Monthly Archives: June 2017

Real-World Problem Solving

The Jasper Series is a technology-enhanced learning project based on Anchored Instruction. In which instruction is “situated in engaging, problem-rich environments that allow sustained exploration by students and teachers.” The designers were responding to research indicating that students “do extremely poorly when faced with situations that require them to generate the relevant subproblems and figure out what data are needed to satisfy the subgoals that they generate on their own” (Cognition and Technology Group at Vanderbilt, 1992a). While students can calculate numbers in isolated situations, they are relatively weaker at understanding how to apply these abilities within problem-solving contexts. The series of videos provides a guiding framework and presents “meaningful problems for students to solve that capture the intricacies of real-world mathematical problem solving” (Vye et al., 1997). Students explore information in interdisciplinary contexts, generate solutions collaboratively and critically reflect on their existing conceptions. This approach significantly differs from traditional direct instruction methods and recognizes “that the course of learning is not a simple process of accretion, but involves progressive consideration of alternative perspectives and the resolution of anomalies” (Confrey, 1990).

I think that many of the current video-based supports that exist for math are essentially virtual lectures and typically focus on procedural understanding. Many Khan Academy lessons demonstrate how to carry out calculations using a variety of operations and algorithms. One website that uses video in a somewhat similar way to the Jasper Series is called When Math Happens – 3 Act Math (https://whenmathhappens.com/3-act-math/). Like the Jasper Series, students generate an understanding of the sub-problems and the relevant information collaboratively. In each problem, three short video clips provide a real-world engaging context and helps to guide student thinking. The first video provides a visual context for a real-word problem. The second video scaffolds students’ generation of knowledge about sub-problems which they will need to solve the larger problem. The last video provides feedback for the student so they can evaluate their solutions. Some problems provide a “sequel” so students can extend their thinking. The technology serves to create a context which guides, motivates, and provides feedback for students. Student can repeatedly explore the videos for relevant information and visual clues help support their decisions regarding how to use the information.

Anchored Instruction connects to my understanding of Problem-based Learning. This year my class started a school snack cart to raise money to purchase technology. The math required to run the store provided content for PBL instruction in class. The kids had to figure out how to balance inventory, calculate profit margins, make decisions about which products to buy, etc.  We used Excel Online to work with the secretaries to manage the account. They used iPads to compare prices, record sales, evaluate nutritional information, etc. One thing I have come to understand while teaching with a PBL design is the significant PCK required to differentiate the experience for all learners when engaging in real-world explorations. The experience was great for many students, but it became complex very quickly. Some kids became lost due to “the intricacies of real-world mathematical problem solving” (Vye et al., 1997). Inclusion of all students depended on the anticipation of the math concepts that arise throughout the experience. I found this significantly more difficult than when I was selecting the content to introduce. Technology definitely helps, in this case digital pictures and video, because the students can access the problem through visuals instead of text. It also supported by reducing demands on memory. Many kids would take pictures of objects relevant to the problem and, through apps like Explain Everything, connect their mathematical thinking to the pictures.   

Cognition and Technology Group at Vanderbilt. (1992). The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design. Educational Technology Research and Development, 40(1), 65-80. Retrieved from http://www.jstor.org.ezproxy.library.ubc.ca/stable/30219998

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56.

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.

Motivating and Engaging Students of all Abilities

When it comes to visible thinking routines and the integration of technology, Jasper provides many opportunities for students to find success. Within a constructivist approach, Jasper sets students up for success by providing a framework that is student centered. Looking at the work of the Jasper Project based out of Vanderbilt University, there is much research and reporting regarding this method of constructivist teaching. Through Anchored instruction educators use video narratives or stories, which provides a specific context, that aim to motivate and engage students during the learning process. Evidence suggests that when students are presented with anchored videos that are interesting, realistic, and require active involvement that opportunities for deep-thinking occur. Projects similar to Jasper situate learning in a real-world context, these videos provide both the what, how, and why.

