Misconceptions in the classrooms

Introduction

Students come to class with pre-existing ideas about the world around them. Some of these ideas are incorrect due to their lack of knowledge or understanding of the concept. Leading them to form misconceptions that they bring to the classrooms. These misconceptions aren’t just the lack of knowledge but deeply embed way of thinking which makes it difficult to change then just the lack of knowledge.

As teachers it is very important to be aware of the ideas the students come to class with, as these misconceptions are a part of the students reasoning. Studies have shown misconceptions are hard to change (Campbell et al, 2016). Traditional instructional strategy are ineffective to debunk the misconceptions (Khourey-Bowers, 2011). Therefore correct strategies need to be implemented in the classrooms to address and prevent the misconceptions students take into adulthood.

Misconceptions of decimals

Decimals is one of the key concepts taught is schools yet studies have shown various misconceptions about decimal numbers among students (Steinle and Stacey 1998). Understanding decimal values can be very challenging as it requires coordination of whole numbers and fractions knowledge (Moloney and Stacey, 1997).

Misconception and their causes

Steinle and Stacey’s study identified many different thinking pattern about decimals among students and their causes.

• Longer is larger way of thinking is caused by the “whole number rule” (Resnick et al, 1989). Students are taught from a young age that the longer whole number is the larger number thus leading to the longer decimal is larger thinking.

• Shorter is larger thinking is caused by students incorrectly view decimals as fractions (eg. 0.3 is 1/3 and 0.4 is ¼.) or as negative numbers (2.3 is -2.3) thus leading them to believe the shorter decimal is smaller.

• Apparent experts behaviour have students correctly viewing and handle decimals but lack the understanding why the correct concept works (Steimle and Stacey, 1998).

The different misconceptions arise for a variety of factors. Steinle and Stacey’s study concluded these misconceptions stem directly a result of instructions in schools and interfering ideas (1998). The way students are being taught is effecting their ability to correctly comprehend decimals.

Strategies to prevent and address the misconception

Griffin’s studied Ms. Campos teaching strategy used in grade 4 to introduce the concept of decimals (2016). He outlined the following strategies:

• Pre-assessment - Ms Campos starts her lesson on decimals by posing the question, “What do you already know about decimals?” The students answer gives an inside into the pre-existing knowledge and misconceptions they may have (Griffin, 2016). This pre-assessment is a vital step to planning a lesson to address misconception (Campbell et al, 1994).

• Use visuals - Ms Campos introduces decimals using minimally labelled strip of adding machine tape where students can create a number line, allowing students to visualise the numbers as they understand it (Griffin, 2016). By using visual tools, students are able to understand the logic behind the correct concepts instead of just memorising it without truly comprehending the concept (Khourey-Bowers, 2011).

• Reduce the use of different concepts and ideas- Ms Campos used sticky notes to divide the number lines and purposely leaves out the use of units of measure. This reduces confusion by interfering of other ideas (Griffin, 2016).

• Math dialogue- group work discussion and debriefing helps solidify learning and allow teachers to identify any misconception and addressing it (Griffin, 2016).

• Slow pace - Introduce new concepts and ideas slowly. Let students completely understand one concept before introducing new ideas to prevent confusion. Ms Campos used few lessons to slowly introduce new concepts only after one concept was well examined and learnt (Griffin, 2016).

• Investigative study- Allowing students to investigate their understanding lets them test and illuminate their misconceptions which has been identified by Cobern to be a vital in debugging misconception (1996) and investigate further to conclude and come to the right answer help develop logical thinking (Griffin, 2016).

Misconceptions of the equal sign

Many students see equal sign as an operator, a symbol that announces the answer (Ciobanu, ..). Students see equal sign just a sign that comes in the middle of an equation with the calculation of the left and the answer on the right.

Cause of the misconception

This misconception of viewing the equal sign as an operator stems from:

• Schools and textbooks- From a young age students are shown equations with the calculation on the left followed by an equal sign and the answer of the right (Ciobanu, 2014). This leads to the rigid operational thinking of equal sign as identified by Rittle-Johnson (2011).

• Calculation devices - require equal sign to be pressed to process the calculation and give an answer. This also led to viewing the equal sign as an operator (Ciobanu, 2014).

Strategies to prevent and address the misconception

Knuth et al suggests some strategies to avoid misconception of equal sign:

• Math dialogue- consistently about math and equal sign to help students comprehend the value of equal sign. Dialogue need to start early in the low grades and extend throughout their schooling career, to allow them to completely understand of the equal sign (Knuth et. al., 2008).

• Use equivalent equations- which shows calculations on both sides in a balanced equation. This weakens the belief of calculation being on the left and answer on the right (Knuth et. al., 2008).

• Use visuals balance models- especially in early grades to develop the rational meaning of the equal sign (Small, 2013). Allow students to investigate and balance visual models to develop a comparative relational view of the equal sign (Knuth et al, 2008).

Misconceptions of Astronomical distances

Miller and Brewer’s study found that majority of the students overestimated the distance between the earth and the moon but greatly underestimated the distance to the sun and the next nearest star (2010). The results show that there is a widespread and systematic nature of misconceptions about the astronomical distances. Therefore it isn’t just the lack of knowledge but a prevalent misconception (Miller and Brewer, 2010).

Causes of misconceptions

There are variety of factors that leads students to misconceptions about astronomical distance:

• astronomical distance is virtually incomprehensible to most students as the scales are very different to what human’s experience in our everyday life (AAAS, 1989, P130). The actual special distance in the universe is vastly beyond our everyday understanding of distance (Miller and Brewer, 2010).

