMC/Digital%20Technologies%20files/JMC_Digital_Technologies_Report_2011.pdf, Retrieved February 22, 2012

One laptop per child program http://one.laptop.org/ Retrieved 29 February 2012

Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303. http://ezproxy.library.ubc.ca/login?url=http://dx.doi.org/10.1007/978-0-387-76898-4_14

Vye, Nancy J.; Goldman, Susan R.; Voss, James F.; Hmelo, Cindy; Williams, Susan (1997). Complex Mathematical Problem Solving by Individuals and Dyads. Cognition and Instruction, 15(4), 435-450. http://www.tandfonline.com/doi/abs/10.1207/s1532690xci1504_1

Technology Enhanced Learning Environment:T-GEM, IWB, Web 2.0 and simulations

Integration

Subject: Mathematics

Concept: Quadratic equations

This concept is a challenge from personal practice. Another pedagogical challenge experienced is adding relevance and real world application.

Digital Technologies: Interactive Whiteboard (IWB), Graphing Simulation, Web 2.0 technology

The interactive whiteboard was chosen for its interactive capabilities as well as strength in visual display, ease of use for student individual use and manipulation and for ease of integration of real world components and internet access and use.

Pedagogy: 3-step T-GEM cycle

The National Centre for Excellence in the Teaching of Mathematics (NCETM) in their 2010 report on Mathematics and Digital Technologies -New Beginnings highlight that IWBs did not make the impact on learning expected, particularly given its affordances. This was concurred in the 2011 report by the Joint Mathematical Council of the United Kingdom. Both highlighted potential problems in the pedagogy, a lack of opportunities for meaningful interaction, and too few opportunities for the use and application of concepts across subject areas. Sutherland et al. (2011) elaborate this point to define a major need for ‘student-led mathematical modelling, problem solving and computer programming which makes use of the powerful mathematical digital technologies that are widely used in society and the workplace’ (p. 3).  The use of pedagogy and models that are centred on presentation and exercises were also highlighted as weaknesses that relegate the use of IWBs to primarily presentational use.

To this end the T-GEM model will be used to inform pedagogical practice alongside digital technology that encourage interaction at the student level and that enables application of concepts across subject areas.

References

Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905.

Khan, S. (2010). New pedagogies for teaching with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.

National Centre for Excellence in the Teaching of Mathematics (NCETM)

Mathematics and Digital Technologies -New Beginnings

A report Date: September 2010

https://www.ncetm.org.uk/public/files/3399763/NCETMDigitTechReport2010.pdf , Retrieved February 23, 2012

Joint Mathematical Council of the United Kingdom.(2011). A report from a working group of the Joint Mathematical Council of the United Kingdom. Chaired by Professor Rosamund Sutherland. Edited by Dr Alison Clark-Wilson, Professor Adrian Oldknow and Professor Rosamund Sutherland

http://cme.open.ac.uk/cme/JMC/Digital%20Technologies%20files/JMC_Digital_Technologies_Report_2011.pdf , Retrieved February 22, 2012

Extensions for the mathematics classroom

WorldWatcher and LFU

Edelson et al. (2002) explored the implementation of Worldwatcher based on the LFU design model (see table 1 below) within a middle school use and application of a project, the ‘Planetary Forecaster’ model and software support, in the school’s curriculum unit for Earth systems science. The emphases were computer-supported investigations of geospatial data with hands-on laboratory activities. Students observed and measured the phenomena under study.

Table 1:  Overview of the Learning-for-Use Design Framework

Source: Edelson et al. (2002)

Challenges

Students’ misconceptions, alternative or incomplete conceptions, for example the reason for seasons and or earth-sun relationships, shown by Russell, Bell, Longden, and McGuigan (1993), Dove (1998) ,  Atwood and Atwood (1996) , Philips (1991) and Jones, Lynch, and Reesink (1987) are a major challenge as they affect how students construct knowledge and the support needed to clear misconceptions as well as to apply and analyse concepts/data to create and or interpret results. These challenges were also experienced in the ‘Planetary Forecaster’ project.

Experience and additional design features – Suggestions for the Mathematics environment

I like the emphasis on inquiry and investigation and the open-ended element to tasks within the LFU model. These are potentially strong and transferable elements within my college mathematics environment. However, the challenges with misconceptions are not adequately addressed in either the pedagogy, the environment or the technology. Within my practical experience in teaching College mathematics and based on my interview and further extension with my framing issues assignment the steps that are most critical for at risk adult learners within fundamental mathematics education are that of knowledge construct, particularly having an interactive means for observing and experiencing the phenomena and in applying understanding (the knowledge construction and knowledge refinement stages respectively) (Edelson et al., 2002).