According to Hasselbring, et. al, in Technology-Supported Math Instruction for Students with Disabilities, “Students with math difficulty can be successful in attaining high levels of fluency in mathematical operations with the appropriate assistance of technology; however, this assistance must go beyond simple drill and practice if students have not stored the problem and the associated answer in long-term memory.” Therefore, when considering current technologies and software for math such as Mathletics, it is necessary that a balanced approach be taken into consideration. The three types of knowledge, declarative, procedural, and conceptual, as Hasselbring, et. al reference, will only come to life when a solid foundation of declarative and procedural understanding are in place. Anchored instruction provides this real-world scenario where students are motivated and compete to solve the answers. As well, it provides opportunities for students to expand their thinking skills and ask further questions. Inquiry-based approaches to learning also allow for this teaching and learning to occur, and videos such as Jasper make it possible for students to engage in exciting opportunities of learning.

Therefore, within a TPC framework, “Instead of having teachers “transmit” information that students “receive,” these theorists emphasize the importance of having students become actively involved in the construction of knowledge.” (292) Anchored instruction again provides students chances to engage in activities that are meaningful.

However, as technology within the last few years have become more accessible for students to use within the classroom, as well as the ability to easily create such videos, how often does this practice come into fruition? Especially when we consider a differentiated approach to teaching, to meet students with all ability levels. Within elementary schools where teachers are expected to teach all subjects, should there be more emphasis on specialist teachers in math and science to ensure that best practice is possible? What role does administration play in supporting teachers who aim to integrate intricately woven concepts that provide chances for students to extend their thinking through narratives in anchored instruction? For myself, I believe that students will always rise to meet a challenge when given the opportunity. Meaningful action is possible when students are engaged and motivated.

References

Cognition and Technology Group at Vanderbilt (1992b). The Jasper series as an example of anchored instruction: Theory, program, description, and assessment data. Educational Psychologist, 27(3), 291-315.

Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2005). Technology-supported math instruction for students with disabilities: Two decades of research and development.

Kose, Sacit. Diagnosing Student Misconceptions: Using Drawings as a Research Method. World Applied Sciences Journal 3 (2): 283-293, 2008

Shyu, H. Y. C. (2000). Using video‐based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69

Anchored Instruction in the modern mathematics classroom

As a high school math teacher, I was excited to read about the Jasper series and think about how it could have been implemented today. Although the concept of TPCK did not exist back in the 1980s when the series was first introduced, it was clear that teachers that wished to teach using the series had to have had experience working, and teaching with technology (needed to know how to use a video, and teach students how to learn from it). If the same series was used today, I can imagine that students would have been able to view, or construct the problem in a multitude of ways:

1.Video, or VR simulations – When Rescue at Boone’s Meadow was first introduced, the problem was given through video, with the Cognition and Technology Group at Vanderbilt (1992) suggesting that the video based format increases motivation, and allows the videos to be searched much more easily. One can imagine that such a scenario be delivered using modern day simulation technology like VR that could allow students to live through the problems. One can also imagine being able to simulate their solution through virtual reality. Although this technology is still undeveloped, we are pretty close to seeing VR entering the educational realm in full force.

The concept of teaching with video is widespread in today’s education system, especially for mathematics. Many YouTube channels, such as the Khan Academy, offer a variety of mathematical tutorials, and lessons that students utilize in order to learn concepts independently from school. As a teacher though, I believe that if one were to utilize videos effectively, one would often have to rely on videos produced by other teachers, as the time and resources required to create a video of high quality is often too much for a single teacher. As a result of that, the instructor must always adapt their teaching style or methods around what is seen in the video.  This is not a tremendous issue, but when teachers use videos, they are often placed in more of a facilitator role, as opposed to being more direct with their teaching. Although this is encouraged in many modern research, indirect teaching may be resisted by certain students.

2. Online discussion of solutions – Rescue at Boone’s Meadow was introduced before the internet era, and as a result, discussions around solutions would take place synchronously in a classroom across a couple of periods. However, in today’s internet age, one could imagine online resources in playing a large role in influencing students development of a solution. Just like a video game, students across the country could pick apart, and dissect the situation faced by Jasper in the scenario, and naturally, multiple feasible rescue methods are likely to be found on the internet. If students were resourceful and found these solutions online and used them to develop their own solutions, how should teachers assess for student learning?

