Tag Archives: problem solving

Considering WISE Design and Jasper Adventures

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Wise research aims to bridge the gap between the research that shows the efficacy of inquiry learning in science and the method in which science is generally delivered. In science specifically it has been found that students have many misunderstandings developed either through experiences, concepts or examples (Linn, M., Clark, D. & Slotta, J., 2003). In order to address these, WISE curriculum projects promote knowledge integration through providing inquiry projects which are flexible, customizable and adaptive. They also believe in sustainability. Through field testing and multiple cycles of trial, adaptation and refinement the inquiry projects are continually honed to meet the specific needs of the students. In this way WISE is a bottom up approach rather than a top down approach and is meeting the educational goal of delivering curriculum in a differentiated way, which is one of the goals of education.

In addition, WISE supports the provision of an instructional pattern to assist students through the inquiry. These include eliciting student ideas, adding ideas to these and supporting the process learning to improve understanding. In this way WISE is able to scaffold the students’ learning in an indirect way, while still providing them with many pathways to reach their conclusions. WISE guides the students through the inquiry project without being prescriptive, which leads to deeper learning.

In addition, WISE project teams are made up of diverse partners so as to provide a more holistic inquiry. These include pedagogical specialists, scientists, teachers, and technology designers. WISE framework design principles include making thinking visible, making science accessible, helping students learn from each other, and  promoting lifelong learning, all goals of 21st century education as well as sound pedagogy.

Further to this, many WISE inquiry projects have been designed with detailed steps for the first inquiry investigation and then providing less detailed steps in subsequent projects. In this way students are able to move from supported learning to more independent pathways. This method is debated. When considering the Jasper Series, the belief that students can develop basic skills in the context of meaningful problem posing and problem-solving activities rather than isolated “targets” of instruction seems to refute this. That being said, the Jasper Series coincides with WISE with its emphasis on complex, problem solving, communication and reasoning and in connecting mathematics to the world outside the classroom. (Cognition and Technology and Technology Group at Vanderbilt, 1992).

Looking at this more closely in WISE design it has been found that students prefer to not have a lot of detail before they begin their inquiry, but rather work well with an  initial page that provides an entry into the disciplinary knowledge and provides hyperlinks for students who wish more detail. In this way, making science accessible may not mean making it simple (Linn et al., 2003). This mirrors the anchored instruction shown in the Jasper Series as well.

Another link between the Jasper Series and WISE seems to be the belief that the educator should be a facilitator rather than the disseminator of information. In WISE an inquiry map helps students work independently on their project with prompts that help guide through process. Teachers can also easily customize the projects to match their curriculum and students.

The flexible, continually changing approach to WISE is based on the need for scientific materials that enable local adaptation along with support from multiple cycles of trial and refinement. Students’ needs and what scientific inquiries which engage them are also closely considered. Providing students with content they are interested in and that may have an impact on them is part of the real-world problem solving that is encapsulated in anchored instruction.  This continual refinement is also found in the Jasper Series. Technology can provide for this, whereas traditional textbooks cannot. Furthermore new technologies can be integrated into WISE and the system itself scaffolds the use of offline activities by providing a project context, a pedagogical framework, and proven curriculum design patterns.

Customizing WISE would be beneficial. If I were to use any of the inquiries I could integrate the climate and realities in Northwestern Ontario or the Canadian Shield. In addition I could integrate information about Lake Superior, one of the largest freshwater lakes in the world, which is situated in Thunder Bay (the students’ hometown). Local flora and fauna could be considered. The seasons and the weather locally could also be integrated. These are just some examples.

Linn, M., Clark, D., & Slotta, J. (2003). Wise design for knowledge integration. Science Education, 87 (4), 517-538.

Cognition and Technology Group at Vanderbilt (1992). The jasper experiment: An exploration of issues in learning instructional design. Educational Technology Research and Development, 40 (1), 65-80.

