1.2 – SHARE: Math Misconceptions: What would you do?

. TRUE; As a student several times I thought about this and I only focused on solving problems automatically.
FALSE; Now as a teacher I try to help my students have a better understanding and reflection on mathematics and how it helps us in our daily lives.

. TRUE; When I was a student, the teachers emphasized this point. It was essential to learn the formulas.
FALSE; Nowadays, when I teach, the formulas are always in front of the students because I think it is more important that the students know how to apply the formulas rather than knowing them by heart.

.TRUE; As a student I was always in the category of
bad at math, and it was something I believed in even when I attended college.
FALSE; Now as a teacher I try to never categorize any student as good or bad. I always try to teach them that we can all learn and solve math problems, we just have different learning rhythms.

.TRUE; I remember that when I was a student, there were evaluations where the development was fine but I was wrong in the final answer. that made all my exercise bad.
FALSE; Now, I try to evaluate the process and results and give them the opportunity to correct the result if the answer is wrong and then ask them to reflect on what they think happened regarding their error.

.FALSE; I never thought that mathematics had some creativity, but that it was a repetitive process.
TRUE; As a teacher, I take advantage of my students’ creativity to formulate questions and have possible answers.

.TRUE; the exploration approach that she had when she was a student was to search for data and then solve the exercises. Now, as a teacher, I understand that the approach is different. It is that exploration goes beyond the data, but rather contemplates different processes and analyses.

. FALSE; At school I had teachers who only cared about the way they taught how to solve a problem. If we did it any other way, it was bad.
TRUE; now I try to teach different ways to solve the same exercise and each student can feel free to choose the one that suits them best. Also, if there is any student who finds another way to solve the exercise, I ask him to demonstrate it to the rest of the class.

.FALSE; As a student, I always thought that mistakes slowed down my learning process.
TRUTH; Today I try to teach that mistakes are part of the learning process and that they always help us improve through individual or group reflection to clarify different points of view.

Mathematics is computation. – As a student, I thought this was very much the case. Math included learning various operations and how to come to a correct answer using those operations, procedures, and strategies. As a teacher, I know this is not the case. Mathematics is more problem solving than basic computation.

Math is just memorizing rules. – As a student, I remember learning a bunch of different “tricks” for memorizing the operations/procedures/formulars/steps in math. As a math teacher, I try to avoid only teaching those tricks, at least when initially introducing a topic. I want to give the students the proper strategies to solve the problem without those tricks, first.

You are either good or bad at math. – I’m totally guilty of calling myself “not a math person” when I was a student, and even in my adult life. As a math teacher, I know all students are math people!

Math is just about getting the right answer. – I absolutely agreed with this statement as a student, and even remember my friends who considered themselves “math people” saying that they enjoyed math because you could reach a correct answer and there was only one right answer. As a math teacher, I know math is about problem solving and the strategies/reasoning/understanding it takes to get there.

Math is creative. – I definitely had a hard time seeing this as a student. I don’t have very many memories using modeling and working with manipulatives when doing math, but as a teacher, this is the majority of our math instruction which gives students the opportunity to be creative when working with math concepts.

Math is exploration. – As a student, no. Math was just about numbers and computation and operations. As a teacher, absolutely! We have built in tasks in our curriculum to give students the opportunity to explore various ways to model math word problems and math equations.

There are many ways to problem solve. – As a student, I think I probably would have agreed with this statement. However, when it came to math (especially in higher grades like high school), I’m not sure I remember being given many opportunity to vary how we problem solve. As a teacher, I know there are SO many ways to problem solve! The students are explicitly taught multiple strategies to do so.

Mistakes help our learning. – I was one of those students who got really down on myself for making mistakes because I typically did pretty well in school. So, I didn’t view mistakes as necessarily helpful for my own learning because I got really down about them. As a teacher, I know that when students make mistakes, this is a great way for them to grow, learn, and better understand a given concept.

With a student who completes the following problem like this, 320+50=820, I might first recognize to myself (internally) that this student is needing support with recognizing place value in the problem. I would then prompt the student to walk me through the strategies and thinking they used to solve the problem. If they can recognize their own mistake, I might engage them in a conversation regarding how they might fix it. If they are unable to recognize their mistake or if they aren’t sure how to fix their mistake, I might have the student solve the problem using a place value or HTO chart and base-10 blocks.

1/5/23 at 4:42 pm ahuyck

Back in the day math was taught as computation,memorizing rules, you were told you were either good or bad and if you did all these things you would end up with the right answer. The right answer was looked at as the most important thing.
What I have learned in my life from coaching student athletes is that you have to use many strategies to find what works for you.You need to be creative,explore new territory,make lots of mistakes and learn how to solve problems that pop up.Then it clicks and this is when true understanding happens and you are able to master the problem at hand.

1/5/23 at 4:42 pm ahuyck

Back in the day math was taught as computation,memorizing rules, you were told you were either good or bad and if you did all these things you would end up with the right answer. The right answer was looked at as the most important thing.
What I have learned in my life from coaching student athletes is that you have to use many strategies to find what works for you.You need to be creative,explore new territory,make lots of mistakes and learn how to solve problems that pop up.Then it clicks and this is when true understanding happens and you are able to master the problem at hand.

