Category Archives: A. Conceptual Challenges

One of the challenges that Heather faces in the video, “The Private Universe” is of her not being able to let go of the “theory of bouncing light”. This is mentioned towards the end of the video where Heather seems to have understood the rest of the concept of Earth’s revolution but still holds onto her “theory of bouncing light” that determines the season of the year. I found this part very interesting that she is not able to “let go” of her existing conception, however, she was provided knowledge on this concept and was expected to understand why the seasons change. I think the underlying factor behind any conceptual challenge is to not be able to “let go” of the conception even after you have been exposed to the reality or the truth.

Similarly, I encountered some similar tendencies of not being able to “let go” of conceptions that some of my grade 8 students had when I taught the exponents unit last year. The product rule says if there is the same base with exponents, it is equivalent to the base with the powers added together. Now, my students create their own knowledge about multiplying the powers when two same bases are being added together with powers, without my interference. According to Confrey, a conception is when, “children develop ideas about their world, develop meanings for words used in science, and develop strategies to obtain explanations for how and why things behave as they do” (Confrey, 1990, p. 3).  My grade 8 children developed a strategy to solve the addition of exponents based on their knowledge of multiplication of exponents and no matter how hard I tried, they will not “let go” of the new understanding that they have created for themselves.

Although analyzing Heather’s “theory of bouncing light” further, I also think that it might just be a result of creating explanation when asked a question on the spot. “We assume that mental model is a dynamic structure which is created on the spot for the purpose of answering questions, solving problems, or dealing with other situations” (Vosniadou, 1992, p. 543). I think it is up to the teacher to avoid situations like this with their students where they feel compelled to create their own theories on the spot because they do not have enough background information on it. In the article, Tracking Decimal Misconceptions by Linda B. Griffin, there are some key points that could be beneficial for teachers who find themselves surrounded by students who either would not “let go” of their existing conceptions or make new conceptions because they are put on the spot. One of the key findings in this article is to make connections with what students already know. Instead of giving students pieces of information and leaving it up to them to make connections, these connections should be made by the teacher when teaching material by activating the previous knowledge. In addition to the above, a teacher might want to break the unit in pieces and do a formative assessment before moving on. Technolgy comes in really handy when doing a formative assessment as a quick check before moving on to the unit, such as Kahoot, online jeopardy and other quiz games.

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

Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive psychology, 24(4), 535-585.

www.jstor.org.ezproxy.library.ubc.ca/stable/pdf/10.5951/teacchilmath.22.8.0488.pdf?refreqid=excelsior:681cc559288870a5c054a75882626988.

In general, our minds need to contextualise or conceptualise the information it receives in order to proceed them for understanding. In the video, ‘A private universe’ I will argue that Heather who has little training about astronomy used the information she had to create a mental representation to help her understand how the weather changes. After a formal lesson on astronomy. The way she conceives the weather changes has improved as she was able to replace some wrong mental representation she had with the right ones.

In fact, based on their prior knowledge, the students need to conceptualise the instruction given by the teacher in order to understand and retain them. Students’ experiences are different as they all have different cognitive approach to learning mostly depending on how information is presented to them.

Ball (1993) observes that “current proposals for educational improvement are replete with notions of ‘understanding’ and ‘community’ – about building bridges between the experiences of the child and the knowledge of the expert” (p. 374). She then inquires,

How do I create experiences for my students that connect with what they now know and care about but that also transcend the present? How do I do value their interest and also connect them to ideas and traditions growing out of centuries of mathematics exploration and invention? (p. 375).  (Paul Cobb, Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development, p 14).

