My students struggle most with starting problems. I try and give multiple entry points for each question, but if they do not see a quick way to start they will give up. Because they are afraid of being wrong they often won’t even begin.
My students have a hard time working on difficult/challenging assignments without giving up. Showing persistence is a problem. And checking their work for simple errors is a area of concern.
Some of my students give up to easily when working on problems. Then they want you to just give them the answer. They don’t realize that by learning to persist through a problem, they are learning a life long skill.
The 3 concepts or habits I find my students struggle with the most:
- Reading a word problem carefully and pulling out all of the necessary information and what they are being asked to do with that information.
We spend a lot of time discussing how to translate a problem from words into math, and to make a plan for solving it. I think the process of breaking down the problem into pieces and translating each one is really useful, but no matter what I do, it’s hard to get kids to actually apply this.
2… Working in groups.
We have been using Complex Instruction (CI) at my school over the past year. CI helps train students to work together in groups by fulfilling specific roles, working on complex problems that are “group-worthy” and trying to improve the status of students who aren’t the typical, “good students” by finding what they do well and pointing it out to the group. It is hard to really follow the rules for complex instruction all the time, but if you do it really makes a difference in how kids work together and how they approach complicated problems.
3… Showing their work or explaining their thinking
The Common Core math standards depend on being able to explain your thinking, and this is the hardest thing for all students to do. In fact, very strong math students often have a harder time with this than students who need to think things through more explicitly. Complex instruction helps, making students answer all word problems in complete sentences helps, scaffolding helps, and I also find that praising kids not for getting the right answer, but for explaining their thinking also helps.
My teaching partners and I spent time teaching our students about “Growth Mindset” with Jo Boaler’s online course. It didn’t solve the problem of perseverance, but it helped. We really focused on what you learn from struggle, and that you learn more when you do struggle.
Students need to be able to understand the meaning of the word “function” therefore, if they do not know they will not be able to follow with the rest of the concept. In any case, any mathematical word the students do not understand or are not familiar with should be able to find the definition(s) to increase their vocabulary and knowledge of the concept being taught. I have students create a math vocabulary dictionary for themselves before we start every lesson. Even though they have their math vocabulary dictionary some students have difficulty looking back into their notebooks. I would like for my students to write and explain their thinking when solving a mathematical problems.
I have the same issue in my classroom. They expect me to give them the answers when they want to give up, but I do not let him give up. They need to try different strategies.
It is challenging for my students to complete a problem when we move outside the bounds of that particular chapter/unit. Many of my students become good at the procedure but then have no idea how to solve the problem when they see it a month or more after we have finished the unit. They don’t have a conceptual understanding of the topic, just a procedural one that serves them well for the immediate but causes issues when we try to link ideas that are not as fully formed.
It is also a challenge for my students to persevere through a tough problem. I always encourage them to work through the tough topics and try different strategies but they still seem reluctant. It is almost as if they don’t have a working toolbox of strategies and are so used to just using the strategy presented in class. They become frozen when it doesn’t work for a particular problem.
Vocabulary is always an issue because I want my students to be able to explain what they have done to arrive at an answer but many just don’t have the vocabulary to do so. Others just tripped up with the vocabulary in the problem and struggle to solve the problem because they don’t truly understand it. With multiple meanings of words, it is an added layer for students to contend with. I always try to define important words in a problem and help students brainstorm how the word plays a part in the problem but students have difficulty doing this on their own.
Cooperative learning can easily lead to one or two students doing the work and the other students copying the answers. I ask students to reflect in many types of ways to encourage that there still needs to be collaboration and the ability to show understanding…i.e. written answers, group/class discussions…alternative types of assessment allow you to see if the student copied the answer, but still shows understanding. In connection with the collaboration, students often resort to asking the teacher if they don’t want to use their collective mental power to solve a problem. The “ask 3 before me” policy is established early on in the year so that students know they must show they have attempted the problem, asked their group for help first, then finally seek out my assistance. Lastly, rushing through work/not showing work is a normal issue for this age level. Consistent and timely feedback on work, and practice modeling how work should look helps with this.
Challenging concept for students: Subtracting integers
I keep numbers small and do interactive lessons like “walk the line” where students walk on a number line to represent expressions. We have also used a “good guy (positive numbers)” vs. “bad guy (negative numbers)” concept to help them understand. 3 bad guys take away 2 bad guys and you have one bag guy left (-1). Students respond well to both strategies at first but later say things like -3 - (-2) is 1 or -5 or 5. When I sit down with them and ask them to use a number line to show me how they got their answer or use another analogy they often get the right answer. Many don’t want to take the time to think about their solutions on their own using strategies discussed in class.
