I want my students to verify (check) to see if their solution works and is reasonable.
I want my students take the time to think about what is being asked and show perseverance to solve it without giving up if they don’t immediately know how to solve the problem.
I want my students to work cooperatively together to solve problems, not just look to “the smartest” student to do the work without questioning and thinking on their own.
I want my students to verify (check) to see if their solution works and is reasonable.
One of my goals is for my students to be able to explain the “WHY” and not just the how. I encourage the use of math language in my classroom by having students work in groups. Students also know they can be called upon to explain how they solved the problem so this promotes more group discussion.
Much like the other teachers, my students don’t always like to show all their work. Knowing this, I like to model how I would like to have the problem solved. This helps them to see what I am looking for and allows me to stress the parts that I feel are most important.
Again, like other teachers, story problems always seem to be tricky because students get lost in the problem or just don’t want to read all the information. To support students, we have been working on marking the text. By implementing this technique students figure out the “necessary” information and how to “pick the problem apart”.
My students often have trouble with the concept of substitution in Algebra. While they can substitute a given numeric value for the variable in an expression or equation they cannot seem to extend the concept to substituting in an entire expression for the variable. The concept is necessary for solving problems using systems of equations as well as problems using nested functions or composite functions. Finding ways to demonstrate the concept of equality has helped a great deal, i.e. to say that things are equal means that they have the same value and are therefore interchangeable (e.g. the value of a dime is equal to the value of ten pennies, therefore you would trade a dime for ten pennies.) I have a few hands on activities that I use to help students understand.
Another issue is the idea of making mistakes. I think that “learning from your mistakes” is far more profound than it sounds. Students tend to be ashamed of their mistakes, but I’ve found that when students receive immediate feedback, along with the opportunity to correct their mistakes in the moment, they show more ownership of the mistake and have more pride in their solution. Using an online learning modality that allows for teacher-created assignments is the best way to implement this. Learning to program will provide many of those same opportunities.
Finally, I’ve noticed that many students, even as 12th graders, have the notion that school is about turning in assignments. It seems that in many of their other subjects little critical thinking is expected of them. They produce papers, posters, projects, and presentations that are mere regurgitations of other resources with very little evidence of independent thinking. Because my classroom is a computer lab, students often ask if they can work on these assignments during lunch or after school, so I see what they’re turning in.
They often proudly show me the “A” they received on what is little more than a book report. Many of them are confused by the idea of supporting a claim with logical reasoning. I hope that by introducing computer science curricula early, students will have more experience exercising their logic muscles and will start to see those other assignments as the boring busywork that they are.
Please find that resource for us! I’ve long had an issue with the usual team roles you see: Time Keeper, Resource Manager, Facilitator, Recorder, Reporter etc. Those roles seem to be modeled on teamwork for a business model where everyone truly has a different function in completing the project (Project Coordinator doesn’t do the design of the product, the Designer doesn’t do the Cost Accounting, etc.) But in a classroom everyone has the same role, which is to understand the concept! Too many times I’ve seen the least motivated student choose to be the Resource Manager or the Time Keeper and then when I observe the other team members doing all the work he or she will proclaim “I did my part - I got the materials and put them away!”
Having roles like Ask a Question, or What if we tried this? puts the focus where it belongs, on learning and understanding.
In my classes, whether it be Algebra or Geometry, I find that the students struggle with…
- Multiple Representations
Students tend to find one way to solve a problem and do not challenge their thinking to find alternative methods.
If students find the problem challenging and they cannot solve it right away, they give up. They want to be shown how to solve the problem and guided through the process, rather than tackle it with a game plan.
- Written Responses
Students will write very little or just the minimum to justify their answers and methods.
My students have a really hard time with word problems. I try to start off with easy ones and working up to hard ones, but they really struggle with reading in general.
My students also struggle with working in groups and staying on task. I try to counter this by circulating the room and keeping students on task, but this is difficult with 30 students.
My students also struggle with the concept of pi. This is something that I find very frustrating, so I end up looping it and keep coming back to it.
My students have a hard time with all of those things as well. I find it helps to try to get the students to understand why a formula works, for example with the area of a triangle, I tell them to draw a rectangle, whose area would be base x height, and then just cut it in half, (divide by 2) and you have a rectangle.
My students are reluctant to show their work - I think they feel like it takes too long. I encourage them to show their work by giving them partial credit on assignments.
I require students to check their work before turning in tests or assignments. They almost never do even though they are reminded, and there are often simple errors that should’ve been caught.
Many of my students choose not to do their homework despite the negative effect it has on their grades. I use homework problems, that we go over in class, on their assessments to encourage them to do their homework consistently.
Like many of you, I always have some students who balk at showing their work even after I insist and we have discussed how problems are going to be getting more complex so let’s practice showing our work now while it is still “easy” and how employers are looking for people who can explain their thinking, etc. Eventually, the student will say “but I can do them all in my head” and I’ll give that student something to solve that he will need to be able to solve by the end of the school year that there is no way he can solve in his head. It will be too new or have too many parts to it or perhaps it will just have a couple of fractions in it. Very, very few students will resist showing their work after that point, and the few that do will at least not argue with me about it any more.
Way too many of my middle school students have large gaps in the fluency of their basic facts knowledge. This includes place value and multiplication tables. This makes it difficult for them to do fractions, to estimate, to check for reasonableness, and for them to “see” patterns. Many of them are way too calculator dependent. I do allow calculators sometimes and not at other times, although when they get to use calculators, they still need to show all their work, even what they typed in the calculator. I do model strategies and have students practice math facts, especially when I am working with them in small groups or one-on-one, but I haven’t found any grand solution to this problem.