In terms of modern mathematical tools such as CTC math, IXL, etc. I believe that many of these tools seem to oppose anchored instruction, and the more popular these tools get, the farther we deviate from the design principles discussed by the Cognition and Technology group at Vanderbilt.  Tools like IXL have their place on mathematics education in that they offer students an excellent resource to practice skills that can learn through repetition (for example, arithmetic, algebra, equation solving), but they often offer very one dimensional ways of delivering information. Anchored instruction relies on linkage across curriculum and student independence in formulating their own problems and solving them, whereas online tools such as IXL do the opposite, they create all the problems for the students to solve.

 

It would appear part of having a strong base of TPCK is knowing when to utilize technology, and understanding what the benefits are consequences are when we adopt a new software for the classroom. We can introduce students to IXL and Mathletics and encourage students to work on problems, but sometimes it takes time away from giving students situations like Rescue at Boone’s Meadow, where a large emphasis is on discussion and generative problem solving. An expert will need to properly balance both teaching activities in the classroom.

 

Barron, L., Bransford, J., Goin, L., Goldman, E., Goldman, S., Hasselbring, T., … & Vye, N. (1993). The Jasper experiment: using video to furnish real-world problem-solving contexts. Arithmetic Teacher, 40(8), 474-479.

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

Jasper Videos and Constructivism

The Jasper Videos were designed to create an anchored instruction tool with the goal being “the development of the Jasper series emphasize the importance of helping students – all students – learn to become independent thinkers and learners rather than simply become able to perform basic computations and retrieve simple knowledge facts.” (Springer, 1992, p. 66) I believe this to be a very valid and important goal and the findings from the Biswas e. al. (2012) paper found initially that transfer of the problem solving skills was fragile and added the component of Adventure Player that “(Crews et al. 1997) show that it facilitates initial learning and leads to more flexible transfer.” (Biswas et al. 2012, p. 19) A paper by Gunbas (2014) shows a number of studies that confirmed that student understanding and ability to transfer the skills developed in a problem solving context was greater using a TELE.

When you consider contemporary videos such as Kahn Academy do not support these same goals in design as they are designed in a more flipped classroom style. Here a student would go and preview maybe before a teacher taught a skill or return for extra direct instruction on a specific skill they are struggling with. Fosnot (2005) describes a constructivist classroom as having four main principles that include: prior knowledge, focus on concept, challenge student’s ideas, and apply new ideas to similar situations. In a Kahn academy lesson they are all focused on concept acquisition. While the Jasper Videos require students to use concepts, the challenge their ideas to solve a unique problem that is anchored in a real-life scenario and then are followed up with a similar scenario to see if the ability to apply lessons learned from first video do transfer to the second video.

References:
Biswas, G. Schwartz, D. Bransford, J. & The Teachable Agent Group at Vanderbilt (TAG-V) (2001). Technology support for complex problem solving: From SAD environments to AI. In K.D.

Forbus and P.J. Feltovich (Eds.)Smart Machines in Education: The Coming Revolution in Education Technology. AAAI/MIT Press, Menlo, Park, CA. [Retrieved October 22, 2012, from: http://www.vuse.vanderbilt.edu/~biswas/Research/ile/papers/sad01/sad01.html

Cognition and Technology Group at Vanderbilt. (1992). The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design. Educational Technology Research and Development, 40(1), 65-80. Retrieved from http://www.jstor.org.ezproxy.library.ubc.ca/stable/30219998

Fosnot, C.T. (2005). Constructivism: Theory, perspectives, and practice. (2nd Edition) Teachers College Press

Gunbas, N. (2015). Students’ mathematics word problem‐solving achievement in a computer‐based story. Journal of Computer Assisted Learning, 31(1), 78-95. doi:10.1111/jcal.12067

To Anchor Instruction Or Not?

A great example of anchored instruction is in the Jasper series videos. Anchored instruction, also known as instructional design, includes engaging and problem rich environments that allow learners to understand the how, why and when to use different concepts and strategies (Cognition and Technology Group at Vanderbilt, 1992). This is exactly the direction the new BC curriculum is heading; collaborative, inquiry-based learning. However, for the Jasper series to be used effectively, depends on the teaching model used. Basics first, structured problem solving or guided generation.