Challenging habit: When struggling they instantly want the teacher’s help instead of using notes taken in class or table mate to help them get “unstuck”.
Middle School students do not know how to take notes or how to use a notebook to help them. This concept has to be taught and reinforced every single day of the school year. Holding students accountable for having their notes open on their desk before asking for help, when I do come by to help ask them questions and have them look in their notes where the answers might be…even if they already know the answer to my question I have them show me where in their notes it says the answer. This way students learn quickly that I am going to make them reference their notes when I come over to help them so maybe they should look at them first before I get there.
Challenging concept: Constant of Proportionality
Before Common Core we taught slope and y-intercept in tables/graphs/equations/scenarios. Now we only teach COP and it has been challenging to teach only this and not be able to link it to y-intercept as a way to help kids understand proportional relationships in relation to ones that are not proportional and be able to help them understand in a meaningful way.
My students struggled with multi-step problems. For example when determining the a percent off of an item. Students were able to find the percent off but did not subtract it from the original cost. I would suggest for students to better understand multi-step problem that they talk with a partner about their answer and work. Having students explain their thinking to other another may help them to understand better from a peers point of view. Students also struggled with conceptualizing percents and ratios. They were able to find it but may not have understood the part whole relationship. I would use more a visualization for students to conceptualize this in the future.
Students have a difficult time going back and checking their work. The students who are strong in math, are especially challenging because they have so much confidence in what they do.
Another struggle is seeing student work. I can’t reiterate enough how important it is to show the steps they take so that if there is an error, it will be easier to point out, rather than having the students try to think about what exactly they did (especially in a multi-step solution).
-I have a hard time with students taking time to analyze questions and determine concepts they need to know.
- Get students to go back and check their work
- Get student to come up with their own applications for math content being covered.
I find it challenging to get my students to share responsibility when working in groups. Whether I group students by ability, assign jobs, or have students choose groups, it is inevitable that some students will “wait” or “think” while work should be taking place.
I also find it challenging to get students to use math specific terms. For example, I instruct students not to use the word answer, number, or pronouns. I encourage them to use integer, product, substitution…
My students often struggle with with conceptualizing word problems. I try to use drawings and a process called 3 reads to dissect problems with them and teach them strategies for solving word problems. After reading the article, I plan to also focus more on mathematical language and how these words are used in the real world and can have multiple definitions. Some students also struggle with using the strategies that have been taught to check their work. I try to teach them that checking is a part of the process of solving because good mathematicians must be accurate. My students also struggle with retaining taught information or building connections without my support. I check their notes as we learn to make sure they have accurate examples to refer back to. However, getting them to study the notes is an even greater challenge.
The author cautions us to be careful with the word function because depending on the context, it can mean many things.
I leave much time for functions, but it does seem to be very difficult for students to understand.
I try to spend at least 10 minutes a day on word problems.
I think the author wants teachers to be careful when teaching about functions and to spend enough time on functions so that the students fully understand. Word problems are important to all students because it causes them to think critically.
Three things I find difficult:
I find it difficult to have students go back and check their work. Without fail there is always a handful of students who make the most careless of mistakes that could be caught if they would recheck their work.
I find it difficult to have students explain their thought process when solving a problem. Regardless of how smart a student is and how often they are correct I still find that they have issues vocalizing how they arrived at their answer. I would typically get answers like “I solved the problem and got blah” or “I followed the directions and got blah,” with no real explanation.
I find it difficult to have students show their work. Students try to do too much on the calculator or in their heads and make mistakes. I am wary of taking calculators away from them because it is a tool they have on their SOLs and something they need to become comfortable using, but it must not become a crutch for them.
I don’t have a computer science class but when it is an awesome feeling for the student as well as the teacher when the “aha” moment happens. Students must at some point achieve success in the course. If there is constant failure, many students, especially those that are struggling learners, could lose interest and shutdown.
I like that you call it the “playbook”. It is important for students to identify and correct mistakes. I also emphasize showing work at the beginning of the year. I do more error analysis now than I did when I first began teaching. A lot of changes have been made given the changes in the way students are tested. In class we have “be the teacher” sessions where I intentionally display questions solved correctly and with mistakes for students to correct and explain using math vocabulary how to correct.