Reflections on Jasper Series Symposium

Anchored for Success: Technology-Enhanced Activities

Fig 1. Learning in Technologically Enhanced Spaces. Image credit: BWBR

As education evolves, new approaches to learning emerge, each with its own set of advantages and disadvantages. One such approach is anchored instruction (AI), which utilizes authentic contexts to promote critical thinking and problem-solving skills, collaborative learning, and knowledge construction. Bransford et al. (2000) state that such an approach “helps learners acquire both the knowledge and the know-how required to apply it in real-world situations” (p. 51). Here is a summary of key points benefits and criticisms of the AI approach, specifically in the context of the Jasper Woodbury Adventure Series, as discussed in the Symposium.

Using an AI approach, such as the Jasper Woodbury Adventure Series, offers numerous benefits to students such as improving their engagement and motivation, promoting critical thinking and problem-solving skills, and providing opportunities for collaborative learning and knowledge construction. This is achieved through scaffolding students’ understanding, using authentic contexts, and integrating technology to support learning. Additionally, this approach also allows for a shift in the teacher’s role from being a primary source of information to providing structure, guidance, progress monitoring, and assessment of student learning outcomes, thus the process is student-centered and more likely to result in meaningful, transferable learning outcomes. Kim & Hannafin (2011) propose a three-dimensional framework for scaffolding, which includes purpose, source, and interaction (Fig. 3).

Fig 2. Types of TELE Scaffolds for AI
Image: Stevan W
Fig 3. Dimensions of Scaffolds.
Image: Kim & Hannafin (2011)

Alternatively, the Jasper Woodbury Adventure Series also presents various challenges, such as the cost to purchase the program, potential technology struggles for some students, and the need for additional teacher training. Other criticisms note that AI as a method is not always effectives in that students may require a more direct approach for certain skills and concepts and there are some research  findings that indicate AI methods in mathematics may be less effective than traditional instruction in improving students’ procedural knowledge of algebraic problem-solving.

Fig 4. Pedagogical Frameworks for Instructional Activities. Image Credit: Gayathrie

In closing, the symposium has consistently emphasized the benefits of AI to students in terms of their engagement and motivation, critical thinking, problem-solving, and collaborative learning, yet there are some challenges to keep in mind. Hmelo-Silver (2004) notes that “Effective teaching is not about following a recipe, but rather it involves making thoughtful and strategic decisions that take into account the unique needs and characteristics of individual students and groups” (p. 253), and the symposium illustrated this complexity in the conversations.

References

Bransford, J. D., Brown, A. L., & Cocking, R. R. (2000). Learning and transfer. In J. D. Bransford, A. L. Brown, & R. R. Cocking (Eds.), How people learn: Brain, mind, experience, and school (pp. 51-78). Washington, DC: National Academy Press.

Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational psychology review, 16(3), 235-266.

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The Jasper Series

The Adventures of Jasper Woodbury

(a.k.a. The Jasper Series)

Fig. 1. The Jasper Series and Technology Integration. Credit: Van, S.

The Jasper Series is a math multi-media education project consisting of 12 digital videos that targets students at grade 5 and higher. The project was developed by a group of researchers from the Cognition and Technology Group at Vanderbilt University between the late 1980’s and mid 1990’s to promote students’ interest in and ability with solving mathematical problems and engaging in mathematical thinking. The videos revolve around Jasper Woodbury and relay stories in context rich, authentic, problem-posing scenarios that are designed to engage students in mathematical problem solving and reasoning. The challenges also aim to support student communication and collaboration and provide interdisciplinary connects to other subject areas.

