Students usually encounter difficulty when learning exponent laws in junior math classes.  Whether it is related to keeping the laws straight in their heads, applying them, or conceptually understanding what is really happening.  I identify this as a challenge from the numerous quizzes and tests that I have marked over the years.  Like other challenges in math class, I often see students memorizing the rules so that they can apply them to get marks.  For some teachers, the difficulty in this topic lies in finding a way for students to construct their understanding.  Usually, teachers will show what the rule is and how it works and then let the students practice.

I found a desmos activity that is not necessarily a simulation, but an interactive resource that engages students in creating and understanding the exponent laws.  The students start with compiling cards with various representations of exponents into like piles, I would insert group collaboration to compare and generate the exponent rules.  Then students have a few more activities (that are submitted to the teacher) which encourage reflection of the exponent laws, or evaluation.  Next, students are asked to create their own expression with an answer key and submit to class for more collaboration. This step can encourage modification of the rules if students are encountering incorrect answers. A final challenge can solidify any changes to the initial rules.

*Not sure if other math teachers have seen this resource https://teacher.desmos.com/

WISE is a customizable platform created by professionals from the educational, technological, and scientific fields that is a resource which uses the internet and various interactive activities to facilitate students in knowledge construction.  It is founded on principles of the SKI framework, cognitive apprenticeship, and constructivist pedagogy.  SKI promotes knowledge integration through its technological and curriculum design in four major ways.  SKI make science visible or identifies new goals for learning, makes thinking visible, provides social supports and helps students learn from each other, and it promotes lifelong autonomous learning.

While both WISE and the Jasper series are intended to engage a student in inquiry-based learning, they clearly have their differences.  WISE is a more modern approach that integrates interactive technology to facilitate knowledge construction.  The Jasper series is a narration or story in which a problem unfolds that students need to solve, whereas WISE is a series of activities that take the student on a learning journey in a more structured format.

I think WISE projects would make for excellent resources for students with alternate learning scenarios, whether it be students with learning difficulties or students who miss a lot of school because of sports or health situations.  WISE’s customizability is an amazing feature that puts the teacher in the designing chair so a project can be changed according to its intended use to suit the needs of the learners or teacher.  At this point with my limited exposure to WISE, I don’t think I would change anything, but rather make more projects available covering more subjects and grade levels.

In what ways would you teach an LfU-based activity to explore a concept in math or science? Draw on LfU and My World scholarship to support your pedagogical directions. Given its social and cognitive affordances, extend the discussion by describing how the activity and roles of the teacher and students are aligned with LfU principles.

I would incorporate Google Earth into an inquiry project where the students are challenged to find two or more different shaped real-life world structures (solids) that have the same volume or surface area.  It would be ideal to infuse many opportunities for collaboration/discussion amongst the students when possible. These communications do not necessarily need technology, but rather an opportunity to communicate ideas, difficulties, arguments, and connections.

Motivate

The context of the inquiry itself creates demand.  Students will need to calculate surface areas and volume to complete the task. Using Google search can give students a starting point from which they can build hypotheses and initial projections.  The initial research may present a gap in their knowledge with calculating surface area or volume of real-life world structures which elicits curiosity. Through the process of making predictions students will be relying on prior conceptions.  Edelson (2001) declares that “articulation of prior conceptions has been recognized as a valuable technique for identifying potential misconceptions and for activating existing knowledge structures to which new knowledge can be connected” (p. 376).

Knowledge construction

Using Google Earth allows students to compare, take measurements, and observe the solid structures from all over the world via firsthand experience, which could not be done otherwise. Students or teachers may interact with media or each other to foster communication to support knowledge construction.  I think it is important to note that knowledge construction does not always happen on the first exposure of a step by step process.  Often it is a “continuous, iterative, often cyclical process that consists of gradual advances, sudden breakthroughs, and backward slides” (Edelson, 2001, p. 377).

