Category Archives: A. Conceptual Challenges

Accidental Transfer

Jenkins (1990) makes an interesting statement about the fallacy of the tabula rasa assumption in teaching; that students come to you as a blank slate ready to have your teachings fill their head with the correct information. Students and their minds are not kept in vacuums ready to receive information when they enter the classroom; rather they bring with them a slew of partially formed ideas and impressions. Depending on the age of the student you often have to contend with the teachings of the other teachers/faculty/parents/peers that have influence what the student brings with them. In the video, Heather demonstrated this by describing her ideas of a wonky orbit path. What I found interesting was that part of Heather’s misconception was accidentally transmitted by a misleading diagram in a textbook.

This led me to think about how often are we as educators unintentionally the source of student misconceptions? I am reminded of faculty that would point out diagrams, pictures, and narrative in textbooks that in their effort to simplify difficult concepts simplified it to the point of error. Or in other cases diagrams that in an attempt to engage the viewer with colour and annotation, missed the mark and instead became confusing jumbles of nonsense. This relates to higher education, but think of all the different sources of information that kids (K-12) consume and how these can relate to the development of their misconceptions. For example ‘Magic School Bus’ was a popular kids show back in the day. For the most part the science discussed in this show is pretty solid, but there are some inaccuracies introduced, which, since the medium is so engaging, do have a high likelihood of sticking. For example, I still thought planets were balls of highly compressed gas….wrong. Watch this short video that points out these inaccuracies:

Top 10 Lessons The Magic School Bus Got WRONG – (Tooned Up S2 E1)

One way that we can help students address misconceptions using technology is through stop-motion or slow-motion videos. Schwessinger (2015) discusses her use of slowmation to help students overcome misconceptions in physical sciences. In slowmation, the creator produces a video or animation of an event by sequencing thousands of pictures. The claim is that this technique helps students overcome their misconceptions because they are forced to revisit the concepts so many times and provides them with ‘hands on’ time.

For those interested in reading about using slowmation in practice I would highly recommend reading Schwessinger’s paper. It also has an excellent overview of student misconceptions in science.

References

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

Schwessinger, S. (2015). Slowmation: Helping Students Address their Misconceptions in Physical Science. Doctoral Projects, Masters Plan B, and Related Works. Paper 1. http://repository.uwyo.edu/plan_b/1.

Why Are Veins Blue?

Watching the video on common misconceptions about the causes of the seasons and the phases of the moon, I was reminded of when I taught Biology 12 this summer and just how challenging it was for students to adequately grasp certain concepts within human physiology.  To be fair, Biology requires the art of imagination- the ability to animate a sequence of events from information taken from text and diagrams.  I will note, I was teaching to 24 students often outside in parks while backpacking through Belize and the internet, let alone Youtube, was not at my disposal.  So I relied on vivid storytelling and gave emotion and relevance to fairly dry and ordinary process like DNA replication and the beloved Kreb’s cycle.  I was hoping to pass on the mental model I had spent years crafting in my mind over the years by using using analogies and manipulatives but I I found many students would erroneously add details or fill in gaps with incorrect information.  I was surprised that they decidedly chose to invent facts when their mental model failed instead of seeking further clarification.  It should be noted these kids were extremely bright and motivated.  I was never given the impression that they were too shy to acknowledge their own misconception.  There was something going on subconsciously.  I assumed our brains are great at finding patterns and filling in for any missed information.  Similar with Heather, who filled in her own gaps in understanding with erroneous information about celestial motion and optics.

To further support this theory, take a look at the familiar image below.  Each time I see this image I struggle to not to see the unbordered white triangle in the middle.  Similar to how our brain fills in what it can’t see, students fill in for missing information with the most plausible explanation.  Unfortunately in science, if these assumptions go unchecked, students risk carrying the burden of their misconceptions year after year.  