What the Jasper series does by using videos, is it allows students to put real world problem solving skills to the test. I know for a fact that many teachers, including myself, are stuck on the basics first model instruction. This is where the teacher finds the need to implicitly teach a certain concept before allowing the students to run free with the problem being presented to them. Cognition and Technology Group at Vanderbilt (1992) are arguing against this and says it defeats the anchored instruction model. They are more aligned with the structured problem solving and guided generation practices. In the structured problem solving theory, students are given possible outcomes to a problem. They have to determine which one is correct, which eventually eliminates student errors. The ideal theory, according to Cognition and Technology Group at Vanderbilt (1992), is guided generation. The teacher acts more of a facilitator while the students are the leaders and asking themselves questions in a collaborative environment.

Something that the Jasper series allows students to see, is the complexity of real-world problems.  A misconception that students face, is that everyday problems don’t involve a simple step to solve it (Cognition and Technology Group at Vanderbilt, 1992). If teachers are stuck doing the basics first model, then students might not understand how to solve real-world problems.

What happens if learners are reluctant to work in group settings? What if they get frustrated? According to McCombs and Pope’s (1994) discussion on hard to reach students; the learning environment needs to include instructional practices that allow students to see real world experiences by using their minds (as cited in Hickey, Moore & Pellegrino, 2001). The Jasper series is a perfect example that showcases just that. There’s very limited reading involved too, just watching and listening. This might motivate some students as well.

Assessment? How does a teacher effectively assess their students who use the Jasper series? Ongoing formative assessment is key according to Gersten, Chard, Jayanthi, Baker, Morphy and Flojo, 2009. It can be in the form of written or verbal feedback which will help students be accountable and engaged in their learning.

I have used Khan Academy with my math group before and have heard about Mathletics, although you have to purchase the latter and therefore have not used it. What I liked about Khan Academy, is that students can complete missions. Missions are tailored math programs depending on their ability. At our school, we platoon for math and I had the ‘low’ ability group. I thought Khan Academy would capture their interest, but it was anything but. My students didn’t want to watch math videos, collect badges or take the time to learn themselves. They wanted direct instruction. I thought this was strange since they were using school iPads to complete their work and it was a self-pace program. This is not like the Jasper series in that the students were working in groups, but rather alone. I wonder if they would be more engaged if they completed the missions in partners or in groups? Would collaborative learning work better in this case? What if the range of math abilities is so wide in class, such as in mine? Would collaborative work be more beneficial to the students or using the basics first model so they know the multiplication chart before they work on the problem?

Another pitfall I had with Khan Academy, is the assessment portion. I was able to see on the teacher’s account what they completed, but there was no online quizzes or feedback other than calling each student up to my desk and showing them how they were doing in each lesson. I would have appreciated a quicker assessment model with this program, but in the end I cancelled it since my students didn’t’ want to do it anymore.

 

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

Hickey, D. T., Moore, A. L., & Pellegrino, J. W. (2001). The motivational and academic consequences of elementary mathematics environments: Do constructivist innovations and reforms make a difference?. American Educational Research Journal, 38(3), 611-652.

 

 

Video-based anchored instruction to enhance learning

The theoretical framework underpinning the development of the Jasper series is closely related to situated learning (Cognition and Technology Group at Vanderbilt, 1993). The creation of the series concludes that the traditional methods of teaching mathematics are inadequate for teaching students with the goal of achieving a conceptual understanding of mathematics. By utilizing anchored instruction, the Jasper Series attempts to create an engaging learning environment for learners that are actively participating.

As explained by CTGV (1993, p52) “the goal was to create interesting, realistic contexts that encouraged the active construction of knowledge by learners”. The series’ anchors were real life scenarios and not merely traditional math problem-solving activities. The learning was designed to encourage both learners and teachers to explore the content (Cognition and Technology Group at Vanderbilt, 1993). The role of technology –  interactive videodisc – was to help students easily explore the content and encourage teachers to be a part of the learning community.  The series’ creators intended for a community of learning to be built. Therefore, learners and teachers embody the theory of constructivism.