I believe we should give time to our students to cognitively process the information they receive. Also, technology is a good mean to help the students to mentally represent their knowledge. In mathematics, my students usually struggle to represent the phase shits of a sinusoidal functions on a graph.  Their misconceptions are generally cleared out with the use of math software such as Geogebra and Demos, where we can visualize dynamic graphs. Also, graphic display calculators (GDC) is a great tool to make mathematics accessible to the students. When I was in high school we were not allow to use GDC to represent and interpret function, and solve algebraic equation. I used to be confused with function transformations. In math and science, collecting and processing data should be done with fastidious care, in order to avoid errors while solving problems. This stage in problems solving can take quite lots of time while we still need to analyze and interpret our results. GDC helps a lot in reducing the time spend on collecting and processing data and provide good opportunity for analyses and interpretation.

Technological environment helps to develop good understanding of concepts taught in math and science. The challenge remains to find activities rich in skills and experiences to help the students develop their own cognitive approach.

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

Paul, Cobb. Where is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development. Educational Researcher, Vol 23, No. 7 (Oct., 1994), pp.13-20.

Sara, Hennessy., Pat, Fung., Eileen Scanlon. The Role of the graphic calculator in mediating graphing activity. International Journal of Mathematical Education in Science and Technology.

The video this week, “A Private Universe,” pointed out something I have seen a lot over the years as a teacher and an administrator: what we perceive as basic concepts as teachers are not necessarily basic. It is something that needs to be addressed through better teaching practice (clearly established and communicated goals of each lesson, diagnostic, and formative testing). For any student, assuming prior knowledge is dangerous but Heather’s case is somewhat different. Her theories are based on her own efforts to construct knowledge and the theories themselves show an active mind wanting to learn. Her theories were incorrect but this is due mainly to the fact that her teachers did not have an accurate picture of what she previously knew. This speaks to Catherine Fosnot’s understanding of constructivism (2013).

In his book, “the pupil as scientist” R. Driver (1983) accurately explains Piaget’s concept of dissonance and how it relates to learning. I would argue that Heather concept of the astronomy was never challenged and no dissonance occurred, making it impossible for assimilation to occur. He in class learning did not build on her knowledge but rather had little impact because it didn’t address the misconceived notions she had already constructed.

Heather’s struggle resonates with me because I have gone through many similar experiences as a student in school. When one lacks the basic understanding or has a misconception this leads to an inability to reinforce factual conceptions because they do not match (Chi, 2015). Other misconceptions can occur from a teacher’s own misunderstanding of the material that can confuse the student (Burgoon, Heddle, Duran, 2011). As we saw in the video very prevalent myths survive in the minds of students and it was truly fascinating seeing the well-accomplished science grads at the beginning of the video so consistently get “basic” information wrong. In this case, the explanation is so prevalent in society it shouldn’t surprise most to think that High School students would not know this but the video itself shows just how these gaps in knowledge can be sustained over time and theories much more advanced and complicated can be understood and explained. It speaks to the fact that teachers can have a lasting effect that is not always positive.

As an educator, an important motto I live by is that one must know where a student is to be able to help to get them to where they need to be. Certainly, we are doing a better job of this than in the past but a firm commitment must be made to be meet students where they are rather than where we assume they should be.

Burgoon, J.N., Heddle, M.L., Duran, E. (2011). Re-examining the similarities between teacher and student conceptions about physical science. Journal of Science Teacher Education, 22(2), 101-114.

Chi, M. T. (2005). Commonsense conceptions of emergent processes: Why some misconceptions are robust. The journal of the learning sciences, 14(2), 161-199.

Driver, D. (1983) The pupil as scientist? Milton Keynes: Open University Press

Fosnot, Catherine. Constructivism: Theory, perspectives, and practice. Teachers College Press, 2013 Chapter 2: Constructivism: A Psychological theory of learning

The nature of science is such that it challenges students to grasp a conceptual understanding of the world around them. This inevitably leads to misconceptions as students try to grapple the way they view the world and trying to understand the fundamental laws that govern it. It is therefore no surprise that numerous studies have been done to try and understand how students’ misconceptions arise (Confrey, 1990). Some researchers have argued that it is fundamental for science teachers to have knowledge of the main misconceptions students possess in order for learning to take place (Sadler & Sonnet, 2016).