My experience has lead me to believe that oral assessment, where a teacher makes time to listen to the students defend ideas and construct explanations based on scientific arguments, is fundamental to good assessment.  I was intrigued when reading an article by Rivard and Straw (2000) who claim “that talk is important for sharing, clarifying, and distributing knowledge, while asking questions, hypothesizing, explaining, and formulating ideas are all important mechanisms [for learning]”.  In their study, students were given similar tasks based on similar content yet one group (T) discussed a particular problem, another group (W) wrote responses to each task and a third group (T+W) discussed and wrote responses.  They found that both discussing and writing are important mechanisms for transforming rudimentary ideas into coherent and structured arguments for students.  This supports my advocacy for greater oral assessment in the classroom, whereby students are provided opportunities to orally describe their understanding of particular processes.

While students may be prone to inventing misconceptions, in many cases, students are, in fact, taught misconceptions.  There is mounting research that shows that misconceptions concerning science are prevalent among teachers who then pass them along to their students.  Nancy J. Pelaez et al. (2005) for instance, investigated the prevalence of blood circulation misconception  among prospective elementary teacher in the US and found that “70% of prospective elementary teachers did not understand the dual blood circulation pathway, 33% were confused about blood vessels, 55% had wrong ideas about gas exchange, 19% had trouble with gas transport and utilization, and 20% did not understand lung function”.  While many of you might be concerned by these statistics, let’s take moment for introspection.  How many of you believe that your veins are blue because they carry deoxygenated blood?  Don’t worry if you do, this is a common misconception even amongst many well-educated adults.  In fact, we all hold misconceptions about science and even our correct understanding of science is laced with generalizations and assumptions that are not always correct.  The future will lie in teaching our students how to criticize information and always seek the most robust understanding of scientific process possible.

 

References:

Pelaez, N. J. “Prevalence of blood circulation misconceptions among prospective elementary teachers.” AJP: Advances in Physiology Education 29.3 (2005): 172-81. Web.

Rivard, L. P., & Straw, S. B. (2000). The effect of talk and writing on learning science: An exploratory study. Science education, 84(5), 566-593.

Does gas have mass?

In 1968, David Ausubel wrote “The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly.” (Ausubel, 1968, p. vi).  Unlike an earlier idea that learner are blank slates that need to be filled by the teacher, more recently, the Personal Construct Theory recognizes that the person is a meaning-make, capable being an active participant in their learning, and of making judgements about their interpretations of evidences (Shapiro, 1988).   If students enter a topic or concept with various misconceptions or alternative frameworks, this will negatively influence both their ability and willingness to incorporate new understandings.  In science, this is quite prevalent, perhaps because we first use simple analogies to explain a concept and then elaborate more fully later, or perhaps the nature of science allows children to make their own observations and interpretations first.  Whatever the reason, many students have misconceptions about various aspects of science.  For example, many of my Bio11 students believe penguins have fur not feathers!

I have chosen to work with the misconception that gases don’t have mass, or even have a negative mass.  This common misconception is likely due to students observations that adding more gas to a helium balloon causes it to float higher (Mayer, 2011), or trapping air bubbles under a toy in the bathtub allows it to float instead of sinking.  According to Mayer, (2011), even after students performed an experiment in a sealed flask demonstrating that the mass doesn’t change when a substance (iodine) goes from a solid to a gas, the majority still stuck to their false preconceptions and assumed they must have made an error in the experiment.  This lead Mayer to recognize that preconceptions are very difficult to remove (Mayer, 2011).  This phenomenon was also seen in the video clip about Heather and how she continued to stick to her theories about the strange curlicue orbit of earth and how light bounces to give indirect light.

So what do we do about these misconceptions.  Elliot (2016) notes that teachers who are aware of common misconceptions among their students were more effective, and that the common teacher approaches of avoiding students’ existing beliefs altogether or telling students clearly they are wrong and that they need to think differently are ineffective.  Posner et al (1982) view learning as a “process of conceptual change” where accommodation of misconceptions is needed to reorganize their current beliefs.  For accommodation to occur, learners need to be dissatisfied with their current idea or model, and the new model must be rational, intelligible, plausible, and fruitful for further research (Posner et al., 1982).  Teachers can use anomalies to point out limitations of misconceptions, thereby bringing the cognitive conflict (dissatisfaction) that drives new understandings (Elliot, 2016, Posner et al., 1982).  I would suggest that using technology is a good way to do this for many abstract concepts.  There are many online simulations (for example PhET) that enable learners to view the concepts, play with them, and visualize the greater explanatory ability of the scientific idea such as the states of matter and properties of gases (https://phet.colorado.edu/en/simulation/states-of-matter).

