Category Archives: A. Conceptual Challenges

Lesson Learned

What’s interesting to note here in the video titled, “A Private Universe,” is how recent Harvard graduates still don’t know why the Earth has seasons. One would think after years of post-secondary education that there would be far fewer misconceptions on this question coming from 21 out of 23 students who were interviewed. Either, these students still don’t understand after being taught why Earth has seasons, or they missed school that day. This proves that misconceptions can happen to anyone, from any educational background. Aguirre, Haggerty and Linder (1990) realize that children bring their own theories on how things work and on the world into the science classroom and us educators have to recognize this and embrace it. As in the case with Heather.

For Heather, she had many misconceptions about Earth Science. For one, she believed the orbital path of the Earth around the Sun is in a figure eight movement. Why does she think this? At first, she has no idea and then remembers that she saw another diagram from her science textbook about something different and assumed this orbital path was for the Earth too.  Posner, Strike, Hcwson and Gertzog (as cited in Shapiro and Bonnie, 1988, p. 99) presented a great argument; that learning is a rational activity where learners make their judgements solely based on the evidence available at the time. I agree with this statement. Learning needs to be inquiry based. For example, every science unit I teach to my students I have a wonder wall where they ask questions that they want to know the answer to. I hope over the course of the unit that they will have answered many of them, if not all. We use science interactive notebooks, have guest speakers, conduct experiments and ask each other questions. There are times where I will teach facts, but mostly I want my students to learn through inquiry.

Posner, Strike, Hcwson and Gertzog (1982) have outlined student’s misconceptions through a process called conceptual change. More specifically assimilation and accommodation. With assimilation, students use existing concepts and theories to deal with new phenomena. With accommodation, student sometimes can’t grasp new concepts or ideas and thus need to reorganize his/her previously learned concepts. In Heather’s case, I believe she needed to assimilate her concepts with the new one learned on Earth’s rotation around the Sun. She had the right idea, just needed to modify the orbit to a more elliptical pattern.


Aguirre, J. M., Haggerty, S. M., & Linder, C. J. (1990). Student‐teachers’ conceptions of science, teaching and learning: a case study in preservice science education. International Journal of Science Education12(4), 381-390.

Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science education66(2), 211-227.

Shapiro, B. (1994). What Children Bring to Light: A Constructivist Perspective on Children’s Learning in Science. Ways of Knowing in Science Series. Teachers College Press, 1234 Amsterdam Ave., New York, NY 10027


The video documentary, A Private Universe sheds light upon an important issue many educators face on a day-to-day basis, the question of a student’s metacognition. A question highlighted and discussed in this video centres around the notion of what exactly is a student thinking about regarding their own learning and understanding, before, during, and after a lesson. While watching the video it is intriguing to note that Heather, considered a more competent, intelligent, and insightful student from the perspective of the teacher, is unable to accurately and thoroughly explain how seasons work and the rotation of the earth and moon. It is clear from the video that as Heather is being interviewed, she is looking for validation from the interviewer to support her thinking, and continue the dialogue. When she begins to draw her ideas she is better able to have confidence in her thinking strategies.

According to Sacit Kose (2008) research into diagnosing student misconceptions can be better explored when coupled with allowing students to draw their ideas alongside interviews. Kose (2008) states, “That’s why; the results obtained indicate that drawing method is effective in determining the student’s’ misconceptions. One of the probable reasons of the determined misconceptions may be the difference between the scientific and daily language.” As students learn to use the vocabulary associated with new topics, they are then able to better communicate their understanding of these ideas with confidence and accuracy.

For myself, I have realized that importance of the simple KWL activity, and how within science classes, this tool is often misused. When students begin a new unit of study, accessing prior knowledge is critical. It is an opportunity for students to reflect upon their learning, understanding, and knowledge, but also to spend time thinking about what they wonder about. The challenge lies in finding the time to sort these reflections and ideas into meaningful lessons that will lead to clarity in future lessons. As Galen Erickson, (1979) mentions, “with knowledge of what the learner brings to an instructional setting recognized as such a vital component in planning educational programs, it should have become an important stimulus in educational research.” Therefore, what the children are thinking is the epicenter of true inquiry. Learning to be flexible in planning to avoid continued misconceptions of understanding being perpetuated means the teacher must put the student first.