Students’ misconceptions stem from contradictions that arise from the way students view the world they have of the world versus the accepted view of the world (Confrey, 1990). Researchers have noted that misconceptions can be very difficult to overcome (Burrows & Mooring, 2014) because they require a radical shift in the learner’s view of the world. As Posner, Strike, Hewson & Gertzog (1982) explained, conceptual change, which is what is required for misconceptions to be altered, requires assimilation or accommodation of new concepts. If the learner is unable to incorporate the new notion or modify their conceptual understanding to fit the new notion then the misconception will remain.
In the video, A Private Universe (Schneps, 1989), Heather is faced with struggle of trying to make sense of new information presented to her about why seasons occur. Heather had a conceptual understanding of this phenomenon that was developed, from her interaction with the world, knowledge given to her by previous teachers and from other sources of information such as books. These sources provided Heather with the information on which she built a conceptual framework of why seasonal changes occur. When she was presented with the new information, the video shows her trying to assimilate the information into her conceptual framework and eventually her willingness to accommodate the information into her conceptual framework once she lost faith in her previous conceptual understanding. The video highlights the rigidity of the conceptual framework students have and how difficult it can be to try and reshape it.

In chemistry many of the misconception students possess stem from them trying to relate abstract and microscopic principles in a concrete and macroscopic way. One area in particular that proves rather challenging is the concept of chemical bonding. Burrows and Mooring (2014) note that chemical bonding proves to be a challenging concept for students to grasp because it requires that students have a proper knowledge structure. A knowledge structure is “the schema in which students organise and relate various concepts in order to make sense of a particular topic” (Burrows & Mooring, 2014, p.53). The understanding of chemical bonding is dependent on so many other concepts that if the knowledge structure is poor then students will have significant difficulties and misconceptions will exist.

Misconceptions can be overcome by guiding students into reorganising their conceptual framework to remove them. Technology can be vital in this regard by helping both students and teachers to see the conceptual framework the student possesses and what changes need to be made to alter it. For example, digital technology affords us the opportunity to simulate and model experiments that help in the building of the conceptual framework. If we therefore use the technology so that students demonstrate their understanding of a particular scientific process, teachers would get to understand where exactly the trouble lies in their conceptual framework and hence be better able to guide the student into fixing it.

References
1. Burrows, N., & Mooring, S. (2015). Using concept mapping to uncover students’
knowledge structures of chemical bonding concepts. Chemistry Education Research and                               Practice, 16, 53-56.

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

3. 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 education, 66(2), 211-                  227.

4. Sadler, P. (Producer) & Schneps, M. (Director) (1989). A private universe:
Misconceptions that block learning. [Motion picture]. (Available from Harvard University &                        Smithsonian Institution)

5. Sadler, P. M., & Sonnert, G. (2016). Understanding misconceptions: Teaching and
learning in middle school physical science. American Educator, 40(1), 26-32.

The idea of the human mind as originally an empty vessel or a blank slate has a long history dating back at least to Aristotle. Over the years, this notion has been argued and debated by many learning theorists, for instance Dewey believed that two essential components in education are the experience of the learner and critical inquiry (Dewey, J., & Bentley, A. F. 1960). In the video Private Universe, Heather’s errors and misconceptions occured because she has the wrong or inappropriate generalization of Space Science. Driver et al.,1985 argues “experienced teachers [need to] realize that students do have their own ideas about phenomena, even if at times these ‘ideas’ may seem incoherent at  from the teacher’s point of view” (p.2). There is no doubt that Heather’s misunderstanding or interpretation came from another source which made an impact on her learning.

According to Cordova, J. R. et al.,2014  there are several affective and motivational variables that may lead to misconceptions.   

Confidence prior knowledge– “refers to a retrospective judgment of whether one’s current understanding of the topic is correct” (Cordova, J. R. et al., 2014, p. 165)

Self-efficacy-”prospective judgment of one’s capabilities to learn about a specific topic” (Cordova, J. R. et al., 2014, p. 165)

Interest– Situational interest is a short-term form of interest generally facilitated by something in a person’s environment.  Individual interest- internal, and long-term form of interest that is less dependent on an environmental cue being present (Hidi, 1990).