  • Ausubel, D.P. (1968). Educational Psychology: A Cognitive View. New York: Holt, Rinehart & Winston.
  • Elliott, K., & Pillman, A. (2016). Making science misconceptions work for us.Teaching Science, 62(1), 36-39.
  • Harvard-Smithsonian Center for Astrophysics. (1987). A private universe. ISBN: 1-57680-404-6.  Retrieved from http://learner.org/vod/vod_window.html?pid=9
  • Mayer, K. (2011). Addressing students’ misconceptions about gases, mass, and composition. Journal of Chemical Education, 88(1), 111.
  • 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.
  • 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.

Uncovering Misconceptions with Pre-Assessments

As Shapiro (1988) describes, traditional classrooms assumed that when students came to school, their minds were ‘blank slates’ ready to be filled with knowledge and ideas taught by the teacher. To be successful and succeed, students would have to recall facts and figures, regurgitate information on tests based on questions posed by their teachers. As we have observed from Heather in the Private Universe video, however, students do not come to school without any prior-knowledge and have many personal opinions and theories on different topics. They come from diverse backgrounds and have a wide range of different experiences. These experiences lead them to some misconceptions on various issues and topics. As teachers, it is essential to find out what students already know about topics and draw out any misconceptions to teach and guide students effectively. To do this teacher cannot assume that a student knows or does not know content before it is assessed or taught. They should have a multitude strategies in their toolkit to find out what students already know or think about a topic before any explicit teaching and assignments are given. Mix et al. (2013) reaffirm this idea by explaining that teachers often assume that young students have a strong conceptual understanding of multi-digit numbers early on in school. Because multi-digit numbers are commonly seen in the world around us, such as phone numbers, menus, addresses, etc. and they can read many young children we assume they know what they represent. Many children, however, struggle with knowing precisely what multidigit numbers represent and mean and how to break them apart. Explicit instruction and many hands-on experiences with manipulatives are often required for children to build their number sense to understand multi-digit numbers (Mix et al., 2013).

I am working at an IB school, and part of our pedagogical approach to teaching and learning is to administer different types of pre-assessments to find out what students know, or think they know on a subject before starting a new unit. I recently did a pre-assessment on mixed fractions where students had to tell me how they could divide ten chocolate bars evenly among four people. They then had to represent their answer using a fraction, words and pictures. I was fascinated by many of the student’s answers. Some students, for instance, wrote 2.5/10, while others wrote ‘two in a half’ (at first I thought this may have been because of his New Zealand accent but when I asked him to read his answer he was adamant it was two in a half and had an elaborate reason as to why). Others had no idea where to begin and could not come to a final answer. The data revealed that many students had no conceptual understanding of what mixed fractions were, while others had an abstract idea but could not represent their thinking concretely. From this pre-assessment, I was able to make strategy groups based on what students already knew before any explicit teaching on this outcome. The Private Universe video was a great reminder that assessments like these, as well as good questioning, is vital in the classroom and be should be embedded into practice across the curriculum.

References:

Mix, Kelly S., et al. “Young Children’s Interpretation of Multidigit Number Names: From Emerging Competence to Mastery.” Child Development, vol. 85, no. 3, June 2013, pp. 1306–1319., doi:10.1111/cdev.12197.

Shapiro, B. L., (1988). What children bring to light: Towards understanding what the primary school science learner is trying to do. In P. Fensham (Ed.), Development and dilemmas in science education. London: The Falmer Press.

