Reflection Post 8

For this final reflection, we were asked to consider peer review as a tool. As I read the resources provided, two articles in particular stuck out to me. These sections caught my attention:

“In many classrooms that use traditional assessment methods, teachers ask students to present their final projects to the class. The usual result? One student at the front of the room reading PowerPoint slides aloud to a room of dozing fellow students. Peer critiques, in contrast, demand dynamic participation. Listeners must not only attend to each presentation, but also offer concrete suggestions for its improvement while commending aspects of the work that they appreciate” (Reynolds, 2009).

“Lastly, students must learn to see mistakes as natural. This helps them take risks and understand that reworking is normal. Otherwise, the students can never be convinced that reworking their products will actually benefit them. Fail early and fail often, though it sounds crazy, is a great classroom mantra” (Ruff, 2010).

Keeping students engaged when they are not the ones speaking can be a challenge in the math classroom. By encouraging students to critique the work of their peers, it can help them to practice their abilities to find problems in their own work down the road.

Math is a subject of which most students have an innate fear. By fostering an environment where students can make mistakes without their peers being overly negative, students will not have the penalty to feelings of self-efficacy that can otherwise come from errors, and students will learn to see mistakes as stepping stones to solutions.

One way that I’ve seen this incorporated into a classroom was in a physics class. The teacher didn’t directly grade the homework. Instead, she would randomly call on a person to work one of the problems on the board and would continue to do so until there were no more problems. This allowed the other students in the class to critique your work, but since the grade was on whether you had done the problem, not done it right, there was no stigma against making a mistake. The only way you could fail the homework assignment was to not have the problem you were called on to do finished. If you didn’t do the work, you didn’t get a grade, but if you made the attempt, you’d have the chance to discuss what you’d done. As I read these articles and reflected back on those assignments, I decided to that I’m going to look to incorporate something similar into my current classes. Peer feedback is a powerful tool, and one that I would like to utilize more.

Reynolds, A. (2009). Why every student needs critical friends. Educational Leadership, 67(3), 54–57.

Ruff, J. (2010). Collaboration, Critique and Classroom Culture. UnBoxed, (6). Retrieved from

Reflection Post 7

After the project presentations, it is important to look back and debrief. What worked? What didn’t?

For the project I designed, an ideal activity would be a low-stress discussion and party. I would ask the students which design elements impressed them and why, which presentation techniques grabbed their attentions and how it improved over they typical presentation, and what enticed them to interact with the project websites and what didn’t. I would also (if possible) have the guest judges appear to comment on what they saw that impressed them as professionals and what they look for in a presentation.

We would then enjoy food. While this may be partially because I enjoy eating, it is also because the more informal environment would allow students to continue reflecting on the projects and give students who don’t enjoy addressing the class as a whole to approach students from other groups and give feedback.

After weeks of stressful deadlines, I think it is important to give students an event to look forward to to help them relax and process what they’ve learned.

Reflection Post 6

When moving from the role of lecturer to that of facilitator, there are some fundamental shifts that have to take place. However, there are also some misconceptions about what it means to be a facilitator.

Shift 1: Stepping aside
In a traditional lecture based class, the learning is centered on the instructor. At least in math, this can lead to, to coin a term, the problem of divine origin; students can be made to feel that an equation or technique is what it is because the instructor and/or textbook says it’s so, and that those sources of information are infallible. Students also tend to have a locus of control further outside of themselves, making comments that their “teachers got them through math” instead of feeling that they themselves were proven capable. When switching to the role of a facilitator, the focus for learning moves from the instructor to the students. They construct the knowledge themselves by experience and internalize their locus of control. After all, it’s hard to give credit to the teacher when you found the way to solve the problem yourself.

Pitfall 1: Stepping out
When shifting from the “sage on the stage” to the “guide on the side,” instructors must be careful not to become (or appear) as the “slack in the back.” Just because the instructor isn’t the center of learning doesn’t mean that they aren’t still a source of information. Abandoning students all together can greatly increase the experienced cognitive load. It’s okay to still impart knowledge to the learners as long as you and the students both see it as a help to them on their journey of discovery and not the journey itself.