Mathematics Instruction for Students with Learning Disabilities-Jasper and Reflections on my Teaching Practice

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The article, “Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components”, helped me to further analyze the Jasper series and its goals. Within this study the researchers sorted the studies by major types of instructional variables. Their interest was in the detailed curriculum design and teaching practices that resulted in enhanced mathematics and they focussed on the essential attributes of effective practice. They went further and defined “explicit instruction”, which in previous research has shown positive effects in terms of increased understanding of mathematical skills for students with learning disabilities. The researchers broke it down into three components: (a) The teacher demonstrated a step-by-step plan (strategy) for solving the problem, (b) this step-by-step plan needed to be specific for a set of problems (as opposed to a general problem-solving heuristic strategy), and (c) students were asked to use the same procedure/steps demonstrated by the teacher to solve the problem (Gersten, Chard, Jayanthi, Baker, Morphy & Flojo, 2009). They also looked at the methods that exemplify a generic approach for solving a problem, student verbalizations of their mathematical reasoning, using visual representations while solving problems and range and sequence of examples. They further investigated providing ongoing formative assessment data and feedback to teachers on students’ mathematics performance, providing formative assessment data and feedback to students with LD on their mathematics performance and peer-assisted math instruction.

The results of the meta-analysis rendered some interesting data. Firstly, peer assisted learning did not provide much benefit, whereas being tutored by a well-trained older student or adult appears to help significantly (Gersten, et al., 2009). When assisting students with LD in my classroom, this finding is important, as I often pair my students with LD with their peers in order to provide more scaffolding or scaffolding when I am busy helping other students. I will need to rethink this approach.

In addition the two instructional components that provided significant benefits were teaching students to use heuristics (a process or method) to solve problems and explicit instruction (Gersten et al., 2009). When reflecting on these findings I still have some questions. I do teach my LD students a certain process or method to solving mathematical problems but I also don’t want to limit their strategies as we are being told to allow them to explore mathematical problems with a variety of strategies. Now that I think about this, perhaps students with LD do not benefit from a variety of strategies but are best served with a limited number of strategies to use, at least initially. In terms of explicit instruction, I do provide this to my students with LD, although they are also part of any open-ended problem solving that we do in class. I feel it is important to expose them to this type of mathematics as well, but perhaps they would be better served working on other math during this time. That being said, the researchers found that explicit instruction should not be the only form of instruction, so perhaps I should continue to expose the LD students to our open-ended problem solving discussions.

They also found that the sequence of examples is of importance when new skills are being taught, so scaffolding is critical for student success. Examples and problems should move from simple to increasing complexity (Gersten et al., 2009). When reflecting on my own teaching, I find that I do this naturally with all students, as it makes sense to me to move from simple to more complex problems. That being said, and reflecting on the Jasper series, perhaps introducing complex problems that students have to work through and problem solve through may be of more benefit.  The Jasper experiment believes that engaging students in real-world problems that are inherently interesting and important helps students understand why it is important to learn various sub skills and when they are useful. The Jasper adventures are purposely created to reflect the complexity of real world problems (Cognition and Technology Group at Vanderbilt, 1992).  As part of inquiry teaching (a method I use to teach some of the time in my classroom), I often introduce mathematical problems based on math explored in read-alouds. For example, when reading the book “Iron Man” we explored measurement as we explored how big we thought the Iron Man, the science fiction character in the story, would be compared to us as students. So in this way I attempt to introduce concepts that lead the students down possibly unexplored mathematical pathways and see what they can produce. I am left with the wondering: Do LD students benefit from this?

Importantly, the study showed that the process of encouraging students to verbalize their thinking or their strategies, or even the explicit strategies modeled by the teacher, was always effective (Gersten et al., 2009). In my teaching practice I often use verbal understandings to gain a better understanding of student understanding/misunderstanding and for ongoing assessment to move forward. I do this for all students, but particularly for students with LD.

It appears that teachers and students also benefit if the teachers are given specific guidance on addressing instructional needs or curricula so that they can immediately provide relevant instructional material to their student.  Teachers require support!!  This is an important point to discuss as educators are often expected to know what to do in all situations with a variety of different styles of learners, with a variety of curriculum and with a variety of learning abilities. As Schulman (1986) noted in his research, teacher training and the type of training provided needs to be revised to reflect both content and pedagogical knowledge.  The fact of the matter is that educators do not have all of these skills and cannot devote the amount of time required to meet the needs of all students. Teachers require the supports of special education teachers, administration, professional development, etc. in order to gain and implement these skills.  The research further disseminates this as the researchers recommend that providing specific instructional guidelines and curricular materials for teachers  and co-teachers or providing support services, peer tutors, cross-age tutors and/or adults providing extra support would be of direct benefit to students with LD (Gersten, et al., 2009).