Constructivism’s Answer to Children’s Misconceptions in Science

(Disclaimer: It’s been a long time since I’ve taught Science and an even longer time since I’ve taught Math so I found this activity challenging because I don’t really have anything to comment on that is relevant to my personal practice.  I tried to read the course article about Children’s Conceptions of Heat and Temperature because I remember teaching a unit in Grade 7 related to that but the UBC link is broken and I couldn’t find the article online that didn’t cost money to read. I read an article that referenced Erickson’s work however, Children’s Ideas About Hot and Cold (Appleton, 1984).  The last Science I’ve taught has been to Grades 1-3 students and I really wanted to read Children’s Understandings of Science: Goldilocks and the Three Bears Revisited (McClelland & Krockover, 1996) which studied first grade students and their understanding of heat, and compare these ideas, but again there was no access available).

 

From McClelland & Krockover’s abstract and introduction, however, I have found that many of the peculiarities of children’s understandings are echoed in the video and the other readings.  McClelland & Krockover (1996) found that students adopted misconceptions of scientific conceptions based on their exposure to literature, in this case the fairytale of Goldilocks and the Three Bears.  This is consistent with the findings of others in this week’s readings that children are prone to make contradictory statements about the nature of scientific phenomenon when that phenomenon is presented in a different way, for example temperature descriptions and changes described qualitatively rather than quantitatively (Appleton, 1984).

Researchers also found that children often rely on sensory input even when it has been proven to be unreliable, as when a cold hand registers cool water as quite hot despite the actual temperature but they may choose to “live with the contradiction” rather than challenge their personally held conception (Appleton, 1984).  This reminded me of Vygotsky’s ZPD and of Piaget’s understanding of the symbiotic dance of learner-teacher in a child’s schema-construction rather than the “tabula rasa” Shapiro (1988) references which had been the guiding pedagogy of 1960s-80s.  McClelland & Krockover (1996) supported Piaget and Vygotsky’s worldview’s when they found that the first graders were able to change their conceptions when presented with activities that put the contradiction to their previous beliefs.  This is similar to what Heather was able to do in the video when she reassessed what she believed to be the shape of the Earth’s orbit and what Mark (Shapiro, 1988) was able to do when he connected previous lessons to the reflection of light from objects into our eyes, revising his prior hypothesis recorded before the unit began.

All the researchers I read made a strong case for the use of constructivist and constructionist practices in the Science classroom.  Shapiro (1988) did this when she pointed out the value placed on both hands-on and self-directed “experiments” by her research subjects; Appleton (1984) did this when he commented on the value of using relevant, accessible situations rather than abstract examples or those that were beyond the children’s experience; and McClelland & Krockover (1996) directly identified the present view “that learning is the result of the interaction between what children are taught or what they experience, and their current ideas or conceptions (Driver, 1981)” (p.33) and targeted constructivist concepts of prior knowledge and social interaction as active meaning-makers in children’s understanding of scientific concepts.  All of this points to the necessity, in my opinion, of rethinking the amount of information teachers are expected to “cover” in each science unit.  A better alternative is a streamlined curriculum focusing on the topics that most children hold misconceptions in for each strand of scientific thought so that teachers can actively and deliberately tailor learning in a pattern of (1) misconception-identification, (2) contradiction-exposure, and (3) independent-and-guided exploration in order to construct more accurate understandings.

 

References

Appleton, K. (1984). Children’s Ideas About Hot and Cold. Learning About Science Project (Primary). Working Paper No. 127. Retrieved from: https://files.eric.ed.gov/fulltext/ED252407.pdf

McClelland, A.K. & Krockover, G.H. (1996) Children’s understandings of science: Goldilocks and the Three Bears revisited. J Elem Sci Edu (8)32. https://doi.org/10.1007/BF03173747 Retrieved from: https://link.springer.com/article/10.1007%2FBF03173747?LI=true

Shapiro, B (1988). What children bring to light: Towards Understanding What the Primary School Science Learner Is Trying to Do  Retrieved from: https://files.eric.ed.gov/fulltext/ED309081.pdf

 