What was clear from both the video and the research by Erickson (1979), Kose (2008), and Driver (1983), is that students need to be able to describe their thinking with the use of hands-on manipulatives, whether it be drawing ideas on paper or using models. When students are given opportunities to describe their thinking, while working one to one with a teacher, the teacher is then capable of targeting misconceptions and reteaching on the spot. This is where technology can come into play. Students can then use apps on the iPad, such as Explain Everything to record their understanding of the topic being studied, and teachers can provide better feedback to ensure that any misunderstandings are caught, and retaught. Yes, the issue of time will always be a concern, however, in British Columbia with the introduction of a new inquiry-based curriculum is being rolled out, less emphasis is placed on content, but rather on the big ideas within a grade. When educators spent time exploring concepts with the goal of quality understanding rather than quantity of content being covered, students will have a stronger foundation of knowledge, ultimately leading to more curious, inquisitive students, wanting to explore further.


Driver, R., Guesne, E., & Tiberghien, A. (1985). Children’s ideas and the learning of science. Children’s ideas in science, 1-9.

Erickson, G. L. Children’s conceptions of heat and temperature. Science Education 63, no. 2 (1979): 221-230

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

Making Sense

I believe that all learners have conceptual challenges when learning new ideas, similar to how educators teach with assumptions that they may not have noticed before seeing students struggle with the content. I don’t have a lot of experience teaching Science theories to students. However, from my little experience, I did notice that it doesn’t really matter what subject I was teaching, regardless of age, the students usually come into the classroom with some knowledge of the topics to be learned already.  This knowledge is sometimes complete, sometimes not, sometimes correct and sometimes not. It is also quite hard to have everyone in a classroom start on new topics at the same level, so it becomes a bit of a challenge for the teacher to scaffold students.  More than often, I find that the best way that works for me is to start topics from brainstorming together first. Get a sense of what everyone knows already, then review some previously taught material then connecting them to the new topic. More than often for myself, the best way that works is to start topics by brainstorming together first. Through that activity, I would then get a sense of what everyone knows already, from that I can then review some previously taught material before helping students make connections to the new topic.

This prior knowledge, fuels these personal theories developed by students and are often hard to overwrite and can take a long time to do so as they are personal and so “makes sense” to the students much more than something new being taught be the teacher. Most of the time, it’s easier to say “others just don’t understand my idea” than to really see that they’ve made a mistake in their theory because it “makes sense” to them. I believe that this challenge was very visible in Heather. Her theories made sense to her, so even though it was different from what the teacher taught after, she actually tweaked her theory instead of dumped her idea.

With advancements in technology and education, when Heather was later able to remember and recite the correct theory/answer with manipulatives next to her, it reminded me of the Multiple Intelligence Theory and how everyone learns differently, and manipulatives can be helpful for learning.  It helped when she had a 3D visual instead of the 2D representation she was asked to draw. This also made me see the manipulatives as technologies used in classrooms. Though not digital,  they were just as effective. When the manipulatives were first introduced to the classroom before the digital age, it was probably considered new media as well. But now, they are just regular mediums to have in a classroom, while new media are being introduced.

If the same “Four Seasons” question was to be asked by students now, they would have had the chance to learn the same material with digital media, so perhaps their answers may be different. Digital technology may have helped current students “see” the theory better, but may not help them understand or make internal connections though it might be easier.

Just a thought: Maybe that’s why we often find students not retaining course content as much as the need for them to make their own theories have decreased. As answers can just be googled.

Unpacking Personal Theories

Heather’s personal theories of what causes the change in seasons varied from the accepted scientific understanding. I’m not sure where her misconceptions stems from but it was clear to see that her beliefs were deep-rooted. Despite having been present in class and having access to learning material, her personal theory on the topic created a block to being able to fully adopt a new understanding.

