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Abstract
Teaching a profession that is constantly evolving and changing. In order to be a professional in
this field, professional development is key. In order to develop professionally, one area in which
teachers should focus is on correcting common misconceptions. No matter the content area,
students will inevitably make mistakes, and it is the teacher’s responsibility to correct these
issues. InTASC standard 4k states “the teacher understands common misconceptions in learning
the discipline and how to guide learners to accurate conceptual understanding.” Math teachers,
such as myself, need to be intimately aware of common misconceptions and mistakes that will
cause students to stumble in any particular problem. In this paper, I look into two resources, one
article and one video, to help me deepen my understanding of correcting common
misconceptions.
Keywords: Content competencies, education, common mistakes, misconceptions
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As I looked over the inTASC standards for teachers, one standard that stood out to me
was standard 4k. As a math teacher, it is pivotal that I am able to anticipate, spot, and correct
student misconceptions quickly and with accuracy. While I consider myself to be rather good at
delivering content, I knew I could improve on my ability to correct misconceptions. The standard
discusses how teachers should be able not only to understand common misconceptions in the
material, but also be able to guide students to be more accurate and understand more deeply.
Upon reading this standard, I knew it was a skill I wanted to improve upon.
The first resource that I selected in order to improve on this inTASC standard was an
article titled “Misconceptions in School Algebra” (AL-Rababaha et al., 2020). This article would
serve as an artifact to help me find a starting point in identifying common misconceptions in
algebra since I am an Algebra 1 teacher. The article identifies and explains common
misconceptions in school-level algebra and categorizes them. The goal of this article was to
create a curated list of the most common misconceptions seen in school level algebra in order to
guide teachers. In order to do so, the article looks at other scholarly sources in a literature review
style method and summarizes and extracts mistakes that were found in these studies to curate a
single list. The article also discussed how each of these misconceptions can impact future
learning in higher level math classes and the barriers to higher learning that are often built in
algebra. The article lists in detail different misconceptions and offers an expanded explanation
for how the misconception can come about. After reading the article, I went back through my
lesson plans for this unit (functions and graphs) and created slides in our notes that directly
address the misconceptions found in the article. For example, one misconception I wanted to
address was that many students do not understand that a graph can represent a function even if
the graph is not continuous. I know that this can cause problems later on in Algebra II, so I
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included several slides with non-continuous functions for students to see and identify as
functions using the vertical line test. After integrating this directly into my lessons this week, I
noticed that very few of my students had these misconceptions, which made this practice a
success. I will continue to use these slides in my lessons in the future.
After reading through the article, I also found a video to use as an activity as I developed
competency in this area. In this video, a creator called “The PhysicsMaths Wizard” discusses the
top 5 most common algebraic misconceptions. As I watched, I realized that the mistakes he was
addressing were extremely common in my own classes. For example, the creator talked about
indices and how many students believe that a number raised to an exponent is the same operation
as multiplying that base number by the exponent. He also discusses laws of exponents and how
students often mistake one law for another, or assume that because exponents are added when
multiplying base values, that the opposite would stand true and they should multiply exponents
when adding bases. In the video, the creator also discusses common misconceptions about
logarithms and their relationship to indices, correcting the misconception that logarithm logs are
reversible (similar to the misconception involving exponent laws). The next misconception
impacts students in the next class they will enter, geometry. The creator explains how the
negative exponent denoting an inverse trig function is not the same algebraically as a standard
negative exponent, which equates to 1 over the given base. Addressing this misconception in
Algebra 1 can prevent issues in Geometry classes by clarifying this quickly before the
misconception solidifies. The final misconception is that addressed is extremely common in
Algebra 1, which is the idea that an expression raised to an exponent is the same mathematically
as distributing an exponent to each term. This video was short yet thorough, and directly
addressed and corrected 5 misconceptions that I have personally experienced from students in
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Algebra 1 class. After watching the video several times, I opted to share the video with my
semester-long Algebra 1 class (who are currently preparing for their end of year state test) and
pause to discuss with them after each segment. I offered example problems where this
misconception might arise and, after showing the video segment, asked the students to
collaborate with their table mates to solve the problem correctly and explain how the answer
might differ if the mistake mentioned in the video was made. The students in this class are
advanced students who crave an academic challenge, and they thoroughly enjoyed this activity.
In the post activity discussion with these students, most said the activity was helpful and that
they were far less likely to make these mistakes in the future. I will continue to use this practice
in future classes.
Proverbs 10:17 says “Whoever heeds instruction is on the path to life, but he who rejects
reproof leads others astray” (ESV). We are called to accept and learn from our mistakes and our
criticisms. As teachers, I believe we are also called, similarly to parents, to lead those we are
charged with away from potential mistakes and towards knowledge and understanding. I know
that in order to be the best teacher I can be, I need to be able to identify and correct in love the
mistakes that I see my students making, and I also need to be able to create a classroom culture
in which my students can gracefully accept reproof and learn from their mistakes. I know that
through prayer and patience, I can make that a reality.
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References
AL-Rababaha, Y., Yew, W. T., & Meng, C. C. (2020). Misconceptions in school algebra.
International Journal of Academic Research in Business and Social Sciences,10(5).
https://doi.org/10.6007/ijarbss/v10-i5/7250
Holy bible. (2002). American Bible Society.
YouTube. (2021b). Top 5 misconceptions in Math to avoid.YouTube. Retrieved October 29,
2023, from https://www.youtube.com/watch?v=V_ARHhhU0EA.
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