Just-in-time feedback

Students have four options when it comes to dealing with new learning: delete pre-existing knowledge, modify new knowledge to fit existing understanding, modify existing understanding to fit new learning (altering what is known), or reject new information (Sewel, p2). Heather’s misconceptions are the result of incomplete understanding and integrating unrelated ideas into her understanding. For example, she views a diagram of something unrelated to the seasons while learning about the seasons and integrates the wrong diagram into her understanding. While she states that she thinks she understands, not having the opportunity to explain her understanding and receive teacher feedback in a timely manner was a contributing factor to the error becoming a misconception. Heather’s misconceptions could have been more effectively dealt with if the teacher had performed a pre-assessment. In this way she would have known what her students currently understood. In addition, teachers must constantly assess for understanding through the lesson; asking whether or not students all “get it” is an ineffective method of determining what has been understood. While this video is a relatively dated classroom, current interventions including digital technologies might be to use an all-student response system like plickers or socrative to determine student understanding while the lesson was occurring, and addressing misconceptions before they become fossilized.

As a primary school teacher, science concepts are often misunderstood to be obvious concepts without consideration to the fact that the work done at this level is foundational. We take for granted that a child is able to count and understand the meaning of numbers, but an understanding of the importance of zero and not jumping to the conclusion that children understand numbers to one thousand because they are able to write numbers to one thousand. In my personal experience, this has been a teacher misunderstanding that leads to inadequate attention to number concepts. Because it appears a simple concept, teachers often do not recognize that it requires a cognitive leap for learners to use 0. Shapiro underlines the importance of students’ being actively involved in the curriculum in order to construct an understanding of it. As in the video, Heather does not begin to construct or question her understanding until she has the model in her hands and is able to begin manipulating it.

A significant factor in student learning is feedback related to the learner’s conceptions. It is essential to listen for a child’s conception related to the curricular topic rather than to listen for errors or to simply move the conversation toward the correct answer. In order to counter misconceptions, we must understand where students are are and provide not only day-to-day feedback but also minute-to-minute feedback.

Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational researcher 23, no. 7: 13-20.

Mohyuddin, R., Rana, M, & Usman K. (2016). Bulletin of education and research: Misconceptions of students in learning mathematics at primary level Panjab University Press.

Sewell, A. (2002). Australian science teachers’ journal: Constructivism and student misconceptions: Why every teacher needs to know about them Australian Science Teachers’ Association.

Shaprio, B. (1988). Development and Dilemmas in Science Education. What Children Bring to Light: Toward Understanding What the Primary School Learner is Trying to Do. 96-120

A world of misconceptions

One of the first things that caught my attention during this video was that recent graduates at Harvard University did not know why Earth has seasons. Harvard is known to be one of the best universities in the world and one would assume that its graduates would know the answer to why Earth has seasons; this shows that no one is exempt from misconceptions.

In the video, ‘A Private Universe,’ we are introduced to Heather who is in grade 9 and is described by her teacher as “someone who would know the correct answer(s),” however, the audience and her teacher are shown a student who has some interesting misunderstandings about the sun, moon, and the seasons. When Heather is asked about her theories about the orbit of the sun she replies she saw a diagram in her Earth Science textbook in 8th grade and she got confused. Many diagrams and drawings in textbooks cause misconceptions as they are perspective drawings and not completely accurate.

Heather’s teacher assumed that her students had the basic ideas when they arrived in her class and this probably led to more misconceptions as they kept piling on. It is important for educators to understand and find out what their students know and then build from there. Von Glaserfeld (2008) states that “The world we live in” can be understood also as the world of our experience, the world as we see, hear, and feel it.” We all have our own theories as we have all had unique and individual experiences that have led to those theories.

In this video, we see students sitting in their desks listening to their teacher; we see that is teacher-centered and not student-centered. Constructivist theory holds that knowledge cannot be passed down from teacher to student; students must create their own understanding by experimenting so they know how to use that information (Von Glaserfeld, 2008). Students need to be able to experiment and have hands-on education in order to fully understand the concepts (inquiry based learning). Fosnot (2005) states that students need to be “provided with opportunities to actively construct ideas by experimenting” instead of passively being given information. I remember a lot of my high school math and science classes involved students siting at their desks while the teacher lectured at them; there were no hands-on activities, little visual representations, and many confused students- I was one of them. Many students today are just as confused and digital technology can definitely help to ease that confusion. I have used Geogebra, which is an interactive math APP that allows students to “see” equations and math problems come to life. There are 3D models and diagrams that helps the student to understand all sides of the diagram. By using interactive applications and simulations, students are able to understand and comprehend what may not have been understood before.