What became clear to me during the video was the need for the Heather and her teacher to confront their own personal theories. It was interesting to hear the teacher comment, “You assume that they (students) know certain things.” Shapiro (1988), advocates that teachers should understand our own assumptions and consider what impact it may be having on the learning process. Equally important is students being encouraged to share beliefs. Having students unpacked their personal theories allows teachers insight into student thinking and an opportunity to explore ways to introduce new ideas and/or challenge misconceptions.

Conceptual challenges are not just related to what students are learning, but also from how teachers are teaching. In my own profession practice, I have encountered challenges with parents and students in the area of mathematics. I have been present during many interesting debates concerning student achievement in the area of mathematics. Parents and many teachers I know hold firm to the idea that success in mathematics is best achieved through the practice of drills as a way to enhance speed and accuracy. Shapiro (1988), identifies that this approach requires that students not delve into the complexity but rather accept what is being taught. At the other end of the spectrum are those who believe that student should explore different ways to solve math problems instead of using a single algorithm. Shapiro (1988), identifies that this type of approach factors into account the learners’ individual ideas, feeling about the learning.

In support of a more open and exploratory approach to math, a study conducted by Ng and Sinclair (2015), investigated grade 1/2 and 2/3 learning in a dynamic math environment. The learning environment emphasized quality communication as a basis for learning. Whole class dialogue exploring ideas and learning were central to the study. It also focused on the use of digital tools to aid in student understanding symmetry. The results documented a shift in student thinking toward a deeper understanding of symmetry. Although the results were based on only three lessons, the notion that dynamic environments for learning can be enhanced with quality dialogue and use of manipulatives is worth consideration.


Shapiro, B. L. (1988). What children bring to light: Towards understanding what the primary school science learner is trying to do. Developments and dilemmas in science education, 96-120. Available in the course readings library.

Ng, O., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. Zdm, 47(3), 421-434. doi:10.1007/s11858-014-0660-5

Teacher/Student Misconceptions

While viewing “A Private Universe,” I was struck by the teacher centred style of instruction that was presented in the video, and the passive participation of the students in their learning. Regarding student misconceptions, and the instructional approaches to science, some of the key takeaways from the video were:

  • teacher assumptions of basic ideas, unaware of students private, personal theories (deeply ingrained)
  • use of ineffective visuals and/or teacher explanations
  • student confusion of diagrams and information from different sources
  • a need for using varied materials and resources to appeal to different learning styles
  • students struggle with blending of new concepts into original concepts as new concepts compete with preconceived ideas

I remember personally learning about science through similar instructional approaches to those seen in the video. According to these approaches, teachers generally have their own notions of how their students learn best, and they aim to build their instruction through these assumptions about their students’ prior knowledge and learning styles. As teachers aim to meet curricular outcomes and impart concepts and knowledge on to their students, the opportunities for students to engage with content in diverse and engaging ways becomes extremely limited.

Rather than viewing students as ‘blank slates’ or as ‘objects of teacher activity,’ educators need to arrive at a greater understanding of their students in terms of how learning activities affect their perceptions, knowledge, and beliefs (Shapiro 1988). There exists a need for clarifying student ideas about a particular scientific phenomena before they engage in classroom instructional experiences. According to Shapiro (1988), “we know that children’s pre-instructional ideas about natural phenomena can be very different from those which they are asked to accept in school.” From this, students need to develop the ability to interpret available evidence and make judgments about the rationality of arguments and concepts that may contradict their own previously held beliefs. Rather than the teacher being the dispenser of knowledge and information, the students take the lead in their own learning and are afforded the opportunity to engage with materials and generate ideas and questions without the teacher imposing their own personal limitations or restrictions as to how this experience should be carried out.

As presented by Fosnot (2005), constructivist approaches to learning allow students to learn best when they are provided with opportunities to actively construct ideas and relationships in their own minds based on experiences and experimenting, rather than being told what to do by an instructor. Students should be afforded the opportunity to engage in self-directed learning with the facilitation and feedback provided by the teacher and class peers to support students as they work towards attaining fundamental and relevant knowledge and skills.