Constructivist and TPACK Underpinnings

Fig. 2. Constructivist Design. Credit: Gronseth
Fig 3. TPACK Framework. Credit: TPACK Org 

The Jasper Series is formulated around a constructivist learning theory, which posits that both prior and experiential learning, combined with opportunities to develop thinking through process of exploration, investigation, reasoning, justification, and reflection, is a requirement of learning (Cobb, 2005; Fosnot & Perry, 2013; Posner et al., 1982; and Von Glaserfeld, 2005). The Jasper video stories are situated in real-world events with real-world challenges and include multiple forms of connected information. The use of a content-rich context to situate and develop diverse problem-solving solutions is a strategy known as anchored instruction (AI). The pedagogical strategy has connections to case-based learning (Hallinger, Leithwood, & Murphy, 1993, as cited in UBC ETEC533, n.d.), problem-based learning (Duffy, Lowyck, & Jonassen, 1993, as cited in UBC ETEC533, n.d.) and project-based learning (Dewey, 1933, as cited in UBC ETEC533, n.d.). These constructivist strategies highlight authentic, situated, collaborative learning problems as a means to facilitate learning that is more meaningful, memorable, and transferable.

Teacher Questions on Anchored Instruction

I accept the constructivist premises outlined above, and as I consider embedding AI in my practice, I have the following questions:

  • Given a well-developed anchor activity, how could I use it to as a starting point for further customization?
  • What contexts would adult learners in a foundational course find most engaging?
  • What are the advantages and disadvantages of giving different student groups slightly different contextualizations?
  • What modification strategies are recommended for anchor activities when dealing with various learner characteristics and needs? For example, ELL students, students with poor mathematical self-efficacy beliefs, students with weak prior knowledge and/or application skills?
  • What emphasis in graded assessment of anchored activities is appropriate?
  • What would a rubric for an anchored activity assessment include? Is there a starting example that can be customized?
  • Can artificial intelligence tools be used to support the implementation of anchored instruction? For example, can artificial intelligence tools assist with activity customizations and student support?

References

Cobb, P., (2005). Chapter 3: Where is the mind? A coordination of sociocultural ad cognitive constructivist perspectives. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice, (2nd ed., pp. 39-57). Teachers College Press.

Fosnot, C. & Perry, R. S. (2013). Chapter 2: Constructivism: A Psychological theory of learning. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice, (2nd ed., pp. 8-38). Teachers College Press.

Gronseth, S. (2015, November 12). Constructivist approaches [Video]. The University of Houston. https://www.youtube.com/watch?v=krqjqGIuC-A

Koehler, M. (2011, May 11). Using the TPACK image. TPACK Org. https://matt-koehler.com/tpack2/using-the-tpack-image/

Posner, G. J., Strike, K. A., Hewson, P. W. and Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66: 211–227. doi: 10.1002/sce.373066020

UBC ETEC533. (n.d.). Lesson 1: The Jasper Project. University of British Columbia. Retrieved from https://learning.edge.edx.org/course/course-v1:UBC+ETEC533-65A+2022W2/block-v1:UBC+ETEC533-65A+2022W2+type@sequential+block@51113f4c02184ecdacf47e7c47a0a622/block-v1:UBC+ETEC533-65A+2022W2+type@vertical+block@d90e562b36294469b5a5ddbadffe9f1d on February 17,  2023.

Van, S. (2017, February 15). Anchored instruction educational model: Model research presentation [Video]. The University of Memphis. https://www.youtube.com/watch?v=3xOTvc_dKUg

Von Glaserfeld, E. (2005). Introduction: Aspects of constructivism. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice (2nd ed., pp, 3-7). Teachers College Press.

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PCK and TPCK: Two Theoretical Frameworks Describing Teacher Knowledge Required for Effective Teaching

PCK and TPCK are two theoretical frameworks that examine the necessary teacher knowledge and skills required to effectively teach a given body of knowledge.