 

Fosnot, Catherine. Constructivism: Theory, perspectives, and practice. Teachers College Press

Von Glasersfeld, E. (2008). Learning as a Constructive Activity. AntiMatters, 2(3), 33-49.

 

Teach Questions Not Answers

Why? Why? Why? This question seems to come at me a thousand times a day from students, staff members, and my own three children. This ongoing inquisition can range from simple yes and no questions, to complex concepts requiring deep explanation. What is tempting is to provide answers. That shoot from the hip response in order to solve the problem, answer the question, provide the information, and move on. This method of me simply giving the answers was causing a crisis of inquiry in my world and despite me attempting to provide answers as a solution, it actually increased the volume of questions I was being asked…because I was the easy answer. This ask and get an answer was not proving to be deep learning for any party involved.  

 

The questions are actually a good thing, a crucial element to examining one’s own understanding as well as challenge assumptions and conceptions (or in many cases mis-conceptions). We intuitively make sense of the world in any way we can based on our everyday experiences and will structure an understanding prior to any formal “education” on the matter (Confrey, 1990; Fouche, 2015; Vosniadou & Brewer, 1992). Right or wrong, this thirst for understanding is innate to the human mind and drives our learning. In fact, certain kinds of misconceptions which students experience are actually intrinsic to the growth of scientific understanding (Confrey, 1990). Heather demonstrated this confident construction of private theories. These private theories meant to be a jumping off point for inquiry and not an end point for information acquisition. It is safe to make clear that we can no longer assume that students are entering our classrooms as a blank slate ready to receive the information to begin their construction of understanding, or having received the correct prior knowledge based on previous years of instruction alone (Confrey, 1990). The key stone to creating conditions for  flexibility of learning is to question our students’ understanding and private theories  in order to challenge their misconceptions and plan appropriate inquiry opportunities (Confrey, 1990; Fouche, 2015). We also must find the misconceptions and make them clear. Heather’s teacher needed to know not only what she didn’t know, but what she thought she knew as well in order to plan. This to me really explained the use of KWL organizers in classrooms prior to beginning a unit of study. Taking the time to ask “what do you know” being a crucial first step. Teachers can make great strides in STEM education if they “prepare ahead of time questions that will do three things: elicit prior knowledge, uncover student misconceptions, and move students toward their conceptual goal” (Fouche, 2015, p.64).

 

Now enters the ultimate educational temptation…to find provide answers to the misconceptions or missing information. Instead the challenge is to use predictive questioning and give time for inquiry, observation, and explanation based on these misconceptions (Fouche, 2015) in order allow children an opportunity to reinterpret their presuppositions based on these new experiences (Vosniadou & Brewer, 1992). Note the word experiences, it was personal experiences after all that led us to create our initial private theories and it will take experiences to reconstruct our understanding. “All of us need time for our confusion if we are to build the breadth and depth that give significance to our knowledge” (Confrey, 1990, p. 82). It is an incredibly tempting to speed this process up by giving students the answers when you see them struggling.

 

I think this Constructivist pedagogy of teaching questions instead of answers leads to a deeper experiential based understanding especially when it comes to a makerspace environment. This hands on exploration of concepts as opposed to rote memorization allows for a solid foundation of understanding that has been built as opposed to information given in the hopes of retention in longer term memory. In teaching a Grade 5 science class the Electricity unit I decided to use a Makey Makey. The Makey Makey is an electronic invention kit that is full of wonder and whimsy and is hugely engaging to students as well as an opportunity to experience exploration of electrical components. This kit is full of coloured wires and alligator clips. It was amazing to me the misconceptions of the colour of the wire mattering (too many action movies?), the fear of getting electrocuted if you touched the wire (more movies?), and that the Makey Makey was “magic”. By taking the time to question and challenge these understandings led to a purposeful investigation comparing conductivity and electrical current. The students had a reason to challenge their understanding in order to build a successful operation game.