Role of learner characteristics– With respect to gender differences does account for a difference in learner conceptual understanding.

Knowing that students enter the classroom with the conceptual understanding of a topic, as educators, it is important that we tap into those understandings to reveal an inconsistency. Vosniadou, S., & Brewer, W. F. (1992) researchers did an excellent job of investigating students knowledge about the shape of the earth. Unlike Heather’s teacher, these researchers considered asking questions about the topic before explicitly teaching the lesson. The following are teaching techniques to retrieve pre-conceptual understanding.

Concept Inventories

Concept inventories are multiple choice or short answer tests that target fundamental concepts within a domain.

Concept maps

Concept map activities can reveal the underlying structure or organization of students knowledge of a concept or constellation of concepts. These are very helpful when the kinds of causal theories and relations among ideas are critical to them understanding the course materials.

Self-Assessment Probes

Self-assessment probes are indirect methods of assessment that ask students to reflect and comment on their level of knowledge and skill across a range of items.

References:

Cordova, J. R., Sinatra, G. M., Jones, S. H., Taasoobshirazi, G., & Lombardi, D. (2014). Confidence in prior knowledge, self-efficacy, interest and prior knowledge: Influences on conceptual change. Contemporary Educational Psychology, 39(2), 164-174.

Dewey, J., & Bentley, A. F. (1960). Knowing and the known(No. 111). Boston: Beacon Press.

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

Hidi, S. (1990). Interest and its contribution as a mental resource for learning. Review of Educational Research, 60(4), 549–571.

Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive psychology, 24(4), 535-585.Available in the course readings library.

Over the summer I attended a professional development seminar centered around the concepts of student exploration.  During the presentation, we were asked to collaborate with our colleagues to discuss different materials (birds nest, feathers, pictures of third world countries, new articles, etc.) and our understanding of the topic.  Following, we completed a worksheet titled “I Wonder”, similar to the one below:

What initially caught my attention, and has proven to be effective, are the titles “What we think we know” and “misconceptions”.  Teaching grade 2, I was sceptical about my students grasping it.  We first discussed the chart in depth, and one of my bulletin boards was transformed into a large class wonder chart.  On sticky notes, we wrote facts that we thought we knew about spiders (an intro into our spider life cycle unit last term).  As the month continued, I brought out 20-30 books, computers, and artifacts related to spiders.  The student’s goals were to 1. determine if their original thoughts were correct or misconceptions (the sticky note was then moved to one of the columns) 2. find new information that we had not yet discussed (answer the original I Wonder questions) 3. write down any new questions that come to mind as they do their research.

It did take time, and a lot of preloading of instruction; however, once students became engaged it was all they wanted to do.  As a teacher, it also demonstrated to me where my student’s misconceptions were coming from and what I needed to directly teach or questions I could propose to have them investigate and answer.  By using sticky notes, students were also able to visually see whether they were on the right track with the previous thoughts, and also build on the understandings of their peers.  I had students walk up to the board throughout the day and read all the new stickys and then go home to their parents and explain what they had learned (whether they were the ones to find the information or not).

Studies have also demonstrated that using these inquiry based approaches are more effective in identifying student misconceptions, and increase student performance (Prince, Vigeant & Nottis, 2012).  They found that student understanding and overall performance improved from 46.6% to 65.7%, where minimal gains were made using instructional methods.  Windmann, Self and Prince (2014) also summarize the defining features of these inquiry based learning activities, which support their effectiveness.  These include: using peer instruction and collaborative work, using the physical world and materials, evaluating student understanding, making appropriate use of technology (in this case for research purposes), and beginning with the specific and moving to the general.

For anyone who would like to know more, Sandra Ball is an amazing resource and can be found on Twittter or email for those of you in the Surrey School District.