Although there are interactive components I believe there is a level of interactivity that needs to be achieved to best suit the Mathematics exploration and clarification and/or testing of concepts, particularly to enable students to act as independently as desired in the motivation and goal directed stages described in the LFU model. These were very essential elements noted in my framing issue analysis. Also, I believe that the process of inquiry so desired would be better suited for students if it were more user friendly and allowed for onscreen manipulation of content more interactively with the steps being more interactive than just inputting data and generating a visualisation. Students should be able to interact with and change the visualisation seamlessly as well as have access to further information on call that can be used to supplement the process. Perhaps technology that is more interactive such as sixth sense technology proposed  by Pranav Mistry.

In using LFU and or a WorldWatcher based technology and model for mathematics I would utilise activities within the three steps as highlighted and emphasise the digital technology. However, I would make the technology more interactive in both the input of and manipulation of data (sixth sense and interactive white board capabilities) and I would also include a prior learning module before the motivation stage to identify or clarify misconceptions. I would also make adjustments here to the MyWorld and the LFU model by incorporating technology at this stage (clarifications of misconceptions). Misconceptions can be a potential challenge to the model as seen in the case study on ‘Learning-for-Use in Earth Science: Kids as Climate Modelers’ (Edelson et al., 2002).

Traditionally Mathematics education does not have a highly reflective component but I have found that when students reflect on their process and are able to discuss ambiguities and processes of construct and refinement then learning is enhanced and long term wins in correct schema representation and organisation are realised. I would therefore strengthen the emphasis on reflection and thought tracking and include technology that allows for collaboration through the thought tracking process, enabling interactive viewing and discussion on individual constructs with online posting and discussion capabilities.

References

Edelson, D. C., Salierno, C., Matese, G., Pitts, V., & Sherin, B. (2002, April). Learning-for-Use in Earth science: Kids as climate modelers. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, New Orleans, LA. http://www.worldwatcher.northwestern.edu/userdownloads/pdf/LFU_PF_NARST02.v3.doc

servepeet (Poster). The Sixth Sense – part 1 [Video]. (2009 November 19). Retrieved from    https://www.youtube.com/watch?v=gsQ3-aCbydk&feature=related

Integrating content studies and inquiry process learning

Educational challenges

Research and application of the Learning for Use (LFU) and WorldWatcher models were based primarily on the lack of integration of content studies with the inquiry process and for inquiry to play more of a role in scientific learning. The premise was that students were lacking strong ability to critically analyse and processes content and that the inquiry process will give students ‘a firsthand experience of the dynamic processes of questioning, evidence-gathering, and analysis that characterize authentic scientific practice.’ (Edelson, 2001,p. 355).

The major challenge as expressed above was that content and inquiry skills are taught separately  but  ‘the national science standards are based on an inquiry learning model, in which students develop deep, interconnected content knowledge and inquiry skills through activities that incorporate authentic scientific inquiry’ (Edelson, 2001,p. 356).

The researcher investigates the use of technology to support inquiry learning in order to help to create the perceived reform of integrating content and process learning in science.

The author’s theory of learning

The LFU model was designed to support instructional and activity design to achieve the integration of content and process described above. The learning theory is based on the premise that knowledge is constructed and in order to be recalled and reused futuristically it is easier to do so if learning is goal-directed, process driven, and that the conditions used in constructing and using knowledge determine how accessible that knowledge is for future use.

It is largely related to cognitive and situated cognition theories and is also constructivist (knowledge is constructed), goal directed (learning initiated by the learner) and based on context learning  (knowledge retrieved based on contextual clues); ‘ The implication of this principle for classroom learning is that the learning context must support the learner in creating appropriate indices to knowledge structures. Otherwise the learner will be unable to retrieve those structures when they are relevant in the future’  (Edelson, 2001,p. 357)

The LFU model is based on four principles:

‘1. Learning takes place through the construction and modification of knowledge structures.

2. Knowledge construction is a goal-directed process that is guided by a combination of conscious and unconscious understanding goals.