Video technology promotes an environment of flexible, bite-size positive learning. Learning math concepts can be challenging if it is done with traditional methods. However, video instruction can accommodate a different learning pace for individual learners. For example stop, pause or rewind buttons can allow learners to go back to look at certain points in the content, and replay a segment until the difficult math concepts are understood. We can use videos tailored for bite-size learning. Videos are ideal for conveying the intended learning objectives very effectively in a short time span(Eades, 2015). A video is the most effective medium for communicating information in a short period and the most popular content consumed globally regardless of age (Nielsen, 2015). That means instructors can easily incorporate video technology in math classes and that there will be a short learning curve for both teachers and students because the format is universally accepted. Finally, video-based anchored instruction provides a more motivating environment that enhances students’ problem-solving skills (Shyu, 2000

References:

Cognition and Technology Group at Vanderbilt. (1993). Anchored instruction and situated cognition revisited. Educational Technology, 33(3), 52-70.

Eades, J. (2015, June 6). Why Video Is The Best Medium For Microlearning. Retrieved from http://elearningindustry.com/video-best-medium-microlearning

Nielsen. (2015). THE EVOLUTION OF DIGITAL VIDEO VIEWERSHIP.   Retrieved from Nielson.com: http://www.nielsen.com//content/dam/corporate/us/en/reports-downloads/2015-reports/nielsen-google-case-study-sept-2015.pdf

Shyu, H. Y. C. (2000). Using video‐based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69.

Jasper, anchored instruction and PBL

The theoretical framework that underpins the Jasper series is anchored instruction. Anchored instruction is instruction that is “situated in engaging, problem-rich environments that allow sustained exploration by students and teachers” (Cognition and Technology Group at Vanderbilt, 1992). The Jasper series is a video based instruction format that presents students with a complex problem, which requires many subproblems to be generated and solved for the main complex problem to be addressed. It uses an engaging narrative with embedded data to present the students with all the information they may require to engage with the complex problem. This instructional approach promotes several teaching and learning activities that are central to constructivism. This includes generative learning, collaboration, active learning and engagement, and construction of knowledge.

Certainly the Jasper series could be presented without the use of technology. However technology does enhance the teaching and learning activities mentioned above. For example, the use of video could make the material more engaging due to the increased realism afforded by the video format (though it is a little dated now). This notion is supported by several papers, as highlighted by Taylor and Parsons (2011) in their review of the literature on student engagement. It can also be helpful for those students with learning challenges where an audio only narrative or reading only narrative would present a significant barrier.

Medical education has certainly moved in this direction. During the first two years, we have increased exposure of students to real clinical environments where they would learn though clinical encounters in a situated learning environment. In addition to this, their didactic lectures are taught along side problem-based learning activities, which is essentially anchored instruction. Our school currently does not use a video format, but a written digital document is provided to students in small groups, which gives students a clinical scenario. They then discuss the case to figure out what is going on with the patient. In all groups, the members decide on what further knowledge is needed in order to move forward with the case scenario. During this discussion portion, they are not allowed to use any resources other than their own ideas and experiences, which promotes discussion, collaboration and reflection. Once they have established learning objectives for the group, the first session ends and they have 1-2 days to research their learning objectives (either collaboratively or individually, depending on the group). They then reconvene and discuss the learning objectives before more of the clinical scenario is revealed. Typically, each case is discussed over 2-3 group sessions.

I think that in our problem-based learning groups, technology can be used to enhance collaboration and generative learning. For example, concepts maps may be useful to organize the group’s thoughts in a visual manner, adding to collaboration and generation of ideas. The use of something like Google Docs which affords collaboration asynchronously could also be helpful in collaboration outside of the group meetings. A video format could also be helpful to refine students’ observational skills as this is a critical part of the medical assessment, and again help to create an authentic/realistic environment.

 

References
Cognition, Vanderbilt TGA. The Jasper experiment: An exploration of issues in learning and instructional design. ETR&D. 1992;40(1):65-80. doi:10.1007/BF02296707.

