In a my recent blog post The Truth about Equivalent Fractions and Multiplication I had some interesting comments to the statement that I made about assuming that we multiply by 1 to create equivalent fractions. There were teachers that disagreed with me because I said that the model for equivalent fractions does not support multiplying by 1. It was interesting to see teachers defending the multiplicative identity of 1 being taught to elementary students in a way that create misconceptions about equivalence and disrupts the coherence of equivalence, scale factor and proportionality. Based on the findings of Page Keeley most of the students that we teach come to us with a plethora of misconceptions and sometimes teachers add to their misconceptions. A misconception can be defined as a view or opinion that is incorrect because it is based on faulty thinking or understanding.
After presenting my position about multiplying by 1 to create equivalent fractions I spoke with a friend of mine who teaches Geometry and has a degree in mathematics. His response was that you are not multiplying by 1 because when you calculate 1/4 x 1 = 1/4 and 1/4 x 2/2 = 2/8 which creates the misconception that 2/2 is one. His explanation was when you put 1/4 x (2/2) into a calculator what do you get?
The picture to the left shows one of my 4th grade students partitioning 2/4 to create 4/8. There is a huge difference between multiplying by 1 and taking on the properties of multiplying by 1. The idea behind the multiplicative property of 1 is because an equivalent fraction is created it can be viewed as multiplying by 1 because the amount is the same. When a math teacher tells a student that they are multiplying by 1 and does not explicitly explain the thinking behind the concept, the teacher has then created a misconception that will disrupt the student’s ability to connect other concepts to what they already know because the student is looking for the actual 1.
There are misconceptions in all subjects but especially in math and science because many of the concepts are abstract concepts. That is why explicit teaching is so important , especially when teaching students who do not have a solid foundation in number concepts. On Friday I was teaching my students how to find the the greatest common factor and one of my students looked at me and said, ” I get it!” I love it when they tell me that it makes sense because it boosts their math confidence and makes my job a lot easier.
Believe it or NOT….Teachers can Create Misconceptions!
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4 thoughts on “Believe it or NOT….Teachers can Create Misconceptions!”
Here’s a misconception that most teachers create in kids. It’s not so much that they create it, but perpetuate it, and don’t bother to correct it. Most kids have this misconception long before they come to school. It’s that what others say and do, and what happens is really what makes us feel the way we do. Just listen to the way teachers and most others talk about how they feel, and how their feelings come about. i.e. “These kids drive me crazy”. That’s scientifically inaccurate. The formula for feelings is: EVENT + THOUGHTS = FEELING. Anything others say or do, or that happens is technically an EVENT. It’s what we choose to think about such EVENTS that really determines how we feel. Thoughts cause feelings, not events. Beauty is in the eye of the beholder – so is how we feel. It’s actually like that math formula a + b = c, where a is a constant, and b is a variable. If a stays the same, and you change b, c changes. Likewise, if we change the way we think about a given event, it changes the way we feel, for the better or worse, depending on how we choose to think. We allow kids to go through usually at least 12-13 years of schooling believing this misconception, and even reinforce it in so many ways, i.e. telling kids that you can “hurt others feelings” or that “names hurt” in anti-bullying campaigns, not to mention blaming kids publicly for how we make ourselves feel. They suffer so much needlessly because of this misconception, not only while in school, but often the rest of their lives. We teach them so many things about how life works and how to use that knowledge to their advantage in all kinds of classes, and challenge other misconceptions all the time. Yet we neglect to teach them a basic formula that governs every waking moment (and probably sleeping ones too) of their lives, and fail to correct a misconception that does as well.
I agree most teachers will not take the time to address the misconceptions that students have.
But this is a huge one Michelle. Think of all the things that go wrong in kids lives, the many different problems and issues they so often struggle with (i.e. alcohol, drugs, eating disorders, violence, abuse, suicide, anger problems, anxiety disorders, depression, low self esteem) that negatively impact their readiness, willingness, and ability to learn. There’s an important “least common denominator” to all these. It’s that kids generate a dysfunctional amount of emotion of emotion in response to what happens in their lives. More than is helpful or necessary, more than they want to have, more than they know what to do with. A big part of what they do is that they put themselves at the seeming mercy of others and events by looking at life this erroneous way – seeing others and events as the cause of how they feel. If we wrote a formula for it, it would be EVENTS = FEELINGS. They give away power and control over how they feel that they really do have, and give others power and control over how they feel that those others don’t really have. This typically results in them feeling worse than necessary or helpful, for longer than needed. Worse, they miss opportunities to feel better.
The students that I teach don’t give up power that easily. It’s a daily struggle. Most of the time it’s the other way around emotions=event. Students tend to think that because they feel a certain way that they have the right to create this huge event/disruption because of it.