• Measurements used in astronomical distance such as light years are not well understood concepts by students (AAAS, 1989, P130).

• Lack of understanding of large numbers by students leads to the difficulty in comprehending the vast distances.

• Simplification in text books and by teachers using everyday objects such as basket balls and football fields (Khourey-Bowers, 2011) strengthening the misconceptions (Miller and Brewer, 2010).

Strategies to preventing and address the misconception

Miller and Brewer suggest that more effort needs to be given to understand the misconceptions students have. Although many studies have identified the misconception of astronomical distance very little effort has been given to educate teachers on how to implement change. They have suggested a few strategies to implement:

• Education of large numerical values- The misconceptions need to be dealt with throughout the science and math curriculum. Miller and Brewer believe the misconception is largely due to the lack of understanding of large numerical values. Thus more effort need to be put in to teach large numerical values from a young age.

• Education needs to be more sophisticated than just simply emphasizing the vastness of space as it is being done now.

• Appropriate science dialogue need to be employed in classroom (Khourey-Bowers, 2011). The ideas of astronomical distances need to be constantly resisted throughout the different ages to help the students develop a more realistic physiological intuition of very large distance and time (Miller and Brewer, 2010).

Misconceptions of the cause of seasons

The understanding of the seasons caused by the earth’s tilted rotation around the sun is a basic concept taught in schools. But many studies has shown it is still greatly misunderstood (Thomas, 2011). There is a common misconception that the seasons are caused by the earth distance from the sun (Thomas, 2011).

Causes of the misconception

There is a common misconception that the seasons are caused by the earth distance from the sun (Thomas, 2011). This is a very common misunderstanding which may have been caused by many factors.

• Lack of understanding- As the earth’s tilt and rotation around the sun cannot be easily visualised or felt it is a very complex concept to comprehend by students. The lack of understanding lead to developing misconceptions.

• Text book images- widely used image in science text books that show the earth’s axis as an oval around the sun may have lead the students to think the earth is closer to the sun and further away from the sun at certain point of the rotation thus leading to the misconception that the distance from the sun is the cause of the seasons (Thomas, 2011).

Strategies to preventing and address the misconception

Thomas (2011) created a strategy to teach the concepts of seasons to address misconceptions.

• Pre assessment-Thomas asked the students to think of factors that may be affecting the temperatures all year round. This led them to develop a variety of ideas and gives the teacher an inside into the misconceptions students may have (Thomas, 2011).

• Scientific investigation- Students were asked to create investigation to test their hypotheses and collect long term data from the internet. They were then able to modify their thinking and compare and contrast a variety of factors and conclude that the earth’s tilt (angle of the sun) is the cause of the seasons (Thomas, 2011).

• Dissatisfaction- The scientific investigation allowed students to test their ideas and became dissatisfied with their ideas. Becoming dissatisfied with an idea is vital to debugging misconceptions and understanding the correct ideas (Cobern, 1996).

• Use Long term data- allows students to observe and see patterns to develop a logical thinking (Khourey-Bowers, 2011).

Conclusion

There are many different misconceptions students bring to class. These misconceptions can be deeply imbedded way of thinking and cannot be easily debugged through the traditional instructional strategy (Khourey-Bowers, 2011). It is vital for teacher to identify the misconceptions and the causes. Teachers need to put in place appropriate strategies for the students to investigate their ideas and become dissatisfied and only then can they create a logical understanding of the correct concepts (Cobern, 1996).

Bibliography

• AAAS (American association for the advancement of science). (1989). Science for all Americans. Washington, DC: American association for the advancement of science.

• Campbell, T., Schwarz, C., & Windschitl, M. (2016). What we call misconceptions may be necessary stepping-stones on a path towards making sense of the world. NSTA Journals: The Science Teacher, 83(3), 69-74.

• Ciobanu, M. (2014) In the middle- misconceptions about the equal signs in middle school. Ontario gazette, 147(14), 14-16.

• Cobern, W. (1996). Worldview theory and conceptual change in science education. Science Education, 80, 579–610

• Griffin L.B. (2016) Strategic instructional choices can simultaneously address common decimal misconceptions and help students race toward decimal understanding. Teaching children mathematic, 22(8), 489-494.

• Khourey-Bowers, C. (2011). Active learning strategies: The top ten. The Science Teacher, 33(4):28 - 32.

• Knuth, E.J., Alibali, M.W., Hattikudur, S., McNeil, N.M., Stephens, A.C. (2008). The importance of equal sign understanding in the middle grades. Mathematics teaching in the middle school, 13((), 514-419.

• Miller, B.W., Brewer, W.F. (2010) Misconceptions of astronomical distance. International journal of science education. 32(12) 1549-1560.

• Moloney, K. & Stacey, K. (1997). Changes with age in students’ conceptions of decimal notation. Mathematics education research journal, 9(1), 25-38.

• Rittle-Johnson, B., Mattews, P., Taylor, R., McEldoon, K. (2011). Assessing knowledge of mathematical equivalence: A construct modeling approach. Journal of educational Psychology, 103, 85-104.

• Small, M. (2013). Eye on math. A visual approach to teaching math. New York: Teaching collage press, 210-213.

• Stacey, K. & Steinle, V. (1998). Refining the Classification of Students’ Interpretations of Decimal Notation. Hiroshima Journal of Mathematics Education, 6, 1-21.

• Thomas, J.D. (2011) The reasons for the seasons: using temperature data to challenge students’s misconceptions. The science teacher. 78 (4) 52-58.

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