(ChatGPT, 2023)

A Brief History of Teacher Knowledge Frameworks

In “Those Who Understand: Knowledge Growth in Teaching,” Shulman (1987) presents a condensed history of teaching and how the theory and practice of assessing the fundamental skills and knowledge has evolved. Shulman, an American educational psychologist, educator, and reformer, developed a theory of teaching outlining integrated pedagogical and content knowledge as the precursor to developing an effective teaching practice (Bowman, 2023). He argues that teaching consists of three kinds of teacher knowledge: 1. knowledge of the discipline, 2. knowledge of the practice, and 3. strategic reasoning. He coined the phrase “pedagogical content knowledge” to encapsulate these components that bridge the teacher’s subject matter expertise and students’ educational outcomes.

Through time, Shulman’s Pedagogical Content Knowledge (PCK) framework evolved into a range of derivative models that expanded the PCK framework by including additional knowledge components such as curriculum, instructional strategies, assessment, and teaching orientations (Kind, 2009, as cited in Shulman, 1986). As the 21st century heralds an expanding use of digital technology in teaching and learning, Mishra and Koehler (2006) formulate the Technological Pedagogical Content Knowledge (TPCK) framework to reflect the evolving role of technology and the importance of how technology relates to the pedagogy and content knowledge when it comes to good teaching.

Examining A Teaching Example Using The PCK Framework

Content/Curricular Knowledge – Learning Goal

The learning goal is to understand the concept and process of creating equivalent fractions and adding fractions. This is a re-occurring concept and skill that has been addressed in pre-requisite courses. It is a foundational numeracy skill and critical for working with rational expressions algebraically in future courses.

Pedagogical Knowledge

Equivalent Fractions: Learning is contextualized in the life skill of cooking or eating (there is a lot of quantification around recipe ingredients and pizza/pie). Essential vocabulary is presented and represented in different forms (symbolically, pictorially, verbally) to support the fraction concept. Equivalent fractions are developed and analyzed pictorially and symbolically; patterns are identified and generalized to a mathematical process using direct instruction followed by paired or individual practice.

Adding Fractions: Fraction addition (and later subtraction) is the first operation taught, practiced, and (hopefully) consolidated before multiplication and division. A sample question is procedurally developed and analyzed using the Cornell Notes (https://www.mpsaz.org/shepherd/staff/klkastnerlew/math7notes/files/adding_fractions.pdf) method for math as a scaffolding strategy as illustrated in Fig. 1. This scaffolding strategy is repeated with all four operations as they unfold in class.

Fig. 1. Scaffolding as Instructional Strategy. Image: Mesa Public Schools

Contextual Knowledge

Learners are expected to have this background, as reflected by a placement test or pre-requisite course completion; therefore, this goal is approached as an exercise in review, clarification, reinforcement, consolidation, and application activity. However, learner skills can vary widely; thus, the LMS course shell contains supplemental materials for further instruction and practice, such as videos, worksheets, and online games, through the LMS course shell. Many learners are English Language Learners (ELL), and vocabulary can be a barrier. Learners also have access to learning coaches and tutors, and this resource provides individualized one-on-one courses and general learning support. Although there are other instructional methods to consider, this approach addresses time constraints (less than one entire period) and the learners’ appreciation for concise, direct instruction when dealing with review topics.

Assessment

This lesson involves formative assessment. As the teacher, I assess formatively during strategically integrated class discussions and student practice. Students self-assess throughout the lesson practice using the solution key and peer support.

Technology

Technological tools integrated within the lesson are primarily those employed by the instructor for lesson delivery (OneNote and MS Teams for hybrid deliveries). Later, students can use technology to access any supplemental materials. Given that technology is an optional support, not a key strategy in the learning design, I would position this lesson in the PCK framework, not the TPACK framework. My lesson analysis shows evidence of all five teacher knowledge components as outlined in the consensus model of PCK as described by Kind (2015) in Fig. 2.

Fig 2. Consensus model of PCK. Image: Kind (2015)

References:

Bowman, C. (2023, January 1). Lee S. Shulman. Britannica. Retrieved February 13, 2023, from https://www.britannica.com/biography/Lee-S-Shulman

ChatGPT. (2023). How is PCK different from TPCK? ChatGPT. Retrieved February 13, 2023, from https://chat.openai.com

Kind, V. (2009). Pedagogical content knowledge in science education: Perspectives and potential for progress. Studies in Science Education, 45(2), 169–204.