A third habit that many middle school students have that drives me crazy is that they have 5 - 10 seconds of perseverance and then they give up. This is not because they are middle school students; kiddos of the same age in other countries will work on something with which they are struggling for up to half an hour before quitting according to research I was reading a couple of summers ago. (I think this was in the book “NurtureShock” by Po Bronson.) We have teeny lessons on “lifeskills” and growth mindset vs. fixed mindset at our school, but it isn’t enough. I’m not sure something I do all by myself would be enough, but I’d like to do more.
My experience with middle school students is reflected in so many of the things said here. Word problems, perserverence, and fundamental understanding of concepts.
Slope, function, and the input/output relationship is hard for my students. I like how the article pushed to bringing these terms into a real life situation and into a definition that makes sense for students. They need to see the machine work.
Omg!!! You took the words right out of my fingers!!! The second problem has become almost a pet peeve of mine and I can equate it to fingernails on a chalk board. It seems that the longer I teach, students “know” more and more and their old ways become the number one thing holding them back from success. I find that I spend a lot more time at the beginning of the year doing trust activities trying to build this between my students and myself so I can plant that little seed that maybe they should try “my way”!
Bravo! I second this!! I cannot express enough how many times I have used the example of future employers needing employees who can communicate. More often than not, I take the position of the employer and let students know that their lack of work, communication and willingness to think has would lead to me firing them, right then and there. It is essential they understand not only are the mathematical skills they are learning key, but so is their work ethic.
Well written…thank you!!
I struggle getting students to persevere on a task individually if it doesn’t look exactly like the “examples” or other situations we’ve done in class they won’t try it. I’ve tried asking questions to answer their questions as a way to get them to keep trying and stay engaged but it doesn’t always work.
A second habit that I struggle with is students communicating with each other productively. Many students think that “helping” each other is copying down the answers, and then they wonder why they don’t do well on short answer responses.
The third habit is getting them to check the reasonableness of their answers or their work in general. Many times an explanation for a problem will be, “but that is what the calculator told me the answer was!” I haven’t found a solution that works all the time. I encourage my students to show their work/steps and calculations, but that is only a small step.
I see I’m not alone on some of my concerns and struggles with middle school kids. I look forward to ideas to help students see that these are the skills that are needed by employers–perseverance, problem solving and communication.
Deriving an equation from a word problem.
-I introduce this by breaking down the problem into different sections and showing how unknowns become variables and key words are associated with different operations.
Selecting the operation needed to use solve a word problem.
-I make charts with the class to show which words are associated with the various operations.
Critically thinking about if their steps to solve a problem make sense.
-I constantly reiterate that you have to ask yourself questions while you solve a problem, like “why did I do that?” or “does that make sense?”
Students struggle with making the connection of slope as a rate of change (as the independent variable increases/decreases, what does it to the dependent variable). In order to introduce this topic, we look at real life examples of what happens when we increase/decrease the output and what controls it.
Another topic that students struggle with seems to be identifying scenarios that match with the corresponding type of functions. To work through this, we read through word problems and look for key words and match them with either a graph, data chart, or equation.
A third topic would be getting students to check their answers by plugging back into the equation. Usually I just have a discussion about how and when to check answers, using estimation to make sure their answer “makes sense” (ex. the height of a child is 7 feet or some crazy unrealistic number).
some of my students don’t get layers in photoshop. i use real paper to demonstrate. students can’t see various ways to mix layers.
some younger students don’t get the concept of folders on computer. i should them a real folder. it is challenging to show putting a video in a real folder.
some of my students are not convinced that the headphone jack on a computer is broken. they keep switching headphones and believe every set of headphones they try is not working. i take one of those sets and show them that it works on another computer. the students do the same again the next day.
When working with Middle School Math students I have found that students struggle with making connections between examples that we work on in class and problems that are given to them. Unless the problem looks exactly like the example students give in with out preserving to solve the problem. Along this line as well students seem to have a hard time thinking about past concepts and problems that have been taught. They assume that all problems must fit into the same box.
I too like many of you have found that yet it is great to have students work collaboratively and communicate about the math. I struggle with all students participating and sharing ideas. They also struggle to find out how to work together rather many students will work along side one another and not share ideas.
I feel the third habit of my students is practice. Just like any other thing that students want to learn if it is playing a instrument, playing a sport, learning a new language or how to read you must practice. Students that I work with struggle to do this. When given homework problems they dont attempt to complete. I know that not all parents can help with some of the math that we are working on but all students should be able to try to practice some of the work that they are learning.
I see like many of you have said that a lot of us share the same issues regardless of where we teach or what level we teach.
Many students struggle to relate algebra to real life. Despite constantly using real world examples and applications, students still think that they would not use algebra if they actually encountered the problem in their everyday lives. Some students do not want to devote the amount of work that it actually takes to master a concept. They want to take shortcuts with their classwork and homework. This might include not showing work or checking their answers.
Some students struggle to persevere when they do not instantly know the answer. They do not find the joy in discovery or solving a problem.
Concepts that students struggle with.
#1. It is difficult for them to persevere and not give up on the problem. If they run into problems rather than continue to try and solve they just give up.
#2. A second concept for them is that they do not understand the reason for learning algebra. There is no connection for them between the math and the real life concrete problems and areas of life. It has always been my job to show them the connections and why they will need these skills as they proceed in life.
#3. Lastly, students have a problem in that they do not show all the work that is required to get the problem solved.