Interestingly the researchers found at there seems to be no benefit in providing students with LD-specific feedback that is specifically linked to their goal attainment (Gersten et al., 2009). This seems to refute the feedback loop that we are encouraged to use as educators in order to help students to move forward in their learning. I will have to consider this when providing feedback to LD students. Perhaps spending more time on heuristics and explicit instruction and use of visuals would provide better scaffolding for their learning. I look forward to your thoughts on these points.

References

Cognition and Technology Group at Vanderbilt (1992). The jasper experiment: An exploration of issues in learning instructional design. Educational Technology Research and Development, 40(1). pp. 65–80.

Gersten, R., Chard., D.J., Jayanthi, M., Baker, S.K., Morphy, P., Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242.

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

 

Ideal Pedagogical Design in Technologically Enhanced Science/Math

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The ideal pedagogical design of a technology-enhanced learning experience for math and/or science would be based on innovative teacher and student practices. Constructivist activities would allow for student led learning, with teacher as facilitator. As Kozma (2003) notes, teachers are not the disseminators of information but rather act as the “guide on the side”, providing planning, structure and ongoing check-ins and assessment for learning. With this type of learning, the educator must have proficiency using technology tools and platforms in different ways, so ongoing collaboration between educators as well as ongoing training would be an important piece of this puzzle. The pedagogical design would take into account the availability of appropriate technology tools as well as providing stimulating questions or wonderings in which the students would be able to choose their learning path but still be provided with scaffolding throughout. These questions or wonderings could then be linked to the curriculum through purposeful guidance by the educators and through looking for patterns and links between the queries and the curricula. Students would be encouraged to work collaboratively and to reach findings and to use technology to its full capabilities including analysis, problem solving, designing and implementing.  Students would be encouraged to reflect on their learning, share through a variety of presentation tools and continue to incorporate new technology tools in their learning.

Robert B. Kozma (2003) Technology and Classroom Practices, Journal of Research on Technology in Education, 36:1, 1-14, DOI: 10.1080/15391523.2003.10782399

Initial Reflections on the Jasper Series

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Before reading the article about Jasper anchored instruction, I explored the videos just to get a feel for what this series entailed.  I also wanted to get my initial impressions without having much background. The first thing that struck me was that they were posed as challenges, which I believe would be engaging to students. Then I noticed that they were real-life explorations and I reflected that they would foster rich discussion amongst students. These problems or “situations” would allow students to test out, hypothesize, work and rework as they problem solved. It would be messy but rewarding. They may require some facilitation along the way or a sounding board, but the problem solving would be student centered.

Some questions I had after watching the videos were:

  1. Would it be possible to have the students conduct some of these situations in real-life? (as an adjunct to the videos)
  2. What background in mathematical terminology would the students require?
  3. Could the students competently solve these problems without some prior math knowledge in the area of exploration (rate, capacity, range, temperature, etc.)
  4. What software or platform was used to create and share the videos?

After reflecting on the videos I read the essential article, ” The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design Cognition and Technology”. I was happy to see that many of my reflections correlated with the article.

Within the situational videos basic skills are important, but students develop them in the context of meaningful problem posing and problem-solving activities rather than as isolated “targets” of instruction. (    )students must learn to identify and define issues and problems on their own rather than simply respond to problems that others have posed. I also found it interesting that the videos naturally encourage cooperative learning in which students have opportunities to discuss and explain which can assist in solidifying understanding. It is also interestingly noted that working in these cooperative groups allows the students to monitor one another and thus keep one another on track. This would definitely allow the teacher to take on a facilitation role more naturally.

The videos align with the goals of the NCTM as well. These include an emphasis on complex, open-ended problem solving, communication, and reasoning. In addition, connecting mathematics to other subjects and to the world outside the classroom is encouraged. The Jasper videos seem to fit the bill.