Kind, V. (2015). On the beauty of knowing then not knowing. In Re-examining pedagogical content knowledge in science education (pp. 178-195).

Mesa Public Schools. (n.d.) Adding fractions. Mesa Public Schools. Retrieved February 14, 2023 from https://www.mpsaz.org

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

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

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The Intersection of Technology, Teaching, and Learning

What is Technology?

In preparation for thinking about technology-enhanced learning environments (TELEs), I first answer the question, “what is technology?” This expansive question results in different answers, reflecting various perspectives and priorities. Although in this course, our focus is on technology for learning, I cannot shake my commitment to a much broader definition, thus Roblyer’s (2012) description resonates; technology is us – our tools, our methods, and our own creative attempts to solve problems in our environment. Robyer’s description allows for flexibility in outlining technology as a means (using tools and methods) to solve (contextualized) problems.

The Teacher as Designer

TPACK and TELE Design. Image: Smore

I similarly reflect on what I think a learning designer, such as myself, should “do” when creating a TELE. I extract two primary elements for consideration: the pedagogical goal and my perspective as an experienced “expert” teacher, and expand with many others. Not surprisingly, there is no clear answer, only multiple considerations within a heuristic approach of what I think will satisfy the goal as best as possible, given all the different contextual constraints. Teaching and designing can be examined reductively to elements of practice, curricular content, technological tools, and student needs, but it is ultimately a creative endeavor that defies a prescriptive approach

Designing a Trip: A Metaphor for TELE

Image: Travel as Learning Metaphor, by Deb Baff

Previously, in the “Unpacking Assumptions” discussion, I envisioned the characteristics demonstrating the ‘good’ use of technology. I use this to create a travel metaphor where the ideal technologically-enhanced learning environment (TELE) is akin to a perfect travel excursion. My trip begins with a specific destination with some targeted purpose(s). With the expert support of a travel agent to help me, I build my optimal experience. The travel agent ensures that I have the necessities covered for my trip, yet also provides me with various enriching choices to keep me engaged and interested. The travel agent understands the importance of providing activities that reflect the unique environment, including practical and affordable transportation, and providing opportunities to understand, share, and compare cultural aspects of the local community. The travel agent gives me structured yet flexible options whenever feasible. When my trip is over, I have a suitcase of souvenirs and a head full of memories that help me remember, apply, and share my experiences.

The symbolism within my metaphor is mapped in below in Figure 1.

My Travel ExperienceMy Learning Experience
Travel Destination (purpose)Learning Objective (pedagogical goal)
Travel AgentEducational Instructor
Basic Necessities (meals, rooms)Foundational Knowledge and Skills
Selection of In-House Activities or Elective Excursions (build your own itinerary)Choice of Learning Activities to For Varied Interests or Abilities Activities (autonomy, personalization, UDL principles)
Exploration (self-guided or tour guide)Active Learning (scaffolded to varying degrees)
Relevant Local AttractionsContextually Authentic
Mode of TransportationTechnological Tools
Cultural Events & LearningsSocial Constructivist Component(s)
Residuals from the Experience (memories, souvenirs, new appreciations)Growth in Knowledge, Skills, and Affect,
Sharing With and Support From Travel CompanionsCollaborative Learning Community
Figure 1: Travel Metaphor Symbolism

In summary, just as there is no single representation of an ideal travel experience, the same can be said of the quest to construct the ideal TELE experience. Rather, each is a unique and complex blend of skillfully crafted elements that provide the best possible options for the recipient.

References

Roblyer, M.D. & Doering, A. (2012). Integrating educational technology into teaching, (5th Ed.). Upper Saddle River, New Jersey: Prentice Hall.