Shift 2: Focus on learning, not knowing
Often in more traditional instructional settings, students are expected to memorize facts and procedures. However, acting as a facilitator means helping the students learn how to learn more than memorize bits of information. This is especially needed in the math and sciences. A scientist isn’t a person who knows a lot about science, a scientist is someone who knows how to ask a question, review the literature, make a hypothesis, and test that hypothesis. In other words, they know how to learn.

Pitfall 2: Forgetting standards
It is important to keep in mind that as a facilitator you can guide students towards acquiring the information that they need to know in order to meet the applicable standards. While this can involve lectures in small doses, it’s often best done with small nudges or questions. Instead of using a day to explain the constant nature of the speed light in any reference frame, ask the question that Einstein asked; “If a person is standing on a train traveling in a vacuum and tosses a ball, an observer in an inertial reference frame will see the ball’s speed as the speed of the train plus the speed the ball was thrown at, right? So what happens if instead of a ball, it was a flashlight? Would the observer see the light traveling at the speed of the train plus the speed of light?” By giving them a problem that they can solve via inquiry rather than just lecturing on the topic, students can ponder on, research, and connect (with guidance) the various aspects of special relativity. By building the knowledge themselves rather than hearing it in a lecture, they  get the benefits of knowledge construction while heading in the needed direction for the class standards.

In the end being a facilitator is all about emphasizing the students. Whether the method is project-, problem-, or inquiry-based learning, allowing the students to make discoveries gives them agency and helps them to develop self-efficacy. Facilitators aren’t absent, but instead act as a resource for questions and a guide to help prod students down productive avenues. By teaching students how to learn rather than how to memorize, teachers can make a greater and lasting impact on their students.

Reflection Post 5

It would be difficult to make this a reality at my “school” since we only teach math classes. However, I think it is an important topic to keep in mind especially when it comes to math education. The number one question that I get asked that isn’t about a problem we are working on is, “When would I ever use this?” Unless they go on to become mathematicians pushing the boundaries of what is understood, almost everyone that uses math uses it to accomplish something, and attaching that directly to something they would understand and be invested in would cement concepts in their mind faster than simple practice would.

While I can’t do much about this now, it is definitely an aspect of PBL that I will try to incorporate in math classes in future locations. It doesn’t have to be done on as grand of a scale as in the video to be effective. Instead, something as simple as pairing up with a science instructor can make both be much more effective. Even if PBL isn’t used in its entirety, coordinating homework assignments to what is being learned in other classes still makes the math instruction more impactful. As a loose example off the top of my head, “In history you learned about the Louisiana Purchase where President Jefferson purchased 828,000 square miles of territory for $15 million in 1803. How much was paid per acre? Based on inflation and other factors, how much would that be in current dollars? Calculate a value for the territory today and show what the percent increase in value was. Defend your reasoning.” In this way that math is directly linked to something the students are studying, and there isn’t necessarily a single correct answer. Maybe they decide to calculate the current value of the land by using the GDPs of the included states, or by using an average property price on a national or regional level. Maybe they calculate it some creative way I don’t even think of. By allowing students room for inquiry and connecting that inquiry to other subjects, the assimilation of knowledge into their existing schema can be facilitated far greater than considering math in a vacuum.

Reflection Post 4

In my project, there are three principle sources of assessment, each with varying degrees of student input. The first line of feedback comes from personal reflection and peer feedback with the project notebook. In most science and engineering fields, professionals still use paper notebooks to record daily progress in design meetings. While that may seem strange, it is largely because of the way that patent law works. After each entry, there is a space for a witness signature. By adapting this technique for the students in the class, they both learn about a technique used in industry while reflection on what they have accomplished each day as they enter in the information. Because each entry requires a peer signature, there is an opportunity each day the project is worked on for peer feedback. This assessment does not have a set rubric attached to it, though students will be shown several examples of a well-kept project notebook at the start of the project. This will allow students a great amount of say in how this assessment goes and what constitutes high-quality work.