Through providing lessons and experiences that offer authenticity and relevance, with opportunities for deeper collaboration and sharing of feedback, we can support students through leadership opportunities in the role of a creator or experimenter in their learning. According to Seymour Papert (1996), constructivist and constructionist theories support students in taking an active interest in understanding how they think about learning. Rather than passively accepting knowledge, students need to engage in conversations about strategies for learning and problem solving, which Papert described as a process of Learning about Learning (Papert, 1996). This fundamental approach to learning will allow students to access the skills and experience necessary to become full participants in 21st century learning environments. Through these learning opportunities, our students will be able to enhance their ability to articulate personal understandings and perceptions, develop their knowledge and skill through authentic practices, and participate in collaborative learning environments.



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

Papert, S. (1996). The Connected Family: Bridging the Digital Generation Gap. Atlanta, Georgia: Longstreet Press.

Shapiro, B. L. (1988). What children bring to light: Towards understanding what the primary school science learner is trying to do. Developments and dilemmas in science education, 96-120.




Misconceptions in medicine and my reflections on Heather’s challenges

Heather’s challenges
It was really interesting to see Heather before and after formal instruction. Heather is really confident about her theories regarding the seasons, earth’s rotation and the phases of the moon. Then she is confronted with contradicting information, which challenged her own conceptions. Surprisingly, she modified some theories (such as the rotation of the earth around the sun) but held on to other theories (such as her definition of direct and indirect light). Heather’s own theories must have been derived from her prior experience, readings or teaching which she incorporated into her knowledge base. As Driver et al. points out in Children’s Ideas In Science, these ideas and interpretations are personal and sone ideas remain stable (like the direct and indirect light idea), such that formal instruction did not modify her ideas.

Seafood allergy and iodine
A commonly held misconception in medicine is the link between seafood and/or shellfish allergy and iodine. I encounter this quite often as I am a surgeon and we use povidone-iodine as a topical antiseptic that is applied to the skin or other tissues before surgery. I’m not sure where it comes from but many physicians and nurses believe that seafood and/or shellfish allergy is a contraindication to the use of iodine. It seems to be a commonly held belief that is perpetuated in both disciplines. And no matter how much evidence to the contrary is presented, the operating room management refuses to recognize the safety of its use in this population of patients. This misunderstanding likely stems from the fact that seafood and shellfish contain high levels of iodine. But many other foods also contain iodine. In addition, the allergen causing anaphylaxis or other severe allergy with seafood/shellfish is NOT iodine. In fact, we learn in our medical education that iodine is a essential mineral needed for proper thyroid function. Just as in Heather’s example, I can present my colleagues with evidence to the contrary yet their ideas remain stable. I often wonder if these stable ideas are more difficult to change in adults that have completed their education (aside from the mandatory continuing education that is required of our professions). According to Posner et al, who refers to the change in stable ideas as accommodation, there are certain conditions that must be met before accommodation will occur:
1) there must be dissatisfaction with existing conceptions
2) a new conception must be intelligible
3) a new conception must appear initially plausible
4) a new concept should suggest the possibility of a fruitful research program

Given the above, I think the greatest barrier is dissatisfaction with existing conceptions. It seems that there isn’t enough motivation to change their existing conceptions, because there is minimal dissatisfaction with what they believe. One way to address this using digital technology is to use something like simulation to visually show the difference between using povidone-iodine as a skin preparation versus the alternative that is currently used in patients that have shellfish/seafood allergies. Or a visual presentation on molecular mechanism of seafood/shellfish allergy to demonstrate that their ideas are in direct contradiction to scientific findings. Just having a conversation without hands-on activities to engage them may not be effective.

While looking into misconceptions in medical education, I came across a really interesting article that looked at novice biology teachers, and their misconceptions (Yip, 1998). According to this article misconceptions in science after formal instruction can be categorized into three groups:
1) informal ideas formed from everyday experiences which children bring with them to the classroom
2) incomplete or improper views developed by students during classroom instruction
3) erroneous concepts propagated by teachers as well as textbooks.