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Implementing Technology in the Classroom: A Teacher’s Perspective

The following article summarizes key statements made by Teacher T, a veteran educator with over 20 years experience focused in the field of adult education. In the interview he shares his practice, observations, and insights related to his use of technology in the classroom.

Section 1: Tools for Communication and Engagement

Image: Student Engagement, Shutterstock
Interview ExcerptsAnalysis

“They will see well they’ll see me using lots of different types of software, obviously. Things like PowerPoint and OneNote, used through a platform such as MS Teams.”
The descriptor “obviously” conveys an assumption that these tools are routinely used by instructors in most educational contexts. This will not be the case, and such an expectation can be a source of anxiety for teachers that do not fit this mold.
“For student use, I like the classroom engagement kinds of software.”
 
“I use lots of gaming software: Quizizz, Quizlet, a little bit of Kahoot.”
 
“All the [gaming] software is now pretty intuitive and easy to learn.”
 
“If you need something that’s quick, you can just use [Quizizz] questions from other teachers. But even preparing the questions themselves, it’s pretty quick. It’s not onerous by any means”.
 
“[The frequency of gaming activities] depends on the modality, but twice a week for sure.”
 
“…the level of course does not matter.”
Some technology tools are relatively easy to learn. Depending on the content and purpose, there may be developed activities available online to reduce teacher workload. This helps to address the issue that incorporating new technology can be intimidating and time consuming, by selecting tools that perform well according to common usability criteria. (Dix et al, 1998, & Nielsen, 2003, as cited in Issa, & Isaias, 2015). 
“Every now and then I use it just for fun, you know, just to mix things up, but the large majority of time I use it is for formative assessment.”
 
“Poll Everywhere is a good [formative assessment] software.”
This comment speaks to the high pedagogical value of the engagement software. This category of tools provides social engagement, motivation, review and reinforcement of curricular objectives, differentiated instruction, and valuable feedback for the teacher and learners. This demonstrates how technology can address multiple best practice strategies simultaneously.
In order for students to participate, “they’re going to have to either have a laptop or some sort of mobile device … to take part in these games.”The context here is an adult learning program which expects that learners have access to technology. It is a false assumption to rely on this, for in reality, there will always be exceptions, particularly in the class setting. This can be an equity issue, and teachers will need to consider options to accommodate students fairly.
Table 1: Excerpts Related to Tools Used With Students

Section 2: Tools for Developing Course Resources

Image: Teacher Tools,CyberLink
Interview ExcerptsAnalysis
 
“I use [Geogebra] to help me create images.”
 
 “…[Camtasia] is incredible; it’s amazing. [With it] you can edit recordings.”
A common assumption is that effective use of educational technology requires students directly interact with technology. It is helpful to expand this and recognize that teachers’ use of technology also benefits students, indirectly. Here, the teacher uses technology to improve the quality of student materials, implement UDL principles, and increase learner access and autonomy around instruction.
“I had [Math 20-2] for six years in a row, and so I was able to make just about every class example video for that, so now students can work through class examples on their own. They don’t need me around. That’s particularly helpful.”An important revelation here is the amount of time that it takes for teachers to develop comprehensive technology-based materials and activities. A common concern expressed by teachers is the amount of time required to implement technology. This comment legitimizes that concern, and reflects the issue of time required to implement technology to it’s full potential.
Table 2: Excerpts Related to Tools Used for Course Resources

Section 3: Factors Contributing to Teacher Development

Image: Teacher Development, My Cool Class
Interview ExcerptsAnalysis
“I don’t know if I’m a guru for trying lots of things, maybe like being a pioneer … pioneer is not the right word, but we’ll go with that. We’ll call me a guru.”This quote reflects the teacher’s belief that he has been an innovator in his practice, relative to the working context, and that he has now reached a level of comfort and expertise, thus is a “guru”.
“As a department, I’m not sure that we set any direction at all, because we’re very autonomous. We’re told ‘Here’s your assignment, just go do your thing.’ There’s no inventory of what the teachers are doing. Implementation of technology depends on the course, the teacher, and the student.’’The significance of this is many teachers pursue their technological skills and practice in relative independence, sustained over time by various professional developments and their own action research, eventually becoming proficient through trial and error.
Table 3: Excerpts Related to Factors Influencing Teacher Development