1/5/23 5:06 pm ahuyck

320 + 50 = 820 I would ask the student to show me how he arrived at this answer. then I would use a place value chart to show the student
that the 5 and 2 are in the tens place and 50 plus 20 would be 70.The final answer would be 370.

As a math student, I remember being taught rules and completing math problems simply as a computation. I gathered from my math teachers that you needed to memorize specific rules or at least have access to them and plug in and compute. The end result was to make sure you got the right answer, and if you did not you got the realization that you were good or bad at math. At those times, I was fortunate to be good at math. As I became a teacher of mathematics, I did not realize that some of the strategies that I have used as a math student came back out as a teaching tool to my math students. It was a struggle at first to feel defeated that all of my math students were not picking up the material right away after the lessons I taught. At this moment, I realized that not all students in math were like me. Giving light to the generation of students, the math needed to be explored and creative for the students. The mentality of getting the wrong answer and simply leaving it at that was not going to be the end of that math problem. The discussion of the steps to solving the problem and addressing those became a teachable moment. Students were able to address their own strategies and reflect on them.

As a student I considered myself “bad at math”. The memorization and computation techniques I was taught did not explain the why of the solution. I found math boring and uninteresting.
As a teacher, I am much more excited about math because guiding a student through to the understanding of a mistake and the eventual correct solution makes me believe that one less person will go through their school years believing they are “bad” at math.

Concerning the addition problem, I would ask the student to walk me through their thought process as they solved the problem. If they were not able to recognize the mistake, I would provide bas 10 blocks so that they could see the problem in more concrete terms.

Discuss the True/False Statements from the viewpoint of when you were a math student and now as a math teacher.

Mathematics is Computation. – By definition, there is computation in math, however, I think that the true false statement here is that math is solely computation. Math can be very fluid. Numbers can be moved, changed, and reworked to help solve any problem.

Math is just memorizing rules. – Math should never be memorization. The brain can only memorize so much.

You are either good at math or bad at math. – I have heard so many students say this about themselves. I always say that I’m going to teach you that math is a tool you can use in whatever way you need.

Math is creative. and Math is exploration. I think most math teachers fail there students in this way. I remember that, when I was a girl, I tried to tell my teacher a way that I’d discovered to multiply by 9s. She said “students aren’t going to understand that.” As a teacher, I’ve taught my students that method many times and they really understand it. By saying that to me, she negated her intelligence as much as she did mine (not to mention the intelligence of every other student she taught).

There are many ways to problem solve. and Mistakes help our learning. – I really think that people wouldn’t be so afraid of math if they realized that these sayings are true. With all the ways you can alter a problem to find a solution certainly give a person many ways to find their answers.

Mathematics is Computation. As a student that is what I thought about math. As a teacher I try to get my students to understand that there is so much more to math.
Math is just memorizing rules. As a student I remember being taught all the rules in math, and simply memorizing them. As a teacher my goal is to teach my students the process and the why behind it instead of just memorizing the rules.
You are either good at math or bad at math. As a student I believed this, I knew that math was my strength and I was pretty good at it without having to try so hard. As a teacher I know all my students are math people, even if it takes a little extra work.
Math is just about getting the right answer. There is so much more to the process than just getting the right answer. As a student I remember times when my process was right but my final answer was slightly off and it just getting marked as incorrect.
Math is creative. As a kindergarten teacher I feel this is very true. As a student I didn’t see it as more than solving problems.
Math is exploration. I never looked at math this way as a student but am trying to instill that in my students.
There are many ways to problem solve. I understood this as a student, but was often reminded that there is a right way and wrong way. As a teacher there is so much truth in that, and I stay mindful of this when teaching my students math.
Mistakes help our learning. This is the hardest one for me as a student. But it is so important to keep the growth mindset and remind students that mistakes help us grow.

First I would ask the student to show me how they arrived at either answer.
I would then ask them if they thought it may be easier to write the problem vertically.
If they lined up all the columns correctly I would remind them to use their tools.

What feedback would you give a student who completes the following problem like this?

320 + 50 = 820

I would ask the student to show me how they solved the problem. Then I would have place value examples with us so I could review/reteach the concepts. Then, I would give them another problem to solve to make sure their was understanding.

Think about the scenario above and your own classroom experience.

What feedback would you give a student who completes the following problem like this?

320 + 50 = 820

I would ask the student to show me and explain their thinking on how they solved the problem. Based on what I see and hear I will guide them using the error I see them make and their explanation.

I would ask the student to show me how they came up with this particular answer. After they are finished explaining to me, I will go over their misconception and show them how they could answer this problem. I will use math manipulative resources such as a whiteboard, place value cubes and rods, etc.

320 + 50 = 820
fEEDBACK: SHOW ME HOW YOU COMPLETED THE PROBLEM
REVIEW PLACE VALUE, IF NEEDED – HAVE GRID PAPER AVAILABLE FOR THE STUDENT TO USE TO SET UP HIS PROBLEMS TO SOLVE