Difficult Concepts

Pick three concepts or habits that students find difficult (for example, “I can’t get my students to check their work when solving word problems”). For each concept or habit, share the way you introduce the idea and talk about how students respond.

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I found my students struggled with a number of the Standards for Mathematical Practice, namely:

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.

As someone new to middle school level instruction, I was curious how much middle school students still struggle with the above listed mathematical practices. I was most recently working with 4th graders and found that a lot of explicit instruction was required as I worked to model what these mathematical practices look like in action.

When modeled explicitly, some would get it but a good deal would not. It was a lot of effort for the students to persevere in working a multi-step problem out, many simply opting for what they believed was an easy out, often not checking to make sure their response was reasonable or logical.

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My students have difficulty with using correct mathematical concepts to describe their problem solving strategy. They also struggle with coming up with multiple ways to solve a given problem. The final area that my students continue to struggle with is applying multiple concepts/steps when solving a given word problem. With all of these topics we work through multiple examples expressing various ways to solve the problem as well as various ways to explain the meaning behind the words we are using, both in everyday interactions, as well as what those same words mean in algebra and what other more specific algebra terms link to those more common terms we started the discussion with.

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We try to do an introductory activity/connection on the first day where they students must come up with their own strategy and explanation for the scenario. Then on the second day we will use more direct instruction to clarify and build on what they worked on the day before.

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My math students have trouble with word problems, showing their work, and checking to see if their answer makes sense. I think they struggle in these areas simple because they want to get done with their work quickly and do not want to take the time (even just a few extra seconds) to fully think through these problems. Once I get students to take the time to do problems correctly, they enjoy their success and don’t mind doing the little extra they need to do.

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  1. Taking thorough notes - especially when the notes involve words. They copy the example but not the explanation.
  2. Reviewing and referring to their notes when they are completing homework.
  3. Using their notes and homework as a guide to help them prepare for the formal assessments.

We do not use a textbook in Algebra 1 or Algebra 2. This year we moved to guided notes. This resulted in a huge improvement in “your notes look like my notes”. The students were very positive about the idea of creating their own resource. They like that what is in their binder is what they need and what they need is in their binder. We provide class time to work with others to create their own review material (at least at the beginning of the year). We talk about summarizing and key ideas.

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My students typically have issues with problem solving, word problems and small group tasks. A lot of times because the answer is not RIGHT THERE, they don’t want to struggle and therefore give up before really diving into the problem. Many of my students lack problem solving skills when they come to me in the fall and its a skill we work on throughout the year with every topic I teach in math.

What I have realized is that a lot of my instruction had to be modeled not only by me but by other students I’ve named EXPERTS in my classroom. A lot of times hearing the strategy and working on the strategy with a peer, makes the concept sink in better.

When students work in groups I encourage them to each take on different tasks in order to make sure everyone has contributed in some way. Students responded better to the idea that they all had a role identified from the beginning in order to complete the task. If one person didn’t complete the task it affected the whole group which really makes our students hold each other accountable (Important life skills:)

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I find that my students struggle with the possibility of failure. They often want to give up before really trying. They also struggle with utilizing previously learned material with the newer topics. Over the past few years, I have done less direct instruction and allowed students to discover and apply. It has caused some stress for the kids, but great satisfaction and long term learning has occurred. Finally, my students struggle with taking responsibility for figuring out what they do not know. I have tried to ask more questions and give less direct answers.

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My students struggle with understanding complex concepts. I try to take several approaches to pick up different types of learners and pair visuals with verbal and text instruction and explanation. They also do not want to show the steps they take in solving problems. They seem to think if they are able to do it in their head it does not need to be shown on paper. I have gotten some of them to write more down by telling them any step or calculation they make needs to be recorded to look at later when rechecking or studying. Finally, my students to not take the time to go back and check their work. In some of them I think it is laziness and wanting to be done and go onto other things. I like to have them go along each step and put some sort of simple dot, check, or symbol to show they looked at it and checked their calculations.

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I have also seen students not want to take notes down. I have looked into using interactive student notebooks that would appear more hands on to them. I like the idea of using guided notes and it’s good to hear your students took ownership and enjoyed creating.

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My students have typically had issues with the following three concepts:

  1. Word problems. As soon as I even say those two words, I get immediate groans in response. Students have a lot of trouble abstracting from the concreteness of the problem to the conceptual.
  2. Literal equations. Some students seem to have trouble the instant numbers turn into letters, which becomes a huge issue when they get to Physics, which is pretty much word problems and literal equations.
  3. Giving up. Many students feel like if they don’t “get it” right away, they’re never going to understand, which isn’t true. Or they come in the first day with the, “I’m not a math person” attitude, which takes some time to dispel.