My Reflection: Examining My Issue in The Context of the Interview Abstracts

Image: Reflective Teacher, http://mpimentelpro.weebly.com/9-reflection.html

The issue I will be examining is the design of effective STEM activities that support student needs, curricular objectives, and the integration of educational technology. The “Discussion of Interviews” activity contained numerous connections to my multi-layered topic. I derived the following reflections after carefully reviewing and analyzing all interviews posted in the discussion.

Prompt: In what ways was your interview unique or similar to others?

Here I have created a chart that compares the various interview responses as they pertain to the 3 sub-topics of my issue.

Sub-topicsSimilarities to my InterviewDifferences From my Interview
Supporting Student Needs·        Use of technology to increase student accessibility
– LMS is used for communication and store materials, including instructional videos to support asynchronous learning
– modeling and integrating online tools such as Desmos in lieu of the TI-84+ graphing calculator
 
·        Use of student engagement tools to foster feedback, facilitate review, provide active learning, and increase student interest
– Quizizz, Quizlet, Kahoot, Poll Everywhere
·        Integrating assistive technology into student learning and product creation
– speech-to-text or text-to-speech tools
 
Use of educational technology in tandem with UDL principles to provide diverse, student-centered learning and assessment opportunities
 
Curricular Objectives
·        Use of technology to provide multi-modal methods for understanding concepts
– Use of visuals (ie. graphs) to support equation solving
·        Use of technology to replicate real-life, problem-based learning contexts
Use of technology to emphasize STEM learning contexts and 21st century learning competencies
Integration of Ed Tech·        Recommendations for integrating educational technology in the classroom
– explore various PD, including books
– when integrating technology have a Plan B to trouble shoot obstacles (poor Wi Fi, inadequate devices, software failures, etc.)
– it’s okay to start slowly to gain experience and confidence
·        Work collaboratively towards technology goals
– a colleague
– a technology mentor, or
– a community of practice
Table 4: Comparing Interview Responses Related to Designing Effective Educational STEM Activities

Prompt: What does this say about the context/place or the issue?

The complexity of designing and implementing effect STEM activities is dependent on many factors, including the teacher, the students, the environment, and the educational goals. Although there are recommendations for best practices, there is no one right way to approach this. Rather, it is a process that involves many considerations, each likely weighted differently to reflect the given context. As Teacher T in my interview describes, “Your really have to rely a lot on all these moving parts working well together”.

Prompt: How is your understanding of this issue changing?

I am beginning to think differently about what is involved in designing technology enhanced STEM activities that address specific curricular outcomes and diverse student needs. Initially my vision was focused on student-centered exemplars that appeared extensively developed around technology infused activities. Hearing from many teachers in the field, with their unique contexts and perspectives, I realize that effectively designed STEM activities come in all kinds of formats. They can be designed with lots of structure for students, or alternatively, can provide a lot of student choice. They can be a short activity used to gather student ideas or feedback or they can be larger activity that develops a topic in multiple ways. Most importantly, I am seeing the issue of time commitment differently. At the onset, based on the complexity I envisioned, teacher time commitment to was a significant issue in my mind. Now I recognize that integrating technology effectively does not require dramatic and instantaneous change. Instead, change can be approached strategically and incrementally, over longer periods of time, making the process of using new technology a lower-risk for both teachers and students.

Prompt: What more would you like to learn or know?

