I have found that students do not think through their solution to assess if their answer is reasonable or makes sense. I don’t know if t is the testing mindset that has trained them to just think that if they have an answer it makes sense or they are just not thinking critically. This year I have addressed it by modeling for them every time I work out a problem I ask them " Is this answer reasonable? Why or why not? It takes more time but I think it has helped them stop and think does this really make sense. After students are understanding a concept I will make a mistake on purpose to see if they catch my mistake, and if they do and can explain what it is I will give them a reward. Students also struggle with working in groups. I start the year modeling for them what that should look like and have to model what they correct behavior is from time to time. This works for some but there are just some students who do not get along well with others.
My students always want to rush through their assignments just to complete them as quickly as possible.
They hate it when I tell them they have to show their work.
When introducing solving systems of linear equations, my students freeze up when I show them the different ways to solve them.
My biggest problem is getting students to check their work. They feel when they have finished a problem they are done. They are also so very sure they have the correct answer they feel it’s a waste of time for them to do a check to see if indeed they have the right answer.
I have trouble getting students to estimate their answer in order to determine if the answer if reasonable. When they are able to use a calculator to help with the calculations they will write down whatever the “calculator says” and believe it must be correct because the calculator could never be wrong! Sometimes I will not let the students use a calculator to do the work but only to check the work once it is complete. If they are able to use a calculator the deal I make with them is they must write down everything they input into the calculator which also helps with the problem of getting them to show their work.
Another problem I have is with perseverance. Students seem to give up too easily when things get hard. They want someone to give them the answer they want that instant gratification. My school participates in the Continental Math League which is a timed monthly national Math contest. Many of the problems are difficult, worded in an unusual way, or apply one concept to something totally different. It is always interesting to watch those students who give up after just a few minutes and those who will work to the very last minute trying to solve the problems. I would love to know how to instill the desire to persevere through difficult problems to all my students
Our students struggle with ratio, proportion and percent. I believe it has a lot to do with the fact that they are not strong in fractions. When introducing the unit on ratio, proportion, and percent, we try to incorporate real life situations and simulations so that students can see the relevance. Based on the data, we are not doing this well.
One of my biggest problems seems to be a common one, getting students to show all of their work. I teach all 6th grade and I want to instill in them good work habits. This year was my second year teaching math and I finally realized that I needed to show them some more difficult problems that could not be solved so easily. This seemed to convince many of them that even though right now the equations seemed fairly simple, eventually they will need to show all of the steps to solve equations.
Another issue to go along with solving equations is checking their work. They did not want to substitute their answers in the equation and check their work. Again, I demonstrated more difficult equations to show them the need for checking their work.
My third issue would be following directions and or examples. The students want to resist and do it their way. I tried to model examples and show them multiple examples of the methods to be used. This is definitely a work in process and something I continue to strive to teach them.
I teach middle grades math, and I have had similar difficulties like the ones already mentioned. I think my 3 most difficult are:
 Students not showing work
 Students not estimating or checking the reasonableness of their answer
 Students not willing to work a problem out another way
Most of these difficulties come down to one main issue  Students always trying to just get to the answer, without respecting the process or trying to communicate their ideas. They are used to our “instant” world, and have trouble persevering or even appreciating a complex math problem because they want to just “Google it” to instantly get the answer.
I teach computer science and have taught 8th grade math for most of my teaching career. I definitely agree with the responses about students having difficulty with:
 showing their work to support their answer/thought process
 problem solving
 working cooperatively in groups.
As a computer science teacher I also see students challenged with problem solving especially when working with the hour of code. Some students give up because they do not know where to even begin. Most often the students who give up, look for help from another student. This student does not understand how to guide the students thinking and will tell them how to complete the level. I am currently in a technology lab with 35 computers which means I have 35 students. It is impossible for me to work with all of the students who are struggling, so I encourage students to work together. It is at this point where the learning stops because the students are not persevering and using problem solving strategies even when I have modeled and practiced it using several different strategies, etc.
Three concepts/habits I find difficult for my students:
 Showing work when completing homework/tests/quizzes. I get the following excuses: a) I did it in my head or b) I completed it on the calculator. This then makes it difficult for me to see where they are making mistakes and to see if they fully understand and made a silly mistake or if its something I need to go back and retouch on. I have started giving 1/2 points to students who show their work and made little mistakes or calculation errors…this has helped in making them show more work than usual
 Checking their work. Most of the mistakes I see within the classroom could be caught with checking their work. However, this is hard for them to do if they don’t show their work.
 Fractions, decimals and percents. My students are having a hard time understanding how the two relate and how to move back and forth from each. I have tried multiple ways of showing them how they relate to each other but have not found a way that seems to really click…any suggestions?
Students tend to want quick answers. Most haven’t discovered the joy of ‘questioning and connections.’ It’s very easy to take the quickfix and just provide them with a solid answer, without any selfdiscovery integrated. We can say we “taught” the standard even though we haven’t necessarily helped them comprehend the content on a deeper level. It’s better to be committed to changing the expectation and require selfdiscovery within the standard.
As teachers, we have a a pathway for teaching content and sometimes, specific standards, like functions, may require more time and differentiation than the guide or time dictates. Students don’t always grasp the significance of a mathematical concept being introduced until they gain a greater perspective of it’s purpose. Our classroom timeframe and the student’s life experiences may not provide a bestcase scenario for understanding. We need creative ways of expanding their understanding and realworld perspective (videos, handson, etc).
Students also tend to be afraid or negative when realworld word problems are introduced. Helping them to find word clues and connecting those to realworld situations is key in getting them to move toward successfully processing those problems confidently.
I agree this is a weakness in our process. Ratios were very easy for me in school because I had so many realworld examples to fall back on: I helped my mom cook and had to adjust recipes, I built things using my dad’s wood and tools and had to make adjustments, and I had to make comparisons constantly in sports (and without technology!). Our students don’t typically have all of those real world experiences to fall back on like we did  and we haven’t learned how to create those experiences in the classroom well enough, in my opinion.
The three concepts or habits that students find difficult first, understanding some vocabulary. Words that are foreign with them you really need to explain it and provide visualization for them to get it. Second, analyzing the problems and connecting each of the given to find the solution. When it comes to analyzing, some kids are so lazy, they expect you to explain everything. Third, just like with most of the posting that I have read, most students do not check their work. Their idea, I answered it already, then that’s it! They don’t have this tenacity to make sure or confirm whatever their doing is correct.
On occasions I will give students a real world task to complete with their peers. Students within the group will come up with a solution. I will ask how did you arrive at that solution? Most times their response would be I don’t know. I have difficulty with students showing their work and also explaining or justifying their solution. I need students to be able to realize that there maybe several approach to solving problems, however, being able to explaining their thinking can lead to great math talks.
Edna…I agree that vocabulary being a critical part of our curriculum needs to be explained or visualized. I really like how the author is cautioning us as educators to make sure that our students are exposed to functions in a way that they are able to relate; whether inside or outside of the classroom.
Why does the author argue for caution when teaching students about functions? He cautions that we should be sure to make connections between the various representations of functions so that students get a deeper understanding of functions.
How much time do you spend working with your students on writing and understanding functions? I don’t spend enough time doing this (maybe a week) because our curriculum pacing guide restricts the amount of time. If I could, I would personally cut the number of standards in the curriculum in half to give more time on these concepts  so much more important than some of the things we are currently required to teach.
How much time do you spend practicing word problems? Word problems are integrated in the curriculum throughout the entire school year, with heavier concentration in some units as opposed to others.
I struggle with engagement and relevance. One of the reasons I want to introduce coding is to hep kids see the value of algebra. When kids see math can be relevant to their lives, they tend to want to do it.
One of the struggles I have is getting students to rework the problems they get wrong. So many of them want to just change the answer and move on  especially with word problems.
I am having the same problem with group activities. My best students are doing the whole work and the others just copying. What I tried to do is to separate my students based on their level. In one hand they won’t feel behind and on the other hand they will try to compete with each others. The downfall of doing it this way is you will have groups going at different speed. I hope that will be useful to you.