3. The circumstances in which knowledge is constructed and subsequently used determine its accessibility for future use.

4. Knowledge must be constructed in a form that supports use before it can be applied’ (Edelson, 2001,p. 357

Pedagogical design principles shaping the development of the WorldWatcher

WorldWatcher is based on a learner-centred design that empowers learners to explore, construct and utilise concepts based on principles of open ended questioning and design that engaged students in three areas:

• Motivating them to acquire new skills and knowledge
• Working with tools for computational activities needed in the acquisition of skills and  the creation of realistic knowledge structures
• Refinement of knowledge – application and use of constructed knowledge

Integrating digital technology

Digital technology is a key part of the learning experience as it offers the tools and support that enables students to compute necessary information, construct knowledge and to create, analyse and test data. It is interactive, customisable and allows for visualisation of data with affordances of allowing students to enter or create new data. It therefore offers independence and capabilities that are not possible without the technology such as computational skills (real scientific tools).

Pedagogical principles in the design process – reflection and/or suggestions

The design strategies suggest a three step process:

Motivation – (specific type of motivation) ‘the motivation to acquire specific skills or knowledge within a setting in which the student is already reasonably engaged.’  (Edelson, 2001,p. 358).

Knowledge Construction – recognizes that incremental constructs are fundamental to the process and that knowledge constructs/structures should be organised in a way to allow for linking to memory banks and experiences (prior learning) and for making connections. It is goal directed

Knowledge refinement – ‘The third step is refinement, which responds to the need for accessibility and applicability in learning for use’. (Edelson, 2001,p. 358)

Pedagogical Principles in Design elements

There are many pedagogical principles embodied within each phase/step of the design. The overarching design is learner-centred, in that the outcome is driven by learners and is largely self-directed. Motivation involves pedagogical principles of scaffolding, constructivism and contextual cognition. Students are introduced to tasks that are related to their current setting and are introduced to knowledge or skills needed. There are tools to support learning/knowledge construction (scaffolding) and the task is real-life (constructivist) and is solved or approached contextually.

In the knowledge construction phase schema and information processing theories are integral to the organisation and processing of information. Constructivist elements are presented in the self-directed goal oriented process as well as knowledge construction being linked to prior experiences.

In the final stage of refinement connectivist, schema and distributed cognition heavily influence the process. In the former, knowledge is linked to and organised within other knowledge structures. This also relates to schema and information processing theories regarding the organisation of knowledge to be accessed for later retrieval. The reflection and sharing processes support knowledge construction through distributed cognition. Application of knowledge and testing of model structures are central within the process of refinement and are largely constructivist in this sense.

Reference

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

Motivation for WISE

The motivation for the creation and development of WISE was the desire to use the power of easy to use, affordable and accessible technology to support a structured curriculum of science education using theories of inquiry-based learning and scaffolding knowledge integration in order to achieve literacy in science(Slotta & Linn, 2009). Literacy being understood as: i) understanding content, ii) knowledge and development of skills within the course and iii) understanding the nature of the course (Gobert, Snyder &Houghton, 2002) and as such WISE was created to integrate knowledge on these three levels in one learning environment: science content, scientific inquiry skills, and epistemic knowledge is WISE (Snyder et al., 2002).

As such using informed research on how students learn and how instruction is successful the power of the internet and communication tools such as reflection and discussion through distributed cognition fueled the design of WISE in a no software approach,  with embedded tools for cognition and metacognition organized in a step by step process  (Slotta & Linn, 2009).

Four pedagogical principles which motivated the development of WISE Linn (1998):

• Make science accessible for all students
• Make thinking visible – representation of students’ learning processes.
• Provide social support so that students can learn from each other – collective knowledge of the classroom and get students to consider their own and others’ ideas
•  Promote autonomy and lifelong learning, – develop science process skills, and encourage revisit and refinement

Developing a WISE project and comparison with the Jasper Adventures

A typical process for developing a WISE project

A WISE project is developed incorporating internet materials to deliver content and activities and for the completion of and discussion of tasks (Lynn, Clark & Slotta,  2003). The problem/task is designed to enable students to discuss current controversies in science and to design solutions to scientific problems. Web resources are provided to give content background. Hints and notes are a feature of the WISE software and are included in the design to help students to focus on what was learnt and use that knowledge in making predictions based on such integrations. Simulation and data visualisation tools are included to show results of students’ experiments and/or in making and testing predictions. Reflection notes are included in the design and is incdued in the step ny step design to support metacognintion, critical thinking and provide material for online discussions, which are mediated also through WISE software tools. The model also scaffolds student learning and guides process through questioning and providing hints (also included in the step-by-step process using WISE software tools). All content, tasks, problem definition, simulations, reflection, hints and discussions are input online in the WISE software in the sequence desired for students to complete. The teacher’s role during students’ use of WISE is to facilitate the process (walk around) encourage/ guide discussions and bring groups into small discussion groups.