Misconceptions come to life

 

The reconstruction of understanding after challenging misconceptions

This predictive questioning and hands  on inquiry seems to make sense in science class. We have a golden opportunity to use inquiry to improve our understanding and a chance to use technology to observe and interact with the phenomena….but what does this mean for mathematics when conceptual understanding is our greatest area of weakness (according to our PAT regression analysis) but we do not follow the same procedures to uncover misconceptions, or engage in inquiry. We tend to ask questions and teach answers.

 

Can this same method of questioning be applied to math? Have you authentically engaged in authentic inquiry as a way to construct meaning in your math classes?

 

Trish

PS This is a video that inspired me to become a teacher that asked more questions instead of teaching answers. I hope that it inspires you too.

References

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

Fouché, J. (2015). Predicting Student Misconceptions in Science. Educational Leadership, 73(1), 60-65. Retrieved January 8, 2018, from http://www.ascd.org/publications/educational-leadership/sept15/vol73/num01/Predicting-Student-Misconceptions-in-Science.aspx

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

Conceptual Challenges: Cloud Formation and Precipitation

In the video, Heather has a misinformed understanding of the moon’s phases and the seasons. However, her teacher was not aware of these misconceptions before she introduced the unit of study. During her lessons, Heather was trying to merge her existing knowledge with the new information the teacher was introducing. The teacher needed to understand her students’ background knowledge before she began the new unit of study. Only through her understanding of her students’ prior knowledge, will she be able to help scaffold her students’ learning.

As we can see in this video, there are many misconceptions around scientific understandings. This may be because new scientific discoveries have been made that contradict existing theories or that the learner only understood part of the concept and tried to fill in the gaps. Many scientific theories are abstract and therefore, difficult for students to visually see the process. The use of models in science can help with the visualization process. Teachers also need to understand students’ prior knowledge and misconceptions on any given topic before they begin to teach it. This will help guide the teaching process and activities based on what the students already know, what they think they understand, but really don’t, and what they are interested in learning. If students are not interested in a topic, it will be more difficult for them to learn. If they do not see the relevance of the concept to their daily life, they will not take an interest in learning more about it.

When I was teaching primary grades, one of the topics that my students always had a difficult time understanding was cloud formation and precipitation. I often wondered if the difficulty arose because the students couldn’t actually see the process or touch it. The best we could do was create diagrams or models to help with this. However, some of the students still had a difficult time explaining the process. Often times, they would appear to understand, but as time would pass their understanding would diminish. In the Thompson and Logue article, the students ranged in age from six to twelve years old. Most of the students were able to describe how clouds were formed, but had strong misconceptions about precipitation. According to the authors in both articles, scientific misconceptions come from a variety of sources, including misunderstanding information from parents or teachers, as well as from sources, such as mass-media that provide inaccurate information. Misconceptions are often difficult to change and these can impact the learning process. According to the article, Children’s Ideas and the Learning of Science, people who attend the same lecture or read the same book will not necessarily understand it in the same way. Individuals internalize the experience and construct their own meanings. The authors argue that student beliefs are reviewed or revised when a more persuasive or a better theory is introduced, but sometimes “even if students are confronted with what appear to be contradictions to the teacher, they will not necessarily recognize them” (Driver, et. al., 1985, p. 3). Thompson and Logue believe that teachers need to figure out their students misconceptions so that students do not continue to build their knowledge upon these misunderstandings. The issue is not where these misconceptions come from, but rather how we identify them and overcome them in the classroom when teaching our students.