I can’t get my students to clearly show their work and calculations (for example: to show the inverse operation on both sides when solving linear equations), many students say they can do it in their head or that it’s too much writing. I always model several examples.

They also avoid word problems, they purposely skip them when assigned.

Lastly, a math concept they have difficulty with is remembering which number is the divisor, which is the dividend when numbers are represented as a ratio OR they don’t know what it means for “x” to be divided by “y”… they want to know “Which number goes on the inside?”
I agree with so many of you about the same problems my students have. I struggle with the concept of why things work and emphasizing that over simply learning a procedure. I think this is because I wasn’t necessarily taught this way so I have to think about the why behind concepts as well. I do try to introduce new concepts with discussions rather than a set of rules so that they can connect the math to their prior knowledge. i also struggle with getting kids to show their work or getting them to see the importance of it. If time were never an obstacle, it would be much easier. I try to demonstrate examples of how showing work is beneficial, but ti just never seems to sink in. If I grade for it, I am not sure it would change any of my students, but would make them fail. A third thing that can be difficult is the retention of concepts. For example, students will get A’s on unit tests and seem to totally grasp it and then a month later it is as if they have never heard of it before. Not sure if this is because of something I am or am not doing or if it is the nature of a middle schooler, but very stressful for me.
I can’t get my students to persevere when they feel confused. They give up easily and want the “smart kid” or me to do all the work to help them. I want them to work harder before they ask for help.
I can’t get my students to check if their answers make any sense within the context of the problem. They want to get an answer and move on really fast to the next question.
I can’t get my students to learn how to study so concepts stick in their memory for later use. They seem to be able to do things in the current time, but later they forget.