I heard a lot in the “Discussion of Interviews” activity about how teachers use technology to support the needs of students through the principles of Universal Design for Learning (UDL). I would like to learn more about designing activities that have a “low floor, high ceiling” (Boaler, 2022) and provide better opportunity for student access, engagement, and achievement.

References

Boaler, J. (2022). Mathematical Mindsets: Unleashing Students’ Potential through Creative Mathematics, Inspiring Messages and Innovative Teaching. Wiley.

Issa, T., & Isaias, P. (2015) Usability and human computer interaction (HCI). In Sustainable Design (pp. 19-35). Springer.

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Unpacking my Assumptions About ‘Good Use’ of Technology

Guiding Question:

How could we or should we use technology in math and science learning environments? How technology might be used to support or enhance learning

 

Technology Image (Flickr)

My starting perspective about what “counts” as good use of technology in math and science learning environments.

  • Tools that are available for student use in their lives (or maybe future circumstances, such as work)
  • Tools for communication (gather and share ideas with others)
  • Tools that can be used to produce shared knowledge or some product (build common work)
  • Tools that improve efficiency and effectiveness (faster and less tedious, provides a clearer method)
  • Tools that build enthusiasm and interest (allows personalization and differentiation in teaching/learning)
  • Tools that reinforce or generate learning in new contexts (in-situ learning, real-life applications, inquiry based)
  • Tools that increase accessibility and different learning styles (supports reading and writing with read aloud or dictation, can be enlarged to improve visibility, uses student friendly language, and adheres to set quality standards)

My brainstorm of what I consider ‘good uses’ of technology is focused on technology that supports teachers and learners with in a variety of ways. Certainly, curricular objectives need to be a central aspect, allowing learners to better explore and understand concepts, while also developing higher order thinking skills as outlined in Bloom’s Taxonomy: application, analysis, and critical and creative thinking (Armstrong, 2010).

In addition, ‘good use’ of technology aligns with and supports 21st century learning skills (Alberta Education, 2023) in the process, including, for examples, fostering self-reflection, creating technical productions, establishing inclusivity, and adopting assistive technology (Thiel, 2018). Classrooms need to be equipped with modern technology and teachers need to be trained, not only with the operation of the technology, but how to integrate the technology into their classroom practices as part of their pedagogical tool kit, effectively building learning not only for the present, but also for the future.

21st Century Competencies (Alberta Education, 2023)

References

Alberta Government. (2023). Competencies Overview. Alberta Education. Retrieved January 19, 2022 from https://education.alberta.ca/competencies/student-competencies/

Armstrong, P. (2010). Bloom’s Taxonomy. Vanderbilt University Center for Teaching. Retrieved January 19, 2022 from https://cft.vanderbilt.edu/guides-sub-pages/blooms-taxonomy/

Thiel, L. (2018). Professional learning design framework: Supporting technology integration in Alberta. Research in Learning Technology, 26. https://doi.org/10.25304/rlt.v26.1989

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Student Misconceptions as Their Private Universe

“My Brain” by Matthew Purdy, licensed via CC BY 4.0 . Flickr.

In A Private Universe, Heather, a 9th grade student, is formulating her understanding of the movement of the sun, Earth, and moon and how this creates the various seasons and the phases of the moon. Heather has a mixture of correct and incorrect understandings based on her prior knowledge, experience, and her formulated logic. Depending on Heather’s concepts she must either make small refinements (assimilations) of her current understanding to adapt to new or expanded information, or must discard former paradigms and adopt new ideas and structures (accommodations). Heather knows that the seasons are related to the Earth’s tilted axis as it revolves around the sun, despite her initially incorrect, but later resolved, understanding of the shape of the Earth’s orbit.