Yip states that for many complex and abstract phenomena, such as mechanisms of circulation and other medical topics, children are less likely to develop their own explanations/ideas because they would be unlikely to come in direct contact with these topics in daily life. Thus, these misconceptions are derived from the latter two categories. In Yip’s study of 26 secondary biology teachers (all university graduates with majors in biological science), he identified many basic biological concepts that were misunderstood by them. Some of these misconceptions were a result of oversimplification of concepts and erroneous information propagated in some text books, as well as misuse or imprecise use of terminology. Perhaps this is another area that should be explored when looking into the origins of students’ misconceptions.

  • Driver, R., Guesne, E., & Tiberghien, A. (1985). Children’s ideas and the learning of science. Children’s ideas in science, 1-9. Available online: search the title using any engine.
  • Posner, G. J., Strike, K. A., Hewson, P. W. and Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Sci. Ed., 66: 211–227
  • Yip, D. (1998). Identification of misconceptions in novice biology teachers and remedial strategies for improving biology learning. International Journal of Science Education. 20:4. 461-411.

Evolving Paradigm Shifts

While watching Heather in “A Private Universe,” I began thinking about how scientific knowledge develops and its parallels to learning.

In science, when studies disagree with our current knowledge base, there is a portion of time where scientists attempt to tweak their understanding or error analysis to help this new observation fit into the current theory. After many studies disagree with the current knowledge base there occurs a Paradigm Shift where scientists must abandon large portions of their preconceptions in favour of this new, more accurate idea. In much the same way, our learning follows a similar path where we are drawn to rationalize new information to fit our existing model. Fostnot (1994) recognizes this process “as the organization of experience with one’s own logical structures or understandings.”

It is apparent that by the end of the lesson that Heather had adjusted her paradigm to fit the new information that she gained during the lesson but remained unclear about some concepts around light coming from the sun. To make this shift complete, more instruction or investigation would be required to address such areas.

In my own experience in teaching biology, it is apparent that students have varied conceptualizations of Evolution and how it occurs. Frequently, as a result of the use of “evolution” as an idiom, students will believe that they acquire new skills and evolve to become a better person. As a result, it is a very important practice to directly address the misuse of the word. Some of the activities which I have found successful in breaking this preconception is to look at historical science around the topic. To start with the absurd ideas such as Lamarck who believed that traits you gain during your life can be passed on to offspring. I will ask the students what their parents are good at, and if they have the same skill. Lamarck would posit that if your mother and father were good at Math, then you must have acquired that skill as a result. I usually take this to absurd levels in order to break this misconception and begin the talk about what evolution and the passing of genes really means. Such as in the case of Heather, some students will still cling to the cognitive paradigm which they had before the lesson, and continue to believe that evolution is individual, short term, and a choice. As a result, each time I teach the course I try to evolve my teaching tactics to better encourage these paradigm shifts.

(Pun in last line intended)



Driver, R., Guesne, E., & Tiberghien, A. (1985). Children’s ideas and the learning of science. Children’s ideas in science, 1-9.

Fosnot, Catherine. Constructivism: Theory, perspectives, and practice. Teachers College Press, 2013 or 2005 version. Chapter 1: Introduction: Aspects of constructivism by Ernst von Glasersfeld or Chapter 2: Constructivism: A Psychological theory of learning or Cobb, Paul. “Where is the mind? Constructivist and sociocultural perspectives on mathematical development.” Educational researcher 23, no. 7 (1994): 13-20.

Thompson, F., Logue, S. (2006). An Exploration of Common Student Misconceptions in Science. International Education Journal. 7(4), 553-559.