Shayla

Prince, M., Vigeant, M. & Nottis, K. (2012) Using inquiry-based activities to repair student misconceptions related to heat, energy and temperature. Frontiers in Education Conference Proceedings. Retrieved from http://ieeexplore.ieee.org.ezproxy.library.ubc.ca/stamp/stamp.jsp?arnumber=6462344

Widmann, J., Self, B. & Prince, M. (2014). Mini-Workshop – inquiry based learning activities: hands on activities to improve conceptual understanding. IEEE Frontiers in educational conference (FIE) Proceedings. Retrieved from http://ieeexplore.ieee.org.ezproxy.library.ubc.ca/stamp/stamp.jsp?tp=&arnumber=7044165

Heather struggled with reconciling her explanation and the new knowledge; the ability to try and see it from another perspective was blocked out, favouring instead her own understanding of how the seasons happened. Despite the fact that she struggled to explain it, her persistence in perpetuating knowledge that she believed to be true was staggering, or as Shapiro writes, “relat[ing] it to already existing ideas or to language which [she] already possesses” (Shapiro, 1988, p.99). As a result and as information for my own practice, I take this as a cry to have kids explain their thinking as much as possible, and to rely on tools like the Thinking Routines to help clarify and to get students to talk about their understandings at every opportunity, in order to expel the myths that may come up as a result of digging deeper.

I chose to explore equivalence and how the equals sign can be taken to mean “resulting in” or “computes to”. Vermeulen and Meyer describe this as students having an operational view of the equals sign, despite its relational meaning. Essentially, seeing the equals sign as a function of computation, and as such, students being likely to “reject equations such as 8=8 as false, because there is no obvious action” (Vermeulen & Meyer 2017). Many factors perpetuate this misconception, but they “…attribute an operational view of the equal sign to the use of calculators and direct verbal-to-written translation of mathematical sentences” (Vermeulen & Meyer 2017). The article by Vermeulen and Meyer had me thinking quite a bit about my own practice, not only with respect to technology, but also in the language I choose to use.

In thinking about how this affects educators, Vermeulen and Meyer write, “we are of the opinion that the results obtained from both teachers and students do suggest that, owing to these teachers’ limited MKfT of the equal sign, they were not aware that their teaching could, and possibly did, promote students’ misconceptions of the equal sign, nor were they able to identify students’ misconceptions or suggest how to prevent, reduce or rectify these misconceptions” (Vermeulen & Meyer 2017). As a teacher of young children, this is particularly striking, because it brings to light the fact that in something as simple as the way I chose to vocalize and draw attention to equivalence can help promote or expel the myths of math as solely arithmetic and computation.

Technology creates opportunities for students to be able to visualize the problem (and it’s potential solutions) in a different way, making room for them to be critical of their own misconceptions. In the case of algebraic equations and equivalence, the idea of a balance or see-saw helps the students envisage this concept. Sakow and Ruveyda write, “Modern tools like tablet apps may help middle school teachers end the thirty-year stagnation and put these algebraic misconceptions to rest at last” (Sakow & Ruveyda, 2015). In fact, there is an app that the article outlines as particularly effective to this end. Though I’m sure there are many such apps that use the same see-saw analogy, I particularly appreciate that “MathScaled’s weights change in value from problem to problem, erasing student notions of specific values for variables. Furthermore, the app allows students to save screenshots of their work to assist the teacher in efficiently assessing understanding and providing individualized support” (Sakow & Ruveyda, 2015). It is the constantly changing factors and reframing of the problems that allows the concept to solidify, and for the students to hone their skills in this respect.

References

Matthew Sakow, & Ruveyda Karaman. (2015). Exploring Algebraic Misconceptions with Technology. Mathematics Teaching in the Middle School, 21(4), 222-229. doi:10.5951/mathteacmiddscho.21.4.0222

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.

