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I have a few students that need lots of individual attention.

What do you have the other students do during this time? Review problems? Challenge problems? start on their homework? play a math game? Ideally, they would come see me during office hours, but I teach at a community college, and it just doesn't happen.

Currently, I teach Intro Algebra and I have about 30 students in the class. I run a lecture-discuss-solve problems classroom. What do I mean by this? I set up a topic by lecturing for a few minutes. I then ask them to discuss some aspect of it. Then they share out ideas with the whole class, and I lecture/they discuss a bit more. Then we work on problems which are similar to the problem discussed, but may include slight differences. I offer "basic" and "medium" problems, to offer some differentiation. I sometimes offer a "challenge" or open-ended problem, to satisfy the stronger students. It mostly works........but I was just looking for more ideas.

I feel like I am meeting the needs of the A, B, and C students, but I don't meet the needs of the really struggling student.

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    $\begingroup$ What level of class are you teaching? The question is quite broad and a little more information about the specifics can help with some answers! $\endgroup$ – Andrew Sanfratello Nov 6 '14 at 19:42
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As this question still seems vague to me, (I'm curious as to how your classroom is currently structured), I can provide only anecdotal evidence of what I do with my Community College Algebra class. First, some background on the course.

I have found difficulty teaching this course, since I often receive students with a wide range of abilities. Some come in with a strong sense of algebra, but need only minor tutelage to pass the exam; others come in struggling with the very basics of arithmetic; most fall somewhere in between. Additionally, whether or not a student passes hinges entirely on the final exam: If they pass the exam, they pass the class; if they fail the exam, they fail the class (with little else that I can do).

I have structured the class in a different way the past two semesters. Since I am getting students with varying degrees of ability, I do not teach the curriculum in an orderly manner, and because the class is so heavily dependent on the results of the final exam, I make this my primary focus. I have created 8 cycles, with each cycle mimicking different sections on the test. Cycle 1 consists of:

  • Quiz 1: Handed out first, without any discussion. I let them struggle with the material and after allowing some time for individual work, I suggest they "cheat" by going online, asking their classmates, or looking through their notes. At this time I also begin to circulate the classroom. This allows me to help individuals and small groups more intimately on their specific problems. After some amount of time has passed, I have individual students volunteer to put their solutions on the board. I then go through their solutions providing my "expert" opinion and critique their work. This is as close to a "Lecture style" that I get. This quiz has 5 questions. The quiz is not graded.
  • Worksheet 1A: Twice the amount of questions, with two of each type. I let them work in whatever way they prefer going around and working with groups or individuals again. Usually, pockets of students form who like to work together, but I encourage students who I see have done good work to share it with other groups that may be struggling. After some time, questions are presented on the board for critiquing again. The worksheet is not graded.
  • Board Set 1: I "lecture" for 5 similar problems; again providing my "expert" analysis. Questions are encouraged and we dissect each problem.
  • Quiz 1B: 5 questions, 20 minutes, graded. When quizzes are collected, I put the answers on the board.
  • Worksheet 1C: 10 questions, due the next class period. If the worksheet is handed in and it is higher than the Quiz 1B grade, it will replace the Quiz 1B grade in my gradebook. I do not allow extensions, but I let them use whatever resources they can. Students will know how they did on the previous quiz since the answers were posted on the board immediately after they handed it in.

Repeat the cycle for 5 new questions

Additionally, there are also online homework assignments that are associated with each cycle during the timeframe.

This entire process allows me a lot of individual time. It lays a lot of the onus on the students to self-motivate, but this is an issue I had in the past before. My feeling is that students who are really ready to learn and dedicate time to the material, will do so.

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In general, I make it a point to focus heavily on factoring. While the questions that I pull are usually from old exams, many of the issues that my students have fall under the category of "not really understanding the prerequisite material". Most students struggle with basic factoring facts, so I spend a lot of time, early, on factor trees and finding the factors of integers and variables.

Additionally, I emphasize that the laws of exponents involve seeing one operation (e.g., multiplication), and performing a different operation (e.g., addition). I often create a concept map of hierarchy pairing multiplication and division together, but also associating each of those to addition and subtraction, respectively. This extends to the concept of associating raising powers to higher powers and multiplication of exponents.

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How might you incorporate these ideas to your classroom? The structure of quizzes and worksheets allows me to work with individual students who are struggling more closely. It also promotes group learning and creates an overall sense of community for the classroom. Emphasizing this style of teaching, and moving away from the traditional lecture styles that many of have learned mathematics from, is valuable for struggling students. Perhaps if you could incorporate some of the organizational styles that I have described above, you can find more time for these students who require more of your attention.

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I teach basic mathematics among algebra in a Danish High school. My students are also very diverse, with some having a big interest in math and others still lacking understanding of basic concepts. I have 28 students in a class.

I tend to give the good students some challenging puzzle, which build upon the subject we are working with. I write this up on the black board named as a bonus exercise. The students then know that it is not mandatory to do it and that the exercise can be extremely difficult. Sometimes too difficult for even the best students to solve, which leaves them puzzled after class, eager to find a solution.

I like this setup because, it keeps both the strong and the weak students engaged and challenged. But without the strong students moving too much ahead in the curriculum, instead they gain a deeper understanding of the subjects.

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    $\begingroup$ Is there a tension with the clear distinction between those who are "good @math" solving puzzles, and those who are not? I worry about increasing the separation between the haves and the haves-not. I am not criticizing or suggestion a solution, just expressing a worry... $\endgroup$ – Joseph O'Rourke Nov 7 '14 at 1:13

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