Conceptual Challenges and Digital Technology

My educational background suggests that many scientific concepts are taught only conceptually. Examples and hands-on application of knowledge acquired in courses were limited to available resources that were often inadequate and static – we did not have many opportunities to explore the concepts in real-life settings or play with these concepts in a virtual environment. This prevented us from understanding scientific concepts thoroughly. In most cases, the instructors usually stood in front of the class or showed videos as they taught the concepts. This was also well illustrated in the  “Heather’s challenges” course video.

From that video, I learned that students strongly hold onto their private scientific views. I see two reasons that contributed to the misconceptions of scientific concepts. The first one is that such misconceptions are often not challenged in schools during instruction, and therefore students continue to regard the misconceptions as true. The other reason is that students don’t have many opportunities to explore or examine concepts they learned in science classes. How can we overcome these problems?

We find some answers in scientific papers examining how the application of new technologies in the classroom can improve learning. So, “Does the medium change the Message?” The answer appears to be “Yes, and profoundly so” (Yazon, Mayer-Smith & Redfield, 2002). The WebCT content of the auto-tutorial genetics section was chunked, self-paced, and acquired collaboratively through peer interactions. These interactions were further enhanced via the instituted student help desk for individual and small group tutoring. The results of the study strongly indicate the course promoted independent learning and understanding as opposed to rote learning. In effect, the new method allowed students to experiment with the concepts through technology. It also provided valuable feedback, via the help desk, that challenged students’ privately held scientific views.

What else can technology do to address conceptual challenges? It turns out it can keep students more engaged with their learning through the process of gamification. This process improves flow and helps students form new conceptions faster and more accurately. According to Professors Dilip Soman or Nina Mažar from the Rotman School of Management, teachers can gamify learning content by following these five steps: understand the target audience and concepts, define learning objectives, structure the experience, identify learning resources, and apply gamification elements(Stephen, McRobbie & Tom, 2000).

So, if technology can facilitate and enhance learning, why isn’t it widely adopted? To a no small degree, it is because teachers’ conservative culture states that technology would make students lazy – pushing a button should not substitute understanding of the underlying scientific principles(Huang & Soman, 2013). These attitudes can and do change but progress is slow.

I believe that digital technologies – like interactive virtual simulations, videos, augmented reality, and gamified learning content – would help students experiment and understand scientific concepts more inquisitively, in simpler and more engaging ways.  


Yazon, J.M., Mayer-Smith, J.A. & Redfield, R.J. (2002). Does the medium change the message? The impact of a web-based genetics course on university students’ perspectives on learning and teaching. Computers & Education, 38(1), 267–285.

Stephen Norton, Campbell J. McRobbie & Tom J. Cooper (2000) Exploring

Secondary Mathematics Teachers’ Reasons for Not Using Computers in Their Teaching, Journal of Research on Computing in Education, 33:1, 87-109, DOI: 10.1080/08886504.2000.10782302

Huang, W. H. Y., & Soman, D. (2013). Gamification of education. Research Report Series: Behavioural Economics in Action, Rotman School of Management, University of Toronto.

Importance of KNOWING our students

The first challenge that popped into my mind when asking myself this question was that many activities that can come from STEM challenges need access to a variety of resources (i.e. technology!). That being said, many resources can come from such things like recycled materials, but when particular items need to be bought, it is not necessarily in the classroom or school budget and generally comes out of the teacher’s pocket. Bybee (2013) discusses how not having access to technology is one of the main issues when trying to incorporate STEM into the classroom. Beyond having access to technology, there are many other conceptual challenges with regards to STEM that have more to do with the students than the resources available.

In the video A Private Universe we were asked to witness numerous conceptual challenges. The video explores a local high school to see if the students have correct assumptions with regards to various scientific topics. Heather, a Grade 9 student, from a local high school was chosen by her teacher as someone who would most likely have a good answer for any scientific question asked. What the teacher did not realize was that Heather had virtually no knowledge with regards to science and more specifically the phases of the moon. Heather sat through a secondary lesson on the phases of the moon and was then re-interviewed 2 weeks later. However, as her private theories were still very much evident, Heather did not accept the correct information on the phases of the moon.