Cornelis Vermeulen & Bronwin Meyer (2017). The Equal Sign: Teachers’ Knowledge and Students’ Misconceptions. African Journal of Research in Mathematics, Science and Technology Education Vol. 21 , Iss. 2.

Week 2 Discussions – Facades of Misconception

“Why dose this metal fork feel cold after we removed it from the hot water?”

“Well, ‘cold’ goes inside of the fork so it feels cold.”

“Actual, heat is a type of energy. Without heat, something feels cold. In the case of this metal fork, this type of material allows for heat to easily move around.”

In our grade two class, we are investigating the relationship between hot and cold. Most of the students assume that that cold is a concrete and physical attribute that can be exchanged. However, it is the absence of heat that makes something feel cold. If I didn’t ask the question about heat, I may not be able to correct this faulty idea.

Through the video and the selected readings, it is apparent that learners come into a classroom with prior knowledge. More specifically, Piagetian believers would agree that learners have schema (i.e. their own understanding) and ideas about the way and the way it operates. At the time of the début of this theory, the idea that learners have their own independent thoughts and inferences is groundbreaking. Confrey (1990) radically suggest that children are equipped with a personal set of knowledge and perspectives about scientific or mathematical concepts. Other constructivist theorist like Fosnot joins the scholarly conservation and together they propose the idea that knowledge is a variable that can be altered.

More specifically, some misconceptions can be altered if properly exposed and handled. Posner, Hewson & Gertzog (1982) discusses the processes of altering thinking concepts. Misconceptions are rather resilient attributes. However, under favorable conditions (e.g. viable solutions after confrontation of the theory) accommodations can happen. For example, accommodating can happen by linking accurate information with “prior experience, images, or models which make them appear intuitively obvious and which make competing concepts seem not just wrong but virtually unintelligible.” (Posner, Strike, Hewson & Gertzog, 1982, p.213-214)

The narrator in the video also claims that Heather benefitted from having the opportunity to explain and apply her reasoning. Thus, Heather rejects her faulty assumptions about the shape of Earth’s path since it was insufficient to explain her ideas asked by the production team. This explicitly demonstrates the fact that students will not keep faulty ideas if it fails to solve immediate problems. “Central concepts are thus not judge in terms of their immediate capacity to generate correct predictions. They are judge in terms of their resources for solving current problems” (Posner, Strike, Hewson & Gertzog, 1982, p.213)

How should misconceptions be handled and assuaged?

In more recent research, Shapiro (1988) believes that children should be co-architect of knowledge. Upon further inspection, what learners require is an opportunity to reflect about their learning and to apply the understanding in unfamiliar circumstances. The video also suggests that misconceptions require confrontation. Posner, Strike, Hewson & Gertzog (1982) insist that learners can increase immunity to misconceptions by increasing commitment to viable concepts and fruitful experiences.

Making Thinking Visible

Following these ideas, it is important to explore tangible and mobile solutions to encourage externalization of thoughts. Simply, reflecting about their own ideas and verbally materializing thoughts may be sufficient. With these reflective practices, students slowly and objectively unpack ideas to expose misconceptions.

Recent research in technological tools makes reflection an effortless process. There are more digital options to reflect upon experience and demonstrate understanding. Ingram, Williamson-Leadley & Pratt (2015) agrees that ‘Show and Tell’ mobile solutions encourage dedicating a reflective space and time. The application promotes an active reflection of understanding. Beyond providing a reliable and safe place to make learning and thinking visible. Hence, students are more aware of themselves as learners. This is consistent with Confrey’s (1990) discussion about students developing more confidence as they envision learning. More specifically, the scholars believe that students benefit from customizing personal interface and sharing about their mathematical understanding (Ingram, Williamson-Leadley & Pratt, 1016).

In computer supported collaborative learning environments, thinking can be tracked, promoted, evaluated and self-regulated (Lin, Preston, Kharrufa & Kong 2016). Using a touch screen table sized device, users can physically manipulate and reorganize information. They can easily define and redefine the way in which pieces of information are connected to each other. These scholars also claim that these technological tools provide an explicit overview of user’s thinking process. Directional features encourage users to evaluate their thinking process.