The second form of assessment comes from the project website where students will make a weekly post essentially advertising their project. While these posts do have a grading rubric associated with them, students are still encouraged to give feedback on the sites of other groups. While this has less freedom than the previous assessment, it still allows for meaningful interactions between the instructor and the students and allows for some words (like “professional”) to be defined in part by the students’ efforts.

The summative assessment for the final presentation is the one with the least degree of student input. This was done intentionally. When presenting a design to a potential customer, you must meet the needs of that customer. To simulate this, the teacher and guest judges will grade the presentations via the rubric with little direct student input. However, even here students participate in the creation of the standards partially via their involvement in the previous assessment stage, but also in how they participate in the Q&A session following the presentation. If students are interested and make comments that extend past surface details, the judges will notice that it grabbed public attention than a presentation that is only followed by forced, superficial questions.

None of these assessments alone would make for good feedback for the students. By combining the different levels of self, peer, and instructor review for each level of assessment, students can be properly guided towards better practices in the future.

Reflection Post 3

Is it still PBL without an authentic audience?

Short answer: Probably not.

Long answer: It really depends on how you define “authentic audience.” Without an audience in mind for which the project in question would have great meaning, the project moves away from PBL and just becomes a project. Emotional investment is one of the corner stones of PBL, and it is why students stay interested.

However, I don’t think the project necessarily needs to be given directly to the authentic audience for it to be PBL. For example, say a class investigates and plans a way for their city to pick up recycling from residences and/or businesses. The authentic audience in this case could be the mayor, city manager, or maybe a county commissioner who would be capable of enacting such a plan. Even if that leader is unable to come hear the students’ presentation, I still feel that it would be PBL because the emotional investment and intended audience were both present.

So while there does need to be an authentic audience, I don’t think that a representative of that authentic audience needs to directly receive the project, although doing so would increase the impact for the learners.

Reflection Post 2

I’ve often gone back and forth on whether or not I actually like project-based learning (PBL). It clearly works well in some situations, but it certainly can’t be universally better in every instance. For every choice, there is an opportunity cost associated with it, and I feel that a lot of the materials I’ve found on PBL don’t acknowledge any. They either solely delineate its strengths, or simply make blanket statements about failure. Two papers in particular have caught my eye as I have tried to work through my own opinions on PBL; Kirschner et al. (2006) and Hmelo-Silver et al. (2007).

Kirschner and his colleagues are strict cognitivists in how they view student learning. Sweller in particular, one of the coauthors, has contributed a great deal to the literature on cognitive load theory. They view PBL as causing too much cognitive load for novices, inhibiting the assimilation and accommodation of knowledge into mental schema. They point out several studies and meta-analyses that seem to support their points. They make several great points about the potential short-comings of learning without guidance.

Hmelo-Silver and her colleagues responded to the original paper by arguing that PBL isn’t as unguided as Kirschner et al. suggested. Instead, the scaffolding inherent in it keeps the cognitive load low enough that students can still organize gained knowledge into schema. They presented several studies and meta-analysis showing that PBL often leads to better outcomes than traditional modes of instruction.

The frustrating thing for me as a student trying to learn about the method is that both papers are almost certainly right to some extent. Without proper guidance, students will not be able to learn the knowledge they need to succeed. Conversely, students who simply memorize facts from a book without any inquiry or discovery will be unlikely to solve unique problems or to pursue knowledge not already in the literature. However, it has been difficult to understand from the studies I’ve read what causes some cases of PBL to be successful while others don’t produce the desired results. My own past experience in PBL or PBL-esque settings have not been positive ones. Was that because they were individual projects? Is it possible that PBL works better in groups? Or could it be that upper-level math lends itself less readily to PBL than an applied science class?

These are questions that I’m still looking for answers to. Kirschner et al. and Hmelo-Silver et al. have cited several studies each that I can use to springboard into further research. I suppose it’s time to get to work.



Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75–86.
Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42(2), 99–107.

Reflection Post 1

It would be a lie to say that I excelled at reflection assignments. Of all the areas I lack as a student, this is the worst. I tend to prefer to discuss gained insights with a living, breathing person rather than posting to a blog or writing in a journal. I guess it always made me feel like standing in an otherwise empty field at night yelling useful information out into the unhearing darkness.