Within the article it explains that educators allow the students as much time and room to work on these problems without teacher interaction. Some may see this as foolhardy and may contest that certain skill sets need to be taught before complex problem solving can occur. The Jasper Experiment believes that engaging students in real-world problems that are inherently interesting and important helps students understand why it is important to learn various sub skills and when they are useful. The Jasper adventures are purposely created to reflect the complexity of real world problems.

Within the article it is also noted that Jasper developers are continuing to work with teachers in order to collect “scaffolding” or “guidance” information to include  with the videos. So although the goal of anchored instruction is situated in engaging, problem-rich environments that allow sustained exploration by students and teachers, some purposeful scaffolding and guidance can assist the problem solving process in some situations.

The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design Cognition and Technology Group at Vanderbilt Educational Technology Research and Development Vol. 40, No. 1 (1992), pp. 65-80

 

Integration of Technology to Support the Mathematics Program in a Grade 5 Classroom-Pros and Cons

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Abstract for Interview- Elementary Teacher Grade 5-Multi-Disciplinary Teacher-Interviewed Specifically about Math Programming 

Interview Length  22 minutes.  The teacher I interviewed is from a city of approximately  100, 000 people  in Northern Ontario, Canada. The interview took place during the lunch hour in the staff room in the elementary school where we both work.  The elementary school houses students from JK-8 and the school population is approximately 550 students. It is a relatively new school and it has several shared laptop carts, several shared I-Pad carts and an Interactive Whiteboard in every classroom. The interviewee is in her 40’s and has been teaching full time for for 5 years and had previously worked as an occassional teacher for 2 years. Prior to this she worked as an educational assistant for 7 years and prior to that worked as an early childhood educator for 12 years. She has taught grade 5, and worked as a primary planning teacher where she was responsible for teaching the music program from grades K-8.  She has a keen interest in technology tools. I asked questions specific to technology and her mathematics teaching.

Three themes came out of the interview:

  1. There is a need for teacher training and support in regards to technology

2. Technology is being used in the math program, but not to full effect

3. A BYOD (Bring your own device) strategic plan may alleviate some of the concerns about BYOD in the elementary school and  may provide students with more access to technology and more flexibility with the tools they are able to access and use in mathematics.

The integration of technology into the math programming in an elementary grade 5 classroom has many benefits but this also seems to go hand in hand with many issues. Most of these issues are around availability of technology, tech support and teacher training, but the risks inherant with students bringing their own devices to school was also apparent in the interview.

My colleague reported that she was incorporating technology in her math program across several of the elementary math strands including geometry, numeration, measurement and algebra. In addition, she reported enjoying incorporating the technology and a willingness to incorporate more as she learned about new applications. Although she mentioned that she often found out about new applications, websites etc through casual conversations in the school, she also noted that the training was lacking and that she felt that the training should be done in shorter sessions that concentrate on one topic or one tool to try instead of a longer session where too much information is given and teachers feel overwhelmed. She expressed that this type of training is often ineffective because either teachers don’t remember what they have learned or they do not have the proper technology or tools in order to practice what they have learned.

Although my colleague discussed the way she was incorporating technology in the math program, after reflecting on her comments I noticed that much of the technology use was for demonstration purposes or practice and review. If more training specifically focussed on ways that technology could be used for problem solving, creating or sharing and communicating amongst students perhaps this could also be explored in the classroom.

She also spoke about the BYOD (Bring your own device) situation in her classroom. Her concerns were around the students’ lack of responsibility when using technology, including inappropriate use and not thinking critically about their online behaviour. In addition, she was concerned about the students losing their devices and having both of these situations cause her to have to deal with issues that may get her into professional trouble.

The uniqueness of this interview lies in the fact that elementary educators are multidisciplinary educators yet in our school the science component is given to planning teachers to teach, so the homeroom teacher does not teach her own science. In this way, the integration of math/science/technology/engineering may happen less often. So the natural fit between STEM may be stifled. In addition, in the elementary school setting the educators are often the ones responsible for ensuring that the technology students bring to school is not lost, stolen or broken and if this happens the teacher often has to deal with this. This may be different in upper grades, a highschool setting and definitely in higher education settings. In addition, young students may not have an understanding of what it means to be a responsible digital citizen, and this should be explored along with technology so that the students can make informed and reasonable decisions about its use.