It is apparent that there are more mobile tools to help expose faulty thinking and more strategies to reflect concepts. This may positively influence learners by helping them develop habits to assess and retain accurate conceptual understanding.

Discussion Questions

How has the development of communicative landscape influence reflective process?

How was your experience using reflective technology?

Reference

Cone, J., Rowe, S., Borberg, J., & Goodwin, B. (2012). Community Planning for Climate Change: Visible Thinking Tools Facilitate Shared Understanding. Journal Of Community Engagement & Scholarship, 5(2), 7-19.

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56. http://ezproxy.library.ubc.ca/login?url=http://www.jstor.org/stable/1167350

Ingram, N., Williamson-Leadley, S., & Pratt, K. (2016). Showing and telling: using tablet technology to engage students in mathematics. Mathematics Education Research Journal, 28(1), 123-147. doi:10.1007/s13394-015-0162-y

Lin, M., Preston, A., Kharrufa, A., & Kong, Z. (2016). Making L2 learners’ reasoning skills visible: The potential of computer supported collaborative learning environments. Thinking Skills And Creativity, 22303-322. doi:10.1016/j.tsc.2016.06.004

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. doi: 10.1002/sce.373066020.

Sharples, M. (2005, April). Learning as conversation: Transforming education in the mobile age. In Proceedings of conference on seeing, understanding, learning in the mobile age (pp. 147-152). Budapest: Institute for Philosophical Research of the Hungarian Academy of Sciences.

In the video A Private Universe, a student named Heather struggles to understand the concepts surrounding the earth’s seasons. The root of her problem seems to be a misunderstanding of the earth’s rotation, and a lack of knowledge regarding the earth’s axis. While there was much in this video, the part that stuck with me the most was precisely where she got the information that formed her misconception of the earth’s orbit.

As the video progresses, it becomes clear that her incorrect idea of the earth’s path of travel actually came from a different diagram presented to her by the teacher. In essence, her wrong understanding was an extrapolation based on accurate information given to her by the teacher.

This got me thinking about a teacher’s role in forming and breaking student misconceptions.

This past week, I was working with one of my gifted math students on the concept of converting square units. While he routinely works at the grade 7 and 8 level with little support, this young grade 5 student struggled mightily with these conversions.

In conferencing with the student, he explained quite clearly what was going on in his head.

Student: You see, 1cm is equal to 10mm. Throwing a little floating two above the unit does not change the relationship between these numbers. Math is consistent, it doesn’t change on a whim.

Except, this isn’t consistent, at least not in the way he was thinking.

He clearly understood how to convert measurements of length, and was directly applying this to measurements of area. However, he was missing out on a few key points, and was getting frustrated when he wasn’t able to find out the answers correctly.

He was missing the fact that square units involve the multiplication of other measurements, and not just a straight line. I then showed him the following diagram.

After explaining how the conversion process is entirely different the student remarked “I get it now. It’s like how when you square a unit, you don’t multiply it by two, you multiply it by itself.”

This diagram was able to help the student realize that his first comments were indeed correct. Math is consistent. However, he was trying to make this concept be consistent with something markedly different. The student’s misconception made sense because I had taught him a similar, correct concept. In his mind, it was a short jump to apply it to this new one.

This interaction aligns clearly with the observation made by Driver, Guesne and Tiberghien (1985). In the opening paragraphs of their article they observe two students that conclude the higher an object falls from, the faster it will fall, with no limits. Thus, dropping a small object from altitude could easily kill a person down below. They applied their knowledge of acceleration and their observations of gravity to come to a sensible, yet incorrect conclusion. These young men used what they were taught to make reasonable extensions, yet they turned out to be incorrect.

