Areas that I my students have difficulty with are: showing work, explaining their reasoning, and not giving up when they are challenged. For each of these I stress their importance however the students still fall into their old habits.
Students do not like to show their work when solving problems. Students rush through their work making careless mistakes. Students do not understand how algebra will help them in the future.
Overall, I think the importance of math literacy needs to be shared and valued with my students. Within my classroom I have to continuously work with my students on using academic language and incorporating it in dialogue, as well verbal descriptions, documented explanations, etc. My students also struggle with engagement during experiential lessons.
The three habits that my students struggle with are:
- Double checking their work (their goals seem to be to just get it done instead of seeking to understand)
- Working well in groups
- Coming in for help when they are struggling
My students struggle speaking mathematically about topics when explaining. I’ve recently introduced mathematical sentence starters on their tables. They also enjoy having a word wall available.
Students have difficulty with the difference in domain and range. I introduce it by putting up a situation and asking students all the values that could be possible. Then we figure out how to write these (list or inequality- discrete or continuous). Their struggle is that the range is restricted by the domain.
Students often don’t see the point of checking all their work. They know for some types of problems they HAVE TO (for example, to find extraneous solutions in absolute value functions), but figure they’ll “just check for that kind of problem”.
Algebra students spend several weeks writing and understanding functions. Word problems are incorporated throughout the entire year.
I’m not teaching Algebra next year, but want to incorporate this into my advance 6th grade classes.
My students have a difficult time showing their work. They have “the answer,” and to them that is all that matters. From the first day of class to the last day of instruction for the year, I emphasize “the process.” We do error analysis in class and it becomes very difficult for students who do not show their work to complete this task. Forcing them to show their thought process, something they have not had to do in previous years.
Another concept is plugging the x function back in to see if it works for all of the inputs and outputs. They tell me it worked, because they tried it on one of the ordered pairs and it was valid. One thing I did last year was provide the students with a function and four ordered pairs. In partner groups they had to choose if it was a function or not. One student made a suggestion that if they choose two each it would be more efficient. This created collaboration and a higher level of learning occurred as students explained if the functions were true.
Students who don’t want to go back and correct mistakes on formative and summative assessments. On Friday’s we worked on our “playbook” analyzing prior work, prior concepts and identified misconceptions. Students valued this time, being able to sit down and go over questions they had during the week.
What is the set up of your classroom? What plans do you have in place to help your students improve in these areas?
My students definitely hate having to show their work - for anything. They just want to write down an answer and expect me to believe that they really understand how they got it. I try to explain to them that I cannot see what is inside their heads unless they write it down. This helps, but it is still a constant battle.
My students don’t always work well in groups. There are always those kids who want to just work alone because they don’t like/get along with “anyone else” in the class. Sometimes I let them choose their own groups, other times I choose for them. I explain to them that very often these days they will be asked to work in teams when they have jobs and sometimes you may have to work with someone you cannot stand to get a job done.
Perhaps the bigger challenge though is getting them to actually problem solve on their own - to ask those next level questions and actually try to figure them out on their own. I quite often refuse to answer their questions until they have asked a classmate first, and even then I will only hint at the direction they should take to solve the problem at hand.
Those are all good challenges. I agree that understanding the “why” is just as important as the “how” when solving problems.
I teach computer classes, and see similar issues with the whole idea of showing your work. They just want to go straight to the computer and to heck with how they got there.
Functions will be a challenge for me as I work with this code.org program - it’s been quite a while since I’ve used them for anything “real” so I am looking forward to the PD to help me learn how to teach them to my kids.
My students struggle with vocabulary. In fact the entire school struggles with vocabulary on standardized testing. We use prior knowledge to help students connect with vocabulary words. Also, we engage students in whole group, small group and partner discussion. My students also have a hard time showing their work step by step. They do not receive full credit if their explanations are incomplete. Finally, my students struggle with translating word problems into expressions and equations.
My students struggle with making the connection between the different ways of showing results of a function. They see each task as work. They don’t recognize that a graph, table, equation work together to mean the same thing.