Comparing TELE: WISE vs Jasper Adventures

The Jasper series is a collection of videos that present a number of real world problems to be solved. Factual and historical situations are presented and students are required to provide solutions. Like WISE, the Jasper series presents instruction with a problem solving approach. However, the Jasper Series focuses even more on the concept of anchored instruction in that the problem is presented in a compact presentation and students’ learning is anchored on that specific problem, only the problem is presented.  Jasper requires the learner to seek solutions that may require the teacher to use supported environments that simulate/ aid scaffolding activities. WISE is more comprehensive in creating the one learning environment experience.

A lesson from WISE is the inclusion of reflection and metacognitive elements within the tasks themselves. A lesson from Jasper is to use multimedia and presentation tools that motivate and present anchored problem solving using real experiences but also to give students enough motivation to seek out additional information.

Perceived limitations, hindrances or constraints related to WISE

WISE has a number of limitations that have to do with infrastructure, access, training and pedagogy. The internet is the base of the technology and without internet and/or computer access cannot be facilitated.

The knowledge of how to use and navigate the software and environment as well as how to facilitate and/or provide support to students may be not be intuitive for many teachers, which would mean increased time and pressure for training, creation and use. Even for ‘experienced’ teachers development time can be a challenge however teachers are able to change/share or modify lessons

From a pedagogical perspective, while I support the use use of hints, reflections et al. in the scaffold nature of the WISE environment I do think that the structured step-by-step process may limit divergent thinking and the process of discovery and inquiry desired. The Jasper series to this end, in its deliver and structure, would create more independent learner-directed approaches to problem solving and embodies discovery learning more so than WISE. That being said, there is great value in the WISE approach but I see it more beneficial to at-risk-learners and younger students in primary levels and lower graded within secondary levels of education.

Using a WISE project and adding customisations in WISE

A WISE project can be designed and delivered to target different outcomes. To show how to use a WISE project the example of Plate Tectonics lesson by Snyder et al. (2002) will be used as reference. The “What’s on your plate?” unit was used to investigate students’ understanding of models and to explore this understanding on model-based reasoning. Activities in WISE were designed to facilitate the outcome. There were two groups of students who would later discuss their results in collaborative and distributed cognition structures:

1. Students’ Model Building & Explanation of their Models.

One group of students constructed, in WISE visual models of plate tectonic-related phenomena while the other drew models of earthquake or volcanic eruption.

Using prompts embedded in WISE in iterative steps each group wrote,  in WISE a short explanation for their models. Students then posted their models and explanations to be viewed across groups.

2. Students’ Evaluation and Critique of the Learning Partners’ Models.

Students authored responses, based on set criteria of elements to be included, designated by prompts. Two texts were provided to support students’ knowledge of how to evaluate models and elements to be included in the critique. Evaluations were discussed in class and posted online facilitating a two way discussion.

3. Students’Model Revision&Justification.

Students read evaluations and were asked to revise their models based on the critique given and content knowledge and write a revised explanation for their new models.

They were asked to justify changes to their models in WISE. Prompts also guided this activity.

4. Geology Websites.

On-line field trip exploring phenomena was conducted and students were guided to other websites. They were asked to write a reflection on “site visit”, about what they have learned. The reflection was guided by prompt notes.

5. Dynamic-runnable models.

Models enabling visualizations were included.

Customising WISE

I would like to include elements to enable modification/sharing of lessons to facilitate cultural and global collaborative learning and sharing.

Currently teachers are able to take lessons et al. and remodel for culturally specific and reflective content. In the sharing platform at WISE then teachers should be able to see and analyse and perhaps present lessons from different perspectives for their students.

WISE could create a space/category for culturally adjusted lesson (or a tagging system). Here teachers know where to go and compare and/or use lessons for cultural, globally diverse learning experience.