Knowledge refinement

Through reflection and application, students can refine their knowledge so it is established for future retrieval and use (Edelson, 2001).  I would use structured journal entries for students to compile a project journal that they can use to share and discuss with other students. Other teachers or disciplines may choose to use a collaborative learning environment that would facilitate discussions.  I would specifically have students compare their initial projections with their results and reflect on how the thought process has changed in making those predictions.  The students would also use applications that would enable them to create a final presentation of their reflections including their initial/final thoughts. This last step allows technology to be a tool of necessity for students to apply their newly constructed knowledge.

While this activity does not factor in GIS software, this concept is related to spatial literacy.  A teacher may wish to expand on connections to spatial literacy, especially since Google Earth may be a suitable tool to do this with. Realistically, “a spatially literate workforce and citizenry able to access, manage, visualize, and interpret information, also capable of multidimensional thinking, are vital to… address the world’s complex problems (Perkins, Hazelton, Erickson & Allan, 2010, p. 213).

References

Edelson, D. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal Of Research In Science Teaching, 38(3), 355-385. doi: 10.1002/1098-2736(200103)38:3<355::aid-tea1010>3.0.co;2-m

Perkins, N., Hazelton, E., Erickson, J., & Allan, W. (2010). Place-Based Education and Geographic Information Systems: Enhancing the Spatial Awareness of Middle School Students in Maine. Journal Of Geography, 109(5), 213-218. doi: 10.1080/00221341.2010.501457

PCK is essentially how subject material is presented to students for learning. Specifically, how “the teacher interprets the subject matter and finds different ways to represent it and make it accessible to learners” (Mishra & Koehler, 2006. p. 1021). Shulman (1986) presents the urgency for teachers to have knowledge of the most effective teaching strategies that can help counter student misconceptions and how this needs to be a part of the definition of PCK. This thought resonated with me, especially since the beginning of Module A of this course started with misconceptions in math and science classrooms.

TPACK “is an understanding that emerges from interactions among content, pedagogy, and technology knowledge” (Koehler, Mishra & Cain, 2013). This brief description steers educators in the direction of having knowledge of the three individual components, but more so understanding the intricate relationships formed in the intersections of the components, and their applications.  In my reflection of TPACK I was drawn to the idea that effective teachers utilise TPACK every time they teach, and every scenario or context coupled with every unique teacher means that there are endless applications of what TPACK looks like in the classroom.

An example of PCK that came to mind for this post is using BEDMAS to help teach the order of operations in algebra.  That to me is an example of a generic pedagogy used to teach math content.

References

Koehler, M., Mishra, P., & Cain, W. (2013). What is Technological Pedagogical Content Knowledge (TPACK)?. Journal Of Education, 193(3), 13-19. doi: 10.1177/002205741319300303

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.

Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 -14.

There are a few commonly acknowledged issues surrounding motivation, level of understanding and knowledge application when teaching and learning mathematics. As students reach middle school, interest and motivation in mathematics drastically declines and working with unmotivated students becomes the largest challenge during these years (Chao, Chen, Star & Dede, 2016). Students are gaining knowledge at surface levels to jump through assessment hoops, leaving them unsure of why they are learning math concepts or how to apply the concepts in their lives.  It is inarguably important to develop component skills, especially in the context of meaningful problem posing and solving activities (Cognition and Technology Group at Vanderbilt,1992a). The culmination of these issues results in students who are unmotivated, uninterested, and lack thinking and problem-solving skills.  I have first hand experience with students who have factual mathematical knowledge but are not able to use it towards solving word problems either because they don’t know how to, or they become super anxious.  Typically, learners do not know how to apply their learned knowledge to find solutions.

In these situations, the role of the teacher is best enhanced with strong pedagogical content knowledge (PCK) because the teacher “interprets the subject matter, finds multiple ways to represent it, and adapts and tailors the instructional materials to alternative conceptions and students’ prior knowledge” (Koehler, Mishra & Cain, 2013, pp. 15).  PCK can help the educator find effective teaching strategies such as anchored instruction for learning math concepts.  Grounded on theories of constructivism, situated learning, and cooperative learning, anchored instruction (AI) provides opportunities for learners to use generative learning in real-life inquiry scenarios. Park and Park (2011), solidify that using problem-based learning in schools creates an avenue for student to experience real-life problems.  The latest literature that I have read reports increased positive feeling towards using AI to learn. Specifically, AI instruction created a motivating environment to learn in for all abilities of students, problem solving and thinking skills increased and the group interaction supported generative learning as they worked together to create problem structure (Shyu, 2000).