Taylor, L. & Parsons, J. (2011). Improving Student Engagement. Current Issues in Education,14(1). Retrieved from http://cie.asu.edu/

Solution to Literacy related Math Difficulties?

  • How does this technology support learning and conversely how might it confound learning? What suggestions do you have for how the Jasper materials or other digital video might be utilized in your context (include suggestions for activities that do not involve the videos)? What research supports your suggestions? How might the video and/or the activities be augmented for children with learning issues in math? How have or can the contemporary digital technologies and/or their websites also support these suggestions for children with learning issues (eg. Prodigy, Desmos, King of Math, Math Bingo, Reflex Math, or others).

Anchored instruction provides instruction that aid in learning by presenting problems that students can relate to or be engaged in through meaningful content like stories or short scenarios. While reading and watching the videos, I actually started to think back on the “Bill Nye: The Science Guy” videos from when I was young, and thought back to how he used to present information in visually rich and meaning context that was easy to “absorb”, though he never really gave us questions/problems to solve, he would post questions that needed answers and would then answer them himself to us(the audience).  Anchored instruction seems quite similar to problem-based learning or inquiry-based learning pedagogies to me. The use of technology in such a learning environment seems to direct “imagination” in some sense by NOT having students imagine the problem.  By presenting problems in a story or scenario that students can understand showing the why, when and how,  then asking students to come up with a solution, this method seems more focused and I can understand why it works.  I have seen many grade school students who struggle with math problems simply because they have trouble understanding the context, and so have trouble “picturing the problem”. Students often read the word problems multiple times but have trouble understanding what the question is asking, and I have seen this occur in students who are Native English speakers or in ELL.  As it’s the form of instruction that works,  even if videos like the Jasper series aren’t used,  activities like hands-on presentations would likely yield similar results.

This instruction method also aids in the development of crucial critical thinking and problem-solving skills, as pointed out in the readings as well, that developers incorporated that into the Jasper series and would have learning goals that “emphasize the importance of helping students -all students- learn to become independent thinkers “. This form of instruction can likely also support children with math learning difficulties as it aids in the presentation of conceptual knowledge in math. Hasselbring(2005) mentioned that students with math difficulties often struggle to make connections in the problems, and would often solve problems from procedural knowledge. Anchored instruction might be able to help them see the connection needed. Math Videos like the ones on Brainpop can likely do the same, though a subscription is needed.

 

References:

Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2005). Technology-supported math instruction for students with disabilities: Two decades of research and development. Retrieved December, 12, 2005. Chicago

THE JASPER EXPERIMENT: USING VIDEO TO FURNISH REAL-WORLD PROBLEM-SOLVING CONTEXTS: The Cognition and Technology Group at Vanderbilt University. (1993). The Arithmetic Teacher, 40(8), 474-478. Retrieved from http://www.jstor.org.ezproxy.library.ubc.ca/stable/41195446
Cognition and Technology Group at Vanderbilt. (1992). The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design. Educational Technology Research and Development, 40(1), 65-80. Retrieved from http://www.jstor.org.ezproxy.library.ubc.ca/stable/30219998

 

Consider a block of mass m at rest on an inclined plane…

The Jasper Experiment is responding to what I might call the “Block On An Incline” issue:

It is a classic Physics 12 lecture in which students develop an algorithm for analyzing the possible motion of a block that has been placed on sloped surface.  The analysis is completely canned, and stripped of any context, but involves an impressive collage of math and reasoning skills.  It is considered a traditional pinnacle of achievement to solve these problems in the study of dynamics.  The group at Vanderbilt point out that skills or tools transmitted by a teacher in the absence of context or discussion are “inert knowledge” (CTGV, 1992a, p. 67).  I completely agree.  Their main idea is effectively:

CONSTRUCTIVIST + SOCIAL + COMPLEX PROBLEMS = DEEPER UNDERSTANDING

Authentic, complex problems, they argue, are key to use because the act of exploring the solution space of a problem (e.g. What is possible?  Can I estimate values?) is a more relevant ability than memorizing algorithms.  In a related study of complex problem solving, Vye et al. (1997) note that students of traditional classrooms are good at calculating things, but pretty weak problem solvers.  Collaborative work, they find, has the potential to improve the quality of problem solving.  Effectively, if the effort is focused and roles are understood, groups come up with much better solutions to problems than individuals.