The best way for students to understand many of the scientific concepts being taught is in a constructivist learning environment that encourages students to take risks and explore through hands-on experiments. The teacher acts as a facilitator or guide and supports the students throughout the learning process. It would not be an effective teaching style for a teacher to simply tell the students that their existing understanding or beliefs about a given topic are incorrect, but rather he or she needs to provide students with exploratory lessons that “show” the students. Technology is a great tool to help support the science lessons and curriculum in the classroom. Some of the simple ways that it can be used is to watch (up to date) videos or have students create their own videos on a given (or chosen topic). There are some great interactive whiteboard applications that allow students to draw and record their learning and thinking. This gives the teacher another way to identify any misconceptions that may exist.

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

Thompson, F., & Logue, S. (2006). An Exploration of Common Student Misconceptions in Science. ERIC, 553-559. Retrieved January 8, 2018, from https://eric.ed.gov/?id=EJ854310.

Misconceptions: What? Where? How?

As the issue of misconceptions is new for me, I want to elaborate on three basic questions: What are misconceptions? Where do misconceptions come from? And how can we resolve them?

Conceptions of children are “ideas about their world” (Confrey 1990 , p. 4). They help to “obtain explanations for how and why things behave as they do”. Misconceptions are “learner’s deviations from scientists’ view” (Shapiro 1988, p. 99).

In Heathers case, it is not fully clear where the misconceptions come from. The idea of the bizarre orbit may come from text book illustrations. The source of her ideas on indirect light is unclear. Altogether, Heather tries to accommodate different sources of information into a coherent private theory.

After the lecture, Heathers changes some of her misconceptions. Posner (1982) calls such a conceptual change “accommodation” (p. 212). Heather is now able to give a correct picture of the orbit of the earth. Yet, she still has misconceptions on indirect light.

Confrey (1990) confirms that children have “firmly held, descriptive, and explanatory systems for scientific … phenomena” (p. 4), and that these “systems are resistant to change through traditional instruction” (p. 4). So the case of Heather seems to be typical.

According to Piaget, a child “develops certain perspectives and beliefs that are functionally adaptive”, and that “may or may not correspond well with the views of disciplinary experts” (Confrey 1990, p. 8). From this point of view, misconceptions seem a normal aspect of the maturation of a child. According to von Glaserfeld (1982), errors are “key moments” and “opportunities to glimpse our own constructs” (cited after (Confrey, 1990, p. 14)). For Heather, this seems true, as she is able to reflect on her own beliefs during class and correct them.

How can misconceptions be resolved?

First, students should describe their own conceptual framework when working on a problem (Confrey 1990, p. 43). Shapiro (1988) also states that the preconceptions need to be clarified, e.g. by group discussions. Shapiro (1988) proposes a Classroom Profile to document preconceptions of each student, helping the teacher “to understand how individual children are thinking” (p. 117).

Second, when a student understands that the own conception is not appropriate to solve a problem, he or she may get “dissatisfied” and adopt an alternative, better framework (Confrey 1990, p. 43). Posner (1982) also sees “dissatisfaction” as a major condition for accommodation (p.214) and suggests that the teacher should create “cognitive conflicts in students” (p. 225) for this. Accommodation is supported when the new concept is plausible and intelligible (Posner 1982, p. 214) and when the student sees the teacher as a “credible authority” (Saeli, 2011, p. 113).

I am a computer scientist and teach at a university. Misconceptions are not so obvious here, as learning is often not as visible as in a school setting. However, I looked for research on typical misconceptions in computer science classes. One study shows that these misconceptions are very individual, as “different students have different needs and difficulties” (Saeli 2011, p. 81). Thus, Saeli (2011) concludes: There is not one approach to support accommodation that suits all students, and thus the teacher has to adopt different strategies for different students based on his PCK (pedagogical content knowledge) (Saeli, 2011).

References

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

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.

Saeli, M., Perrenet, J., Jochems W.M.G., & Zwaneveld, B. (2011): Teaching Programming in Secondary School: A Pedagogical Content Knowledge Perspective. Informatics in Education, 10(1), 73–88.

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.

von Glasersfeld, E. (1982). An interpretation of Piaget’s constructivism. In Revue internationale de philosophie (142-143). France: Ministere de L’Education Nationale.