# Difficult Concepts

My students have a hard time remembering x from the y axis.
They also have difficulty graphing points
Most struggle with the idea of slope, that it is a ratio.

In my classroom we are working on these three areas of difficulty:

1. Using mathematical reasoning to justify answers
2. Participating in academic conversations
3. Integrating concepts to solve new problems

Working on these areas has involved structured academic controversy, vertical problem solving, and many opportunities for students to practice working collaboratively to solve interesting problems. It takes work to get students past the fear of not knowing and the focus on coming up with an answer. I want to work on how students connect prior learning to new concepts and new problems. I think this article discusses methods that do an excellent job of making these connections so that students can see the big picture.

I see the same difficulties! This year I intend to use number talks, visual patterns, vertical thinking, examples/non-examples to work on these areas. Justifying their reasoning will be emphasized more than I have in the past.

Many students don’t regularly check their messages (which is my primary method of communication with them). This is introduced in our Orientation. Students sometimes skip this step, forget how to check their messages, or ignore them. Idea: Now that I can customize my courses (a new feature this year), I could make the first assignment reading and responding to their Welcome Message.

Many students wait until they are very frustrated and/or very behind to seek help, rather than asking right away. This is introduced in our Orientation. Students often forget/ignore the advice.

Many students don’t see the importance of the details (A and a are different, for example) and exact language. I’m honestly not sure where/if this detail is pointed out in our curriculum. Idea: I can add it!

I love the idea of guided notes! The idea of creating them for all of my preps feels very daunting.

Your #3 makes me think about fixed vs growth mindset.

My students tend not to read. If a problem requires reading, my students usually skip the problem.

In addition, my students have a limited vocabulary (whether we are talking about the English language or Mathematics language) so they have a hard time understanding language in general (regardless if english is their first language or not).

Another issue I have ran into is that my students do not check their answers and/or try to find their mistakes.

I find that 90% of my special education students won’t complete any work unless I am watching over them. There are a few that will take their work home and work with their parents, and those generally do well.

Word problems have more work in them, so they shy away. Breaking the word problem down by sentences helps them through it. I read the problem, then go back through and read each sentence underling the important information. Then build the problem.

I agree about emphasizing justification for reasoning…process as well as product.

1. I have noticed that my students have difficulty with solving word problems. I first ask them to read the problem three times and look up the definition of words they don’t understand in order to better comprehend what is being asked. I also have them circle numbers and math terms that relate to the math operations. I also walk them through the process of how to solve word problems.
2. The students have difficulty with solving problems with fractions or decimals. I usually go over the basics of +, -, x. and / fractions and decimals before moving on to more difficult problems.
3. The students have difficulty with note taking. This year I am guiding them how to take Cornell notes and how to use them when working on assignments and/or assessments.
1. I find my students have difficulty determining what is a logical answer versus one that is completely inaccurate.
2. My students have difficulty with fractions. They prefer to change the fraction into a decimal. It appears less frightening to them.
3. My students have difficulty dividing anything. I have had success with them by instructing them on synthetic division.

I want to start with the concept they used as an example because I have found something that helps and want to share. Getting students to check their work is a struggle because they don’t know why they are doing it. My school makes our students find a reason and evidence for every claim they make in every subject. In math the claim is their answer, their reason is showing or explaining their work and evidence is proving their answer is right (usually by plugging the value in and checking their work).
A topic that is very difficult for my students to conceptually understand is solving an equation with the variable on both sides. They just want to be able to look at it and be able to figure out what x=. When you add steps to their thinking they don’t know why they have to do them. I try to explain that the work they do is to find the one value which will make the statement true but they don’t want to work through the steps to find the value.
The last concept the kids struggle with is understanding that an equation with 2 variables represents a “function” or a linear relationship. They get frustrated that there is an “x” and when I introduce a “y” they think I’m crazy. Even though I introduce it with real world scenarios first.

My students have a difficult time relating functions to everyday uses.

The three concepts or habits that my students find difficult

1. I cannot get most of my students to remember basic math.
As a preview to each topic, I review needed concepts; however, when I release them to complete practice problems, I find that they struggle with basic math.( i.e, multiplication, rules for positive and negative number, etc.). I frequently find myself using 20 seconds “think quick” drills in the middle of my lesson to “jog” their memory.
2. Understanding the concept of “multi-select”
My students do not like to answer “multi-select” problems. They feel that each problem should only have one solution. I consistently provide them with multi-select practice problems and some still select just one answer. Hmmm …
3. Reading comprehension as it related to word problems.
As we complete word problems, I provide my students with problem solving strategies, underline , circle, what is this problem asking me to do , etc. When they are released them to problem solve on their own, I can see the struggle. So, I started reviewing definitions, similar terminology, equations via Kahut. I see progress but they still find word problems very difficult.

My students are Deaf and so they struggle with a lot more things than the the average hearing child.

My students struggle with

Reading and understanding problems
Interpreting what type of answer the question is asking for
Reasoning through a multi-step problem.

The only way I know how to teach this is to do a lot of direct instruction, modeling on various types of questions and then working through problems as a whole group.

My students struggle with the following concepts/habits:

1. Writing and Solving Literal Equations

I introduce the idea by using simple geometric formulas such A = lw. I ask the students how they can use the same formula if they are asked to solve for the length (or width) instead of area. Students typically give the correct response by saying that you need to divide the area by the width (or length). I ask them to write their answer as a new formula (l = a/w or w = a/l). We then talked about how they were able to write the new formula using inverse operations.

1. Laws of Exponents

I introduce this lesson by writing the variables repeatedly without the exponents so that the students can see the patterns and come up with the rules instead of giving them the rules. Students like using “their” rules and explaining them to the other students. Still, they struggle with answering these questions in standardized tests/benchmarks because they are not allowed to use their own notes and they it find it hard to understand the properties the way they are written in the books and charts.

1. The habit my students struggle with is organizing their resources. I notice that mine don’t really have a problem writing down notes or doing foldables but they struggle with keeping up with all the paper. We tried gluing them on composition notebooks and using binders and we are usually successful at the beginning but have trouble following through the rest of the year. I write “we” because I also find it difficult myself to find time during class for the students to organize their stuff. Any suggestions?

I found the article wonderful! I think if students had a flowchart simple to the one in the article that we filled in as each level of function is introduced, they would ‘get’ it deeper and quicker.
The three areas of difficulty for my classroom:

1. Students do not know how to start a word problem. They get road-blocked on what application to use.
2. They do not check their work for reasonable answers.
3. They do not use their notes as a resource. I use interactive notebooks to help bridge the gap of boring note-taking but once the class is over, they never refer back to them, unfortunately.

As a whole, I see students having difficulty with…

• perseverance
• understanding concepts/visualizing vs. surface level “key word” grabbing
• having the time to be able to explain their thinking

Instead of having a myriad of questions to practice, I prefer using one good word problem to “talk and walk” through and have meaningful conversation on their thinking/visualizing. I think after students have had time to solve on their own, having “number talks” and reasoning is an essential part of math.

I appreciate the article’s emphasis on concepts, connections, communication, and core ideas!

A vast majority of our student population also struggles with limited English language, too, which attributes to more challenges in solving word problems.

Some students had problems: Telling whether the pair is a function
What is the meaning of function? How have you may have used the word before now?
I start with explanation of voc
video on identifying the domain and the range
use real world examples
show examples in tables, diagrams
All students are required to take notes
I find that students take notes and do not study them. I might find some in the hall way during the day.

S