More challenging for her to resolve is her confusion about what is meant by direct and indirect solar rays on the Earth’s surface and their resulting effect. Heather is confused by the vocabulary, and even with the visual illustration demonstrating the difference she continues to think that the language is differentiating between non-reflected and reflected light rays. Although her end conclusions about the seasons based on the Earth’s orbit are correct, the underlying rationale is not. Her understanding of the phases of the moon, as a result of the moon’s position relative to the sun and Earth, is more cohesive, and although she indicates some confusion about the difference between a new moon and a lunar eclipse, through logical rationalization she correctly concludes that the lunar eclipse is due to the Earth’s shadow on the moon.

In the field of mathematical education, Booth et al. (2014) outline six types of mathematical errors in “Persistent and Pernicious Errors in Algebraic Problem Solving” that most typically occur. While some errors are quite predictable in their presence and typically resolve with continued practice in different contexts, other errors are indicative of more critical misconceptions and warrant intentional targeting in instruction and intervention. Specific strategies using manipulative tools are recommended to develop and reinforce key concept development. For example, negative number concepts align with the use of number lines and set models, equality concepts benefit from using balance scales and Geogebra (Ko & Keradag, 2012), and variable errors can be addressed with area tiles. Knowing what types of errors are to be expected allows teachers to anticipate and plan accordingly, through additional and varied activities or extra time and opportunity for student learning.

“Learner Ideation”, Image Credit: E. Warren

It is clear that teachers cannot assume that learners arrive in their classrooms with accurate understandings from earlier grades or even recent lessons. Rather, “students enter instruction with firmly held beliefs and explanations for phenomena and relationships, and these beliefs are subject matter specific and can be identified and confirmed only through methods that encourage children to be expressive and predictive” (Confey, 1990, p. 4). Learning is a process that involves rational activity and requires opportunities for students to question, test, discuss, and defend their ideas (Posner, 1982; Fosnot, 2013). Intentional and constructive cognitive conflict is an important and effective instructional strategy that elicits the required cognitive disequilibrium that serves as the fertile mental ground for students to work through the re-organization process of new conceptual paradigms (Fosnot, 2013; Cobb, 2005; von Glaserfeld, 2005). Digital tools can serve to provide necessary visualizations and manipulation to explore, clarify, and generate new concepts.

References

Annenberg Learner. (n.d.). A private universe [Video]. https://www.learner.org/series/a-private-universe/1-a-private-universe/

Booth, J., Barbieri, C., Eyer, F., & Pare-Blagoev, E.J. (2014). Persistent and pernicious errors in algebraic problem solving. The Journal of Problem Solving, 7(1), 10-23. https://doi.org/10.7771/1932-6246.1161

Cobb, P., (2005). Chapter 3: Where is the mind? A coordination of sociocultural ad cognitive constructivist perspectives. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice, (2nd ed., pp. 39-57). Teachers College Press.

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, (16)1, 3-56. https://doi.org/10.3102/0091732X016001

Fosnot, C. & Perry, R. S. (2013). Chapter 2: Constructivism: A Psychological theory of learning. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice, (2nd ed., pp. 8-38). Teachers College Press.

Ko, W., & Karadag, Z. (2013). Fostering middle school students’ relational thinking of the equal sign using GeoGebra. Mevlana International Journal of Education, 3(3). 45-49. DOI: 10.13054/mije.si.2013.05.

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Von Glaserfeld, E. (2005). Introduction: Aspects of constructivism. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice (2nd ed., pp, 3-7). Teachers College Press.

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My Auto E-ography

I have older siblings, and I remember them coming home with their math homework and doing homework with a logarithmic ruler. I was a numerophile from an early age, and although I had no idea what a logarithm was at the time, I was curious and mystified about how the manual contraption could be solving their equations. I never did actually use the old-fashioned log ruler in my own courses, except maybe perhaps once or twice to demonstrate that it approximated the values generated on my calculator. I still marvel at how technological devices can replicate various tasks by different means.

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Welcome

Welcome to my  blog! This blog is being undertaken as I work in the latter stages of my MET program. It will serve as a compilation of my learning process and growth as I work through ETEC 533: Technology in the Mathematics and Science Classroom.

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