This made me reflect of the importance of diagnostic assessments. Teachers need to be aware of what their students know with regards to starting a new topic/discussion. Without understanding where a student is at, how can one program effectively and make sure that all the students are on the right track with their understanding?

Tabula Rasa, a blank slate, is certainly not the case with students, especially students in high school. Catherine Fosnot (2013) describes education and constructivism by saying that “too often teaching strategies and procedures seem to spring from the naïve assumption that what we ourselves perceive and infer from our perceptions is there, ready-made, for the student to pick up, if only they had the will to do so” (p15). Heather came to the class with pre-existing notions that were not addressed at the very beginning of the lesson or unit and as such, she is holding onto her private theories tightly. In the Confrey (1990) article, he mentions a quote by Osborne and Wittrock (1983) that states, “children develop ideas about the world, develop meanings for words used in science [mathematics and programming], and develop strategies to obtain explanations for how and why things behave as they do” (p. 4). Heather developed pre-existing ideas about the phases of the moon and has believed that for so many years that it is now difficult, half way through the unit, to switch her thinking.



Bybee, R.W. (2013). A Case for STEM Education: Challenges and Opportunities. United States of America: National Science Teachers Association.

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

Fosnot, Catherine. Constructivism: Theory, perspectives, and practice. Teachers College Press, 2013 or 2005 version. Chapter 1: Introduction: Aspects of constructivism by Ernst von Glasersfeld or Chapter 2: Constructivism: A Psychological theory of learning or Cobb, Paul. “Where is the mind? Constructivist and sociocultural perspectives on mathematical development.” Educational researcher 23, no. 7 (1994): 13-20. Available in the course readings library.

Schneps, Matthew. (1989). A Private Universe: Misconceptions That Block Learning. Retrieved from:


The formal/informal gap

Once I got over the hair and trying to identify the decade in which the video was shot, I was pretty captivated by the developmental path of Heather’s concept of an orbit.

Because of the montage style of filming, it is quickly apparent that Heather comes to the class with preconceived, informal notions about the movement of planets.  Having taught astronomy, I can attest to there being a ton of information, much of it highly graphical and spread over thousands of years of history and many cultures.  In this case,  she has superimposed orbital motion with formal learning about the analemma—the relative position of the Sun at noon every day over the course of a year.

I was further struck by the importance of clear graphical representation as illustrated by the “perspective view” of a circular orbit appearing to be an ellipse.  At the time of this writing, a Google image search for “orbital motion” delivered this gem:

Hosted proudly on PowerSchool Learning the curriculum clearly shows the Earth in a highly (incorrect) eccentric orbit.  For extra irony, there is a link to a PhET animation, arguably the most reliable and accurate simulation space for physics on the web today.

In my exploration of the readings around conceptual challenges I find the “formal versus informal knowledge gap” the most compelling.  If formal describes the white-washed, devoid of context topics like “block on an incline” from a standard introduction to physics, then informal is all of the real sensory concepts and language that people develop to explain what they experience in “real life”.  Why can’t we spend more time meeting the kids where they are and give them more time to explore?  Learn about things that are directly relevant to the structures that they live within?  Watching Heather come to an astronomy class and “book learn” about things she cannot touch or clearly observe directly to me is just another example in a career litany of curriculum that is divorced from practical application for the sake of, say, academic purity, or following an “accretion of knowledge” paradigm that is demonstrably not very effective for many learners.

British Columbia is going through an interesting change in curriculum that offers an opportunity to address this formal/informal gap.  In broad strokes, the focus has changed from curriculum heavy with “things to be taught” to a reduced list of core competencies and the chances to explore concepts in a way that is deeper and more personally relevant.  Although the details and execution are in early days, I believe this is the best chance we’ve had to move the focus of school from teacher-centred to valuing student-centred study.  It is my hope that allowing for differentiated instruction and more time to learn, students will have a chance to reduce the formal/informal gap.

Confrey, J. (1990).  A Review of the Research on Student Conceptions in Mathematics, Science, and Programming.  Review of Research in Education, Vol. 16 pp. 3-56.