Transcript of Interview

Interviewer will be bolded throughout

How do currently utilize technology in your math program?

Well…I use the Smart Board regularly to demonstrate thinking and so that I can record their math strategies and so that we have a visual way to discuss them. I record number talk strategies as they are shared in class. I also use the I-Pads to, for example, practice elapsed time. Actually….I use the Porter website for that! I go on their website and pick a flight and then I tell the kids, “If I leave at 1:00 and land at 8:00 how much time has elapsed? They like that.
I also use the laptops and I-Pads for different games…I use “Math is Fun” and Prodigy.

So, when you are using these applications, are they aligned with the curriculum you are teaching?

Yes. So when we are doing multiplication the students went on “Grand Prix Auto” racing game for some reinforcing. I also use them for teaching concepts.

What are the differences in student engagement between using technology in math and not using technology?

Well….it depends on the student. Some think it is fun and some find it boring. I think overall they are more engaged.

Why do you think this is?

Well….I think they like the independence, and also the sounds, colors and action in the games.

Do you see any roadblocks to using technology in the math programming in your classroom?

Yes! Wifi is a big problem. The laptops themselves…well there’s not enough and when I sign them out a lot of them are broken.  They are hard to book as well. I prefer I-Pads for quick learning and laptops have certain applications that can’t be used properly on the I-Pads so the laptops are helpful then.
Also some students bring in a device and then it won’t work and I don’t have the know-how to troubleshoot and there is no tech support so the student gets upset. Then some devices get stolen and then I have a crying student on my hands and an angry parent.

How do you think technology could be integrated more fully in the math programming in our school?

Well first of all training. Hands-on training in small steps. I have started inviting people to my class after school on Tuesdays for 30 minutes tops. They try some new technology and then get a chance to use it. When you throw everything at someone in one big course it is too overwhelming. Tech needs to be available when they are learning and the applications need to be available to teachers if they are being trained in their use.

Do you think ideas about how to use technology tools are being shared with the staff?

Well, I am open to learning anything new about technology. I love it. I don’t have anyone sharing with me, or if it is shared it is shared one-on-one informally…like in a hallway or over the lunch hour. Then I will try these “tips” out. But for many people it is in one ear and out the other because they don’t even know where to start.

Why did you take the initiative to voluntarily invite staff to technology training in your classroom after school?

Well…my friend (colleague) didn’t know how to use the Smart Board and I knew that I could be helpful. I’m excited about using technology in my classroom!

Do you allow students in your class to bring their own devices to school?  

I haven’t started that yet. I usually wait until after Christmas.

Is there a reason that you wait and what are some of the perceived drawbacks of BYOD?

Well one time a kid in my class went on porn at home, saved it and then shared it at school. Also one student took a picture of another student and posted it on Facebook and then I got in trouble. The students need to learn responsibility and be held accountable which is hard to control.

What strands of math do you currently support with technology?

Geometry-looking at shapes and building 3-D objects and viewing these objects virtually.
Patterning-I use the “Patterns to Algebra” program on the Smart Board. It is found in the Smart Notebook program.
Number Sense-We use Grand Prix Auto
Measurement- I like using the Smart Board tools for this. The ruler that shouts out numbers is great!
I use the Smartboard for teaching and I use the I-Pad more for practice and consolidation.

Are the students using any of this math technology at home?

Well, I use the e-learning website to link to websites at home, but this year there are far more students not even accessing the e-learning.

Why do you think this is?   

I think parents and kids are just too busy.

How do you see technology tools in the math program being of assistance to students who are struggling?

I really like “Prodigy” for that. It can be set up for the whole class or individualized for the grade level of the student. Two students I had last year, “A” and “D” were performing math below grade level so I used the I-Pad or laptop and they could practice math at their level.

Thank you for the interview! There are some really good discussion points here!
Interview Ended

Video Cases- My Reflections

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The collection of videos I watched in Module A reflected current successes and concerns around the use of technology in math and science classrooms. Although they highlighted the underlying issues with the integration of technology into the math and science classrooms they also showed the light at the end of this tunnel.