I love that you allow students to discover mathematical rules on their own. It gives them a deeper understanding than rote learning, IMO. Of course, that approach often takes more time than teachers have given the breadth of curriculum necessary to cover.

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I find that my students struggle with:
-using previously learned skills to develop new concepts

  • attempting more than one way to solve a problem
    -and, reading a word problem carefully.

I give the students many opportunities to explore and discuss the solutions to word problems. As they continually practice and observe that often there is more than one way to solve a problem, they become more proficient in solving problems.

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I found that my scholars struggled with transference of terms to applying the skill:

  • What makes a function linear?
  • How do you find the x and y intercepts?
  • What is a relation?
    skill is also applied.So I always have them to refer back to the definition of what is a function…for every x there is only 1 y value. Then I model for them what it looks like on a coordinate plane restating the definition while also referring back to what the term linear means . Often times our scholars do not make the connections that the definition of the terms will also guide them to their solution or comprehension of that skill.

My students continuously struggle (and thusly, so do I) with:

  • taking notes or even reading notes, if provided
  • checking their work to see if the answer even makes any sense, let alone is correct
  • pushing to find an answer, starting with any tidbit they may know and critically thinking through it to solve for an answer (they give up too quickly and don’t give themselves a chance)

Because they struggle with these aspects of learning, I too am constantly challenged to find different ways/methodology to coach them into developing better learning strategies. I typically introduce these challenges early in the year as questions to my students; asking them how they handle these topics and what ideas they have to improve their own or each other’s learning strategies. Throughout the year I show examples and have the students provide examples of how when they didn’t utilize notes or check their work, etc, how it hurt them so that they can see the benefits of developing strong study habits. We also try different methods throughout the year so that they may fnd ways that work for them instead of everyone doing the same thing - say guided notes vs strict note taking vs pretyped and handed out notes or links. I am constantly trying different methods myself to hook as many students on the band wagon that I can!

My students struggle with these three issues:
-Learning to accurately choose important details in word problems
-Putting to use the conceptual vocabulary into practice as they solve simple and complex word problems
-Persevering through task by using different strategies other than the ones that may have been presented that lesson, especially when they are stumped by a task

Going through a thinking map helps them process how to tackle word problems, especially taking the time to think about what concepts the word problems refer to and to be able to justify why before ever attempting to sift through the nitty details and finding various strategies to solve it.

I find that getting students to persevere through completing task, using mathematical vocabulary to explain their reasoning and to try different methods of solving problems. I find that having students walk through their methods WITHOUT doing the math sometimes just helps them to get the road map down and have an understanding of why they are going that direction. The next time we work through it, we add the “math” in and they sometimes seem to get a better understanding of what they’re doing and why.

One thing students struggle with is providing 2 different examples in the design recipe. A lot of students just put in the numbers from the word problem in both examples. As I’m walking around, I usually throw out examples for them. (e.g. “I want 347 green triangles.”)
Another struggle is students losing focus. In the previous CSinA course, lesson one introduced video games. Then there are several lessons (design recipe, strings & images, etc) with no mention of video games until we come to “The Big Game”. It was hard to keep jumping focus between the game and the other algebra. The new CSinA Course A and B are a great help. It helps maintain focus.

One area I find difficult is getting students to take effective notes. I like to blend some old school and new school methods. New school for examples: information is readily available to students through Google, on line texts, and other on line references. Students in this technology age are very familiar with looking for info, explanations, etc in this quick and easy format. In fact, I often have discussions/arguments with a colleague who subscribes to this idea: why do I need to know if I can just look it up? :smiley:

My “old school” method links brain research to understanding and comprehension. When writing a problem or notes from the teacher or from "the board ( whiteboard, smartboard etc ) there are multiple opportunities for your brain to “learn” this information: hearing the teacher speak the words, seeing the teacher write the words, “hearing” your brain recite the words, actually writing the words in your notebook and finally seeing the words in your notebook. These multiple impressions are valuable first for recall, and airports nt first step to comprehension, understanding, and of course analysis and synthesis.

Old school also provides a a ready source of examples, in student writing, for further review. It also allows for teacher to better understand the student and to address possible misconceptions.

One way to address this issue is a poster idea is borrowed from a work shop with thes simple words " I write, YOU write." I have also contemplated making a notebook check a grade-able assignment, but have yet to implement this concept.

I am not sure if this idea is exactly what you are looking for in this assignment, but I wanted to share what was in my mind!.

One of the problems students have is understanding abstract concepts, and one of the ways to do it is to make the concepts clear to them by making them concrete. The article really gives ideas how to teach functions in a way students understand.