References

Gobert, J., Snyder, J., & Houghton, C. (2002, April). The influence of students’ understanding of models on model-based reasoning. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), New Orleans, Louisiana.
Retrieved Saturday, October 29, 2005 from: http://mtv.concord.org/publications/epistimology_paper.pdf

Linn, M., Clark, D., & Slotta, J. (2003). Wise design for knowledge integration. Science Education, 87(4), 517-538.
http://onlinelibrary.wiley.com/doi/10.1002/sce.10086/abstract

Theoretical framework

The theoretical framework underpinning the Jasper series is on anchored learning in which instruction is anchored on solving a complex problem. It is a constructivist approach in which students have a meaningful experience. In this experience problem setting is essential and forms the basis of that meaningful experience. Understanding how people think is an essential element to the foundation for the Jasper model (Pellegrino & Brophy, 2008),

Instruction/Materials supported

The type of instruction that materials support are:
• Scaffolding,
• Practice
• Feedback
• Revision
• Reflection
• Community learning (distributive cognition)
• Divergent thinking/ instruction (The what if scenario)
• The inquiry process/discover learning.

Materials supported are context specific and activity oriented developed in levels, with increasing independence. It supports independent learning, all information required are presented in the question, as well as collaborative learning.

The Technology

A series of interactive movies with defined problems.
The technology provided anchors for the instruction, content, and the problem , as well as provide the structure for independent and collaborative work.

Potential Cognitive and Social Affordances of the technology

The SMART and STAR structures enable the tracking of thought patterns, progress and direction setting for both students and teachers (Pellegrino & Brophy, 2008). Students are also enabled to structure problems into manageable and separate and more approachable sections while distinguishing between relevant and not needed data (Vye et al., 2009). Students are also able to understand what they need to research and are engaged in interactive and independent self-paced learning. Learning is further enhanced through the application of concepts rather than learning concepts out of context and then practicing through drills and practice.

Commentary

After reading up on the Jasper series, viewing videos and engaging in approximately one week of discussions with my colleagues on theoretical frameworks, models of instruction and types of instructional media, amongst other considerations, anchored instruction proved relevant and desirable in enabling real-world contexts for learning and increasing problem solving skills. With new media and technology available then interaction with and extrapolation of problem solving activities are strengthened and increase possibilities for meaningful learning experiences.

The Jasper series having a focus on how people think is essential for me. I spend a lot of time questioning to garner such information. However, this competes with the time spent on going through the content. I have turned to technology for assistance by posting videos, notes and practice questions. However, the Jasper series started me thinking that I perhaps need to include the problem solving aspect through video and other media alongside content delivery. My colleague Darren pointed out that as problems become more complex/in-depth then collaboration can be encouraged or becomes necessary.

In my discussion with Diane the structure and representations of theoretical frameworks within learning theories seen in the Jasper series were central to design and effectiveness. The series centres itself in cognitive and pedagogical practice in understanding how people think, across age groups et al. The necessity for Learning theories and continued scientific research in and application of theories of learning, information processing, retention levels and instructional design was apparent.

Anchored instruction in real-life, adventure based contexts, add interest to lessons and content. However, I do not think that real world scenarios are always possible. Students can be structured within an inquiry based and critical thinking model that can achieve application of concepts and so I agree with my colleague, Danielle, that in instances where real-world applications are not readily available then interactive (virtual and hands-on systems) technology and/or processes are necessary in bridging the gap. It therefore provides questions and design challenges and implementation for such when virtual and hands-on ‘manipulatives’ are not available.

I am constantly searching for ways of creating relevance for some topics, for eample quadratic equations. This consideration leaves me questioning problem solving and authentic learning models as to distinguishing them in validating problem solving as a skill not needing the content to be relevant to life but the process integral in creating the skills.

References

Cognition and Technology Group at Vanderbilt (1992a). The Jasper experiment: An exploration of issues in learning and instructional design. Educational Technology, Research and Development, 40(1), 65-80. http://ezproxy.library.ubc.ca/login?url=http://dx.doi.org/10.1007/BF02296707

Vye, Nancy J.; Goldman, Susan R.; Voss, James F.; Hmelo, Cindy; Williams, Susan (1997). Complex Mathematical Problem Solving by Individuals and Dyads. Cognition and Instruction, 15(4), 435-450. http://www.tandfonline.com/doi/abs/10.1207/s1532690xci1504_1

Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303. http://ezproxy.library.ubc.ca/login?url=http://dx.doi.org/10.1007/978-0-387-76898-4_14