The issues seemed to correlate with my thoughts as I unpacked some of my own assumptions. Access to computer labs as well as time came up several times within the videos. In addition, the lack of training or perceived lack of competence using technology to teach was revealed when the new teacher said she felt that she wanted to incorporate technology in her teaching, but that she felt pressured due to time constraints and the fact that she felt that she didn’t have enough prior knowledge of the technology to teach it properly. She also felt unprepared to troubleshoot in the moment, which seemed to make her fearful of trying to incorporate the technology.  Considering student issues with technology, interestingly one of the students videoed reflected on the graphing calculator and although she used it because she said it saved time and she was “lazy”, she also relayed the fact that she felt that it disguised her mathematical problem solving and that she preferred pencil and paper to work out her math problem, at least initially.

I also noticed that technology was viewed as a “time” saver in some ways, and in another way was used for project based work, which tended to take more time and be more in depth. I think this was based on how the technology was used, whether for solving a specific problem or creating a presentation. This was just a reflection.

Another theme I noticed was that the technology used seemed to be limited to a few “tried and true” uses. This is not an underlying issue, just a reflection I made as I watched the videos. I think with technology often educators become familiar with a specific set of technology uses or presentation tools and stick with them. They also share these with other educators and so these get used more and more. One example of this would be the overuse (in my view) of PowerPoint when there are many more varied options available to present information in the same way.  Again, this is probably due to time and training.

On the positive side technology was being used in many of the classrooms. From Powerpoint to podcasting, internet researching, animated GIFs, Flash presentations, graphic calculators to problem solve, videotaping creative dramatic science representations, soundscapes, etc. Both educators and students found it engaging and it helped to promote teamwork and partnered problem solving. In addition, pencil and paper was not thrown out the window but was seamlessly incorporated as part of the learning process, technology working alongside this. Different student learning needs were met with the variety of ways they could both access learning and present their understandings.

In considering a response to some of the underlying issues I chose to focus on using the resources available to the best of their capabilities. New teachers should be mentored and supported through being teamed up with more seasoned educators and then allowed to use technology in their teaching with guidance and supports. In addition, educators should be given time to share technology tools at staff meetings or division meetings. Students should also be utilized as an important resource when integrating technology in your teaching. Often the students are able to figure out how to use the technology, or already know how to use it and can show the teacher. Teachers need to bring the technology in, even if they are feeling a bit unsure. Even if the educator can wrap there head around one new technology tool, it may promote them to use it and to slowly integrate technology into their classroom.

In summation, I think it is important that technology is providing for differentiation. Students are not only bound to textbooks and written work, but are able to act, produce, reflect, create, problem solve, hypothesize, cooperate and present using technology as a tool. This is important and is providing for a deeper and more engaging learning experience for many.  I look forward to reading your reflections.

Observing and Analyzing Digital Technology In Science Classes-Video Reflections

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Following are some of my reflections after watching the first set of videos in the “grounding issues” section of the course.

Firstly, the educators believed that technology allowed them to provide the students with open ended questions that allowed them to do more critical thinking, think more in-depth and to actually try alot harder when they tackled problems posed. So, teacher perspective on the value of technology was a factor.

In addition, when viewing the video in which the students are growing crystals, I found it interesting that this was actually not part of their curriculum but the educator saw the connections between the growing of crystals and his subject area (physics) and so allowed them to do the experiment and find connections betweeen the chemistry and physics organically. This interdisciplinary approach allowed the students to work on an engaging activity while still learning about thermodynamics (for example).

Technology was used through a “mini-computer” that allowed the students to regulate and display temperature, amongst other capabilities and thus combined chemistry with electrical engineering. The learning looked to be cooperative and engaging and one of the students remarked that “experiencing” the learning first hand was of great value to him.

One thing I thought of when watching these videos is that the technological competence of the teacher seemed high, and this may not be so for all teachers. He would be a great resource in a school as his expertise could be used to help other educators to incorporate technology in their classrooms. I also wondered if he learned this on his own because of his self-interest in technology or if there was training provided.

So some main ideas:

Interdisciplinary Approach

Teacher Efficacy

Open Ended Problem Solving Approach

Cooperative Learning