I'm a graduate teacher and what I found is that some low-level students were not listening in class, they have given up and stopped trying. I feel it's hard to make a difference or help them because they don't seem to care.
Honestly, I used to be that "low-level" student. And they for the most part are not low-level students. I mean yeah, there are always going to be kids with a below average intelligence where learning new concepts is just going to escape them, but usually these children are put into a lower level mathematics course.
Since my high school days, where I'm sure my teachers pulled their hair out everyday trying to motivate me to do something, I've changed.
I always had a good relationship with my teachers. I remember once my law teacher got fed up with all of the students for not handing in their homework- so he went around the room pointing at people and asking them what they wanted to do with their lives. Each time it was the same answer: "Well you aren't going to be able to do that if you fail this class are you!?" Finally he got to me and he said "Anheuser!? What do you want to do?" I thought for a second and then said: "I want to travel to Australia." He stopped and looked at me and said "That is completely doable. You could definitely accomplish that."
This was the first time in my life a teacher has ever told me I could accomplish something. Yeah, they've said I was smart and that if I applied myself I could be the best student in the class, but you don't crave that as a student. You want someone to tell you that your dreams are possible.
I am now a PhD student studying mathematics. None of my former teachers know this. I was never known as being a smart student by my peers either, so I'm sure they would be surprised to find out as well.
If I had to teach mathematics, I would share the stories of the people who made up the theories. Make it fun and interesting. My history teacher brought in a guitar and sang a song about Louis the 14th to educate us about his life. Do things like this, and try not to hold their hands too much.
There isn't enough information to answer the question, but I'll speculate, based on what often happens in the world of math education.
People who enjoy & teach math are often shell-shocked at how many people consider math to be a meaningless, tear-filled, horrible subject in which effort is pointless. My guess is that most students have given up on trying because 287 adults before you have told them to try harder, then given them rote or inappropriately difficult work... in which trying doesn't make a difference. See my recent post on fractions for examples of how hard work combines with rote gibberish to demoralize and confuse.
I suspect many of your students view you as the 288th adult who's giving them more rote gibberish and empty pep talks. Some likely signs of this: your lessons are very heavy on symbols and students (rightly?) don't believe you when you say they should pay attention and try harder.
Their response: The bare minimum effort to: (a) get you off their backs and (b) avoid summer school or repeating the course.
Consider doing gentle but probing "math biography" interviews with some of your students. Tell them you need their input to become a better teacher and want to begin by understanding when they stopped trying. Ask them when math became a painful subject for them. In kindergarten, math is for many children the favorite academic subject; among the general population, about 37% of people specifically use the word "hate" to describe how they feel about math. [Many others use other negative words to describe their feelings.]
Expect a lot of stories such as:
- "I loved math until grade 4. Then my teacher didn't really teach us division or fractions and never tested us on anything. Sometimes we'd go weeks at a time without a math class, months without a test. I've been terribly confused in most math classes since then. I noticed that studying really hard didn't help, so I just don't try hard any more because it's not fun." Note that this is likely true: given terrible confusion regarding grade-4-level division, does it matter if you study really hard to master proportional reasoning and ratios? Of course not. Hard work didn't matter then even though adults falsely told them it would. Why are you different from those adults?
- "My teacher made the class do all these timed exercises. I was the slowest one in the class no matter how hard I tried and that's when I realized I was stupid." Notice that maybe the student just needed to learn, say, how $6+6=\_\_\_$ and $6+7=\_\_\_$ are related, then they could have stopped counting by ones to do all calculations. But if you don't know such relationships, then, well, math = counting by ones, which is slow and makes people feel stupid. It's a hopelessly weak foundation for future math. Are you trying to build on their hopelessly weak foundations?
- "The teacher would make me come to the front of the class and tell me to do math I couldn't do and that was humiliating. I hate math. So just tell me how to pass this class so I don't have to go to summer school." How often do your students feel great about what they've learned and accomplished in your class?
- "Math is just all these steps. I just memorize those steps. I'm the memorizing type. I'm not interested in understanding because I don't think there is anything to understand. Just tell me the steps and I'll do them." Are you sure you're really testing for understanding? Are you really convincing your students that math is understandable?
In my opinion a very important tool for the teacher is a lesson plan for every lesson. I was a math tutor in a math center for 8 years and I conducted multiple worshops in a classroom setting with over 20 students at a time. Techniques that worked for me were: inviting students to ask questions during the lesson , polite responses to questions , eye contact with the students , doing a worked out example on the board and then writing a similar problem beside it and asking the students to solve it at their desk while I walked around and looked at their work and gave helpful hints if the student seemed stuck. Also I would have students work in groups of 4 or 5 so they could exchange ideas with their peers. You have to mix it up a little so some students don't get bored.
Hope this helps :)
The answer isn't the same for every educator or every group (or every combination thereof). I find that the key is to consider myself constantly trying to find this answer. In other words, from day 1 to the final second of your time with these students, you are trying to find the "holy grail," so to speak. ...or at least get closer...
In other words, you are trying to reach every student, every small group of students (as they exist), and the larger group (class as a whole). Therefore, I try to connect with each individual and each group as authentically as possible (a little fake-it-til-you-make-it can help here) If it feels forced, it is... but don't give up.
If a strict lesson plan is authentic to you, then do that, but make sure you PAY ATTENTION TO EXACTLY WHO YOU ARE TEACHING. Connect with them.
As you manage to understand them better, you may also find ways to articulate the lessons differently, ultimately framing them in a more relatable way. A very simple example: you find a certain cross-section of students are soccer players, so all of your momentum lessons (physics application here!) have to do with soccer balls. Just be careful you don't get too hokey ;-) ...you don't want the students rolling their eyes too hard. But thy really do appreciate the effort if you're being sincere and totally authentic.