With that said, reflection is still important, and it’s a skill that I will continue to work on as I continue to progress in my studies as a learner and my practice as a teacher. Even in small ways, having students reflect on how they are progressing and to write goals for the future can help them to maintain scholastic excellence as they progress.

Module 4 Reflection

The tools and methods of education are connected beyond what the average person might consider. While usually the use of the tool is modified by the learning theory, occasionally the learning theory is modified by the tool.

An example of the learning theory affecting the tool would be the change from learning logs to blogs. For many years, students in several subjects were required to write in journals and submit this journals to the instructor for grading. This works well with Bloom’s Taxonomy and can meet many of the higher-order thinking skills (Larson & Lockee, 2014, p. 101). However, in light of contributions made by sociocultural theorists and social constructivists, this learning log became a blog. Much of the activity remained the same, but students can how give constructive comments and launch discussions based on the learning logs of their peers. This additional avenue of interaction can improve student motivation and retention.

The effects of technology on the formation learning theories are not as common, but do exist. In fact, the entire learning theory of connectivism* is essentially  a response to how technology has changed learning, with those who advocate for its adoption asserting that the traditional cognitive schema have essentially been outsourced to external networks of sources referred to as nodes (Siemens, 2004). If technology had not advanced, this entire avenue of research and instruction would have no reason to exist.

How does this affect my classroom instruction? Personally, I prefer to focus on how theory informs the tools than how tools inform the theory. Occasionally I will look at my instructional methods and ask myself if there is any part I could improve by introducing a digital tool. I then examine the cognitive opportunity cost (i.e., is the increase in learning worth any increase in effort to learn and/or utilize a tool that students might not be familiar with), and if the examination comes out favorable, I develop a lesson plan for it. While my current job does not allow me a great deal of flexibility to change how I deliver the curriculum, I believe this exercise is still useful and will help me as I continue on in other environments. It also gives me a method of reevaluating how I approach my teaching within the bounds of the learning theories to see if I can improve how I structure each lesson.

As we examine both our tools in light of learning theories and our theories in light of our tools, we will all be able to continue improving instruction for each generation.


* There is some debate as to whether connectivism actually should be considered a learning theory, this some thinking that it is not significant enough to warrant that distinction. Kop and Hill (2008) found that while connectivist ideas can inform and improve instructional design that “it does not seem that connectivism’s contributions… warrant it being treated as a separate learning theory in and of its own right.”



  • Kop, R., & Hill, A. (2008). Connectivism: Learning theory of the future or vestige of the past? The International Review of Research in Open and Distributed Learning, 9(3).
  • Larson, M. B., & Lockee, B. B. (2014). Streamlined ID: A Practical Guide to Instructional Design (1st ed.). New York: Routledge.
  • George Siemens. (2004). Connectivism: A theory for the digital age. Retrieved from

Module 3 Reflection

Due to family emergencies and natural disasters, I am in the awkward position of submitting the reflections for two modules on the same night. “He hasn’t learned anything since the last post,” you would correctly point out, “so this post is rather pointless,” you would incorrectly conclude. While on the last post I chose to focus on my classroom as it stands now, on this one I would like to expand my thoughts to classrooms in which I may find myself in the future.

While it is true that I see the cognitivist approach most useful in my current employment, that is because I feel that learners need to have basic mental schema in place before going on to construct higher-level knowledge. With that said, some subjects are by nature higher-level. For example, a physics class is an example of a class closely related to my current teaching experience that would benefit more from a constructivist approach. Assuming students have preexisting mental schema for math operations and theories, they could rely on that knowledge to see how it relates to real-world situations using basic physics theories. In physics, it is easy to design basic experiments to that students can use to make predictions, analyze the results, and find possible sources of error between theoretical and observed solutions. In fact, there are many that students could design many on their own, increasing their investment and the level of their activity in the construction of the knowledge. That is much harder to do if the basic mathematical vocabulary is not already present.

I do hope to teach a wider variety of subjects one day, and learning how different theories can apply, and imaging lesson plans for different related subjects helps to find where those theories could work and where they wouldn’t. At some point, I will try to do a literature review to see which of my theories based on readings and experience are born out in the research.