This highlights an important point by Philip Sadler and Gerhard Sonnert (2016) in their analysis of science-based misconceptions. Specifically, they looked whether or not it is adequate merely for a teacher be knowledgeable in their content area. They clearly assert that students are often not at fault for forming their misconceptions, as they are ideas that make perfect sense to them. Through a test-based study they come to conclude that a teacher being an expert in their field is simply not enough. A teacher must also have a deep knowledge of student misconceptions, and teach to these misconceptions. Without doing this a teacher is simply presenting material, not presenting the material in the way students require.

In light of these findings by Sadler and Sonnert (2016), I am going to tweak the way I do some of my math instruction from here on out. In the past, I have presented new concepts and then dealt with a student’s misconceptions in a one-on-one manner. However, looking to the future I plan on presenting and defeating misconceptions while I am introducing the new topics. I’m learning that too often as educators we will teach exciting new concepts, but we fail to teach where the boundaries of these concepts lie….and when our students run with these concepts, they often run too far.

Works Cited

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

Sadler, P. M., & Sonnert, G. (2016). Understanding misconceptions: Teaching and learning in middle school physical science. American Educator, 40(1), 26.

As teachers we have a natural inclination to help students understand what we understand to be true. Ultimately, our teaching methods can often be described quite simply in one of three ways:

1. GIVE them the right answer
2. GUIDE them with some clues
3. LEAVE them to struggle on their own

The challenge that we have probably all struggled with is knowing which strategy or combination of strategies is best in teaching a concept or skill. Often times we help students by “scaffolding” concepts which can be seen as a delicate balancing act between the three methods; elements that are beyond the students’ capacity or ability are “controlled” to permit them to focus and learn new concepts and skills (Wood et al., 1976, p.90). The main problem that has been eating at my soul is that our controlling nature does not give enough time for students to struggle, to sit in a place of uncomfortableness and discover the truth.

From the video “A Private Universe”, it was evident that Heather accepted some of the information on the seasons and the phases of the moon as communicated by the teacher. Unfortunately, a few of her misconceptions still lingered in modified and incorrect forms. As described by Driver et al. (1985), “students may ignore counter-evidence or interpret it in terms of their prior ideas” (p. 3). During the follow-up session with Heather two weeks later, the evaluator employed two different strategies to address Heather’s misconceptions. In the first case, Heather was given time to struggle with the phases of the moon and eventually came to understand the explanation supported by current scientific evidence. In the second case, Heather was given direct instruction with a diagram describing direct and indirect light, but continued to assimilate her previous misconceptions into her thinking. This one case certainly does not prove the pedagogical superiority of allowing students to struggle over direct instruction, but it forces us to question our teaching methods and the value of student agency. As indicated by Shapiro (1988), it is important to encourage learners to reflect on their own learning processes, so that they might take an even more active role and responsibilities for their own learning (p. 114).

A related article by Shepardson et al. (2009) emphasized how seventh grade students held rudimentary concepts about global warming and climate change and lacked a rich conceptualization of the issue (p. 563). What would be the best way forward then? One important lesson that can be learned from Heather’s video is that understanding pre-conceptualizations, no matter how deep, can help in developing an effective teaching strategy. You probably have a couple technologies in mind that could help in the understanding of student thinking – here are some that have had impact in my school:

1. Mind mapping apps like Mindomo help students develop concept maps
2. Screen sharing apps like Screencastify help students explain their ideas with illustrations and audio recordings
3. Conversation apps like Flipgrid to leverages the power of video and group learning
4. Journaling apps like Microsoft OneNote helps students record and develop ideas over time

As a final thought, I wonder if we as educators spend enough time sitting in a place of uncomfortableness. Do we blindly accept scientific concepts and theories or do we challenge ourselves and spend the time struggling within them?

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

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.

Shepardson, D. P., Niyogi, D., Choi, S., & Charusombat, U. (2009). Seventh grade students’ conceptions of global warming and climate change. Environmental Education Research, 15(5), 549-570.

Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of child psychology and psychiatry, 17(2), 89-100.