The Jasper materials are designed in such a way that they can meet requirements of the above-mentioned grounding theories of AI.  They have real world contexts that support complex, open-ended problem solving, communication, and reasoning; more connections from mathematics to other subjects and to the world outside the classroom (Cognition and Technology Group at Vanderbilt,1992a).  The key issues of motivation and interest are targeted by the seven design features specific to AI.

For the purpose of mathematical instruction, contemporary videos do not address issues raised in this post when stacked against the Jasper series videos. Contemporary videos might use current technology that offer other affordances, however, they all are based on direct teacher led instruction of mathematical concepts.  They are created for brushing up skills, supplementing teacher instruction, cramming for tests, or supporting weaker students.

References

Chao, T., Chen, J., Star, J., & Dede, C. (2016). Using Digital Resources for Motivation and Engagement in Learning Mathematics: Reflections from Teachers and Students. Digital Experiences In Mathematics Education, 2(3), 253-277. doi: 10.1007/s40751-016-0024-6

Koehler, M., Mishra, P., & Cain, W. (2013). What is Technological Pedagogical Content Knowledge (TPACK)?. Journal Of Education, 193(3), 13-19. doi: 10.1177/002205741319300303

Park, K., & Park, S. (2011). Development of professional engineers’ authentic contexts in blended learning environments. British Journal Of Educational Technology, 43(1), E14-E18. doi: 10.1111/j.1467-8535.2011.01244.x

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. doi: 10.1007/bf02296707

From all the tidbits that I include in my mind that help define technology, I would say it is something that can support meaning making by students when students learn with rather than from technology by utilizing tools and their applications (Jonassen, 2000).  Designers of learning experiences need to know their learners’ strengths/weaknesses, prior knowledge, and a clear precise goal of what they are trying to achieve with their TELE.

The TELE should be designed in a way that it supports:1) inquiry and exploration to acquire new knowledge 2) collaboration to construct and integrate the knowledge and 3) creation to showcase the learners understanding or application of the knowledge.  Technologies in TELEs can be thought of as vehicles whose “functionality relies not only on their attributes but also on their context, the logistical systems and infrastructures that afford their functionality” (Jonassen, Campbell & Davidson, 1994).

References

Jonassen, D. H. (2014). Mindtools (Productivity and Learning). Encyclopedia of Science Education, 1-7. doi:10.1007/978-94-007-6165-0_57-1

Jonassen, D., Campbell, J., & Davidson, M. (1994). Learning with media: Restructuring the debate. Educational Technology Research And Development, 42(2), 31-39. doi: 10.1007/bf02299089

The Jasper series videos are examples of anchored instruction where students are invited to join a narrative story which relates to real-life and leaves them to solve an open-ended complex problem where all the necessary and relevant information is presented.

Through the eyes of an educator I had a few questions:

-Throughout the videos it appeared that there are smaller questions posed to the students? What opportunity do the students have to generate their own sub-goals? Or is this done so that the task seems achievable?

-I was wondering why definitions are provided when that seems like a great opportunity for students to do some inquiry? Is this because of the era (late 1980’s) of the videos and the lack of technological resources? i.e. Google.

A few positive thoughts to note about the Jasper series 2 videos as a TELE designer:

-The videos were more engaging and relatable to students unlike the Jasper series 1 videos ( adults flying and fishing in the woods)

-The notion of a community of learners made the viewer feel included and that their contribution was important

-Some of the videos had students as the speakers which was another relatable feature

-Difficult concepts such as scale proportions were displayed well and made the concept easy to understand

-Digital software uses made it easy to understand spatial representations.