Since I teach engineering - my problems are more functional:
- Students do not want to read through an entire project before they begin. They just start without understanding the purpose or expected goal. They then focus on small aspects instead of what is the purpose or outcome. For example when creating a lifting arm - they fail to read they must be able to extend the reach and rotation of their arm. They will construct something that cannot be modified and then be upset when they lose points.
To help with this problem, I have started by requiring the teams to read the entire project then come to me prior to receiving their materials. I ask 2 or 3 questions about their goals. If they cannot answer correctly, they don’t get their materials and they have to go back and re-read their assignment. After the first project or two, they start reading the entire thing.
Time management is another problem. Students don’t know how to monitor their progress to ensure they reach their goals. To help with this I have started creating checkpoints and assigning due dates. This way students know they should reach a certain point by a certain time. If they are behind, they will have homework. If they get ahead, they have time to receive feedback and make modifications to improve their grades.
Teamwork is also a big problem. I have students watch a couple of videos which show teams who are successful even with interpersonal conflicts. We discuss how they can disagree but still succeed with their goal. Also, it lets them know that conflict isn’t necessarily bad - just how it’s dealt with that can determine success vs failure.
Not giving up is a huge issue with many of our students too. They expect teachers to just GIVE them the answers or credit because they tried. I use a phrase from another teacher - I am like a “no-interest” bank. You will only get out of me what you put in. Zero in = Zero out.
My students find the following concepts or habits difficult:
Group Work: I tend to find half of the group tends to do the majority of the work and the other half of the group watches. To ease this issue, each student will responsible for completing their own assignment so the group will turn in 4 assignments to me. Then, I will randomly choose one person’s in the group and grade that one. Everyone in the group will get that score. I find this process helps the groups work closely to ensure everyone is understanding.
Checking their work/answers before submitting homework: Each day, I ask students to ask questions regarding the previous night’s homework. Half of the time, students will ask me to complete a problem with them when their answer is correct because they didn’t check their answers in the back of the book. It seems students just want to get the work done rather than viewing homework as an opportunity to practice and grow.
Students would rather use “tricks” than do the work to truly understand a concept: We started teaching common core standards to our students last year. Students were used to just using “tricks” in math to solve problems. They didn’t want to think about or understand the concept…they just wanted to follow steps. I had to introduce a lot of word problems and real world problems to encourage students to really understand the math topic we were covering.
When I introduce functions to my students, I start with the idea of a juicer. I tell them a tall tale about how when I was shopping with my wife I found a gadget called a “number juicer” – instead of putting vegetables in and getting juice out, you put numbers in and get different numbers out. I make the story dramatic and funny, and I use my SmartBoard to do “number juicer magic” – students can put a number in and see what comes out of the number juicer. It gets them curious and starts them guessing what the rule is. This has been a great way to illustrate the input/output nature of a function, and it helps me show them how to differentiate between a function and a non-function: If you put the same number IN to your number juicer, but get a different number OUT, then your machine isn’t FUNCTIONING properly.
I am habit the same problems. It seems like the students are looking for answers. Although I do not teach computer science yet, I am incorporating some,of the,team h night ques.
This entry sums up what I ahve seen for many years. We had a curriculum that was more hands-on and taught these processes, but many were not happy that it lacked work in skills. Now it seems the biggest issue is students do NOT see the big picture. They want and easy way to “get done”, but they have little connection to the meaning of their work.
I can’t get my students to check their work when solving a math problem. I always let students make corrections after I have graded something, but I wish they would check their work before.
I can’t get my students to participate on a daily basis. I give them ‘talking tickets’ and when they participate in the whole group discussion or lesson I collect their ticket with their name on it and a drawing for a prize at the end of class.
I can’t get my students to work collaboratively in small groups. I give them rating scales with 1-10 written on them. I cross out high numbers if I find them off task and low numbers if they are working well within the group. The expectations are written on the paper and it is a participation grade at the end.