Over a decade later, Park and Park (2012) worry that the complex and open form of problem and project based learning allows students to spend too much time on failed ideas.  This lost time means fewer topics are covered and their toolkit of knowledge is garbage.  Their fix is to structure the problem solving to cut out the failures, which is ultimately a return to algorithms disguised as real world problems.  This recommendation doesn’t deal with the original Jasper issue that students have trouble identifying what sub-skills are required to solve a problem because of lack of exposure to these types of questions.

The contemporary videos in this question set (c.f. Khan Academy etc.) are not Jasper-type videos.  Instead, they form a fantastic repository of guided practice for the many specific sub-skills that may pop up while teachers get on with helping students learn how to select the right tools for the job.  I use them frequently.

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.

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.

Park, K., & Park, S. (2012). Development of professional engineers' authentic contexts in blended learning environments. British Journal of Educational Technology, 43(1), E14-E18.

Anchored Instruction through Collaboration

The perceived issue the Jasper materials are responding to is a lack of engagement and mathematical understanding for learners when it comes to mathematical concepts. The purpose of the videos is to create learning opportunities that are anchored in meaningful and engaging technology contexts, using anchored instruction. Anchored instruction was “designed to overcome the problem of developing ‘inert knowledge’ – knowledge learned in school that cannot be retrieved when it is needed for another situation” (Zydney, Bathke & Hasselbring, 2014). The Jasper Project uses technology to motivate students to problem-solve as a team and solve relevant chronological problems within a story-line. The program motivates students to help them learn to think and reason about complex problems (Cognition and Technology Group at Vanderbilt, 1992). Using a constructivist approach, students are encouraged to construct their own understanding of mathematical concepts, while developing problem solving and critical thinking skills. I think this is a relevant problem in today’s classrooms, because students often don’t see or make the connection between curricular competencies and real-life scenarios. When students can make connections, it provides deeper learning opportunities for students to explore concepts, take risks, and test a variety of problem-solving strategies (Hickey, D., Moore, A., & Pellegrin, J, (2001). In my experience, students who are English Language Learners (ELL) struggle with math concepts that are solely print-based problem-solving activities. These videos provide opportunities for students to build upon concepts and work in a team, developing communication skills.

In one study, students who used the Jasper materials showed slightly larger gains on assessments (Hickey, D., Moore, A. & Pellegrin, J, (2001). With the advancements made in technology, updated versions of the Jasper Project could be extremely beneficial. Using current topics of interest for elementary learners, paired with apps accessed on iPads, could create deeper learning experiences. Students would have access to the video series, and could possibly share ideas and debate with other classes through Skype, similar to a Mystery Skype (http://psolarz.weebly.com/how-to-set-up-and-run-a-mystery-skype-session.html). Taking this a step further, apps could offer virtual reality opportunities for students to be completely immersed in the problem their team faces, creating an active, rather than passive learning environment.

The contemporary videos that are available for math instruction from Khan Academy address the issue, but fall short because they lack the group collaborative effort provided by the Jasper Project. “The model presented by the Khan Academy proposes a flipped classroom where students take responsibility for the acquisition of key concepts at home and then in class essentially complete extension tasks and gauge understanding” (Lenihan, E., 2013). In inner-city classrooms, students are not able to work through concepts at home because of the lack of technology. The Jasper materials utilize classroom activities and time.

References:

Cognition and Technology Group at Vanderbilt (1992b). The Jasper series as an example of anchored instruction: Theory, program, description, and assessment data. Educational Psychologist, 27(3), 291-315.

Hickey, D. T., Moore, A. L. & Pellegrin, J.W. (2001). The motivational and academic consequences of elementary mathematics environments: Do constructivist innovations and reforms make a difference? American Educational Research Journal, 38(3), 611-652

Janet Mannheimer Zydney, Arne Bathke & Ted S. Hasselbring (2014) Finding the optimal guidance for enhancing anchored instruction, Interactive Learning Environments, 22:5, 668-683, DOI: 10.1080/10494820.2012.745436

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