20 Apr

I teach an “Accelerated Grade 7” math course which covers all of the grade 7 Common Core standards and many of the grade 8 standards.  As such, I teach any student who’s ready to take it – I have mostly seventh-graders, but I have a handful of sixth-graders taking it ahead of schedule, and a handful of eighth-graders who are moving along at a slower pace.

A few of the seventh- and eighth- graders have academic deficiencies to the point that I do not know what to do or how to teach them effectively. It’s keeping me up at night and I wondered if anyone had some advice for me. This is what I mean and what I’m looking for.

I have one student who has very little concept of place value. As in, he holds a centimeter ruler up to an object and tells me “I know it’s between the 5 and the 6. I just don’t know how to write that number.” The idea of tenths never really got there.

Several of the kids don’t have the concept of area as a measure of coverage of 2-dimensional space. They can count squares and work with whole-number areas if they are given a diagram with squares on it. But given an object’s dimensions with rational numbers, and asked to find its area or surface area – not at all sure what that means.

Given an equation, such as “3x + 5 = 17”, they don’t understand what the equation means so can’t even begin to guess what value of “x” would make it true. This is where we are, when the kids are 13-14 years old and about to enter algebra I.

I fundamentally believe in giving the kids access to math that will challenge them and help them grow, and I’m really frustrated – and it keeps me up at night – when we take a test, and the paraprofessionals who help in my class report to me that some students did not know how to even start, what to do, or what anything meant.

During lessons, what makes all of this phenomenally more difficult is that most will hide what they don’t know – pretending to write, hovering over their papers, asking for bathroom or supply breaks, copying answers from a friend, etc. I can only get a sense of where they are if I sit and interview the student, which as you probably can guess, doesn’t happen as often as I’d like.

You might have seen students like this before, you might not – what I’m wondering is what you have done that has helped you and the kids work past it. Please give me some ideas – how can I structure my lessons, how can I use the paraprofessionals and SPED teachers better, how I can systematically identify, help, and give feedback to kids who are working way, way below grade level in a grade-level math class.  What has even been partially successful for you?

Thank you so much in advance!!




Posted by on April 20, 2014 in Uncategorized


8 responses to “Gaps

  1. reilly1041

    April 20, 2014 at 5:54 pm

    I have a wide variety of abilities in my geom class as well and it’s keeping me up at night as well! Some of them will be moving onto advanced algebra2, some to reg alg2, others to a lower version of alg2, and others will go back to Alg1. It’s a crazy mix of ability and effort.
    I can’t water down the content because 20% of the class should really be in an advanced class and they deserve an entire year of geometry. These kids quickly get new material and then are waiting for way too long while I (it’s just me!) try to get everyone else up to speed.
    Here’s my latest plan to try: uber-differentiation. I created a list of standards for the current topic, separated into basic -proficient-advanced. I have 3 versions of the quiz. If they choose the basic version of the quiz, it only covers those standards and the max grade they can get is a D (for the students who are on the verge of failing for the year, this would be a step up). The proficient version covers only the stds in basic+prof and the max grade they can get is a B.
    The adv version covers all stds, they can earn an A on it, and it should be challenging to those top kids (who really have not been challenged yet this year).
    Tomorrow, they can prepare by looking at the standards and solving problems relating to those standards.
    I’ve tried something similar before in physics and it worked well.
    At least the struggling kids can actually learn some part of the curriculum w/out being overwhelmed with problems that they will never be able to complete independently.

    • dawndup

      April 20, 2014 at 6:14 pm

      That’s an interesting idea. I have partially proficient / proficient / advanced questions on my assessments, so I wonder if I separated them out by page if it would help with the communication with the kids.
      I think that this year I have more students than I’ve ever had who are working at around a 4th grade level of mathematics. If I look back at my test data I usually get poor results from kids who were the farthest behind at the start of the year. They need to understand concepts like equations, but also need to get multiplication, and fractions. What if I had work and assessments for them that had the partially-proficient 7th grade material and the proficient/advanced 4th-5th grade material? They could still get the equivalent of a “C” and would know they’d grown…
      Still thinking.

  2. Kate Nowak

    April 20, 2014 at 6:04 pm

    I can’t get past the fact that you’re supposed to teach 2 years of CCSS math in one year. I’m sure that wasn’t your decision, but it sure makes your life much more difficult than it has to be.

    But your reality is that you have to find a way. This is one of the toughest questions for teachers, I think, how do you help kids you’re supposed to be teaching P, Q, and R when they never got L, M, and N. In Algebra 2 I’d try to build in review as needed. For example, to start an exponents unit that was supposed to start off with rational exponents, they’d have an assignment where they had to just remember how exponents basically worked.

    I’m interested to hear what others have to say!

  3. Myra Deister

    April 20, 2014 at 6:54 pm

    I agree with Kate about teaching 2 years of CCSS math in one year. It was designed for one year! That must be very difficult in itself.

    One technique that has helped me with my pre-calculus students is group quizzes. I assign the groups so that I have mixed levels in each group. I tell the students that I randomly select one student’s paper to grade for each problem and the entire group receives the same grade. The students are also informed that if they score better one the individual test, then that grade will replace the group quiz grade. The students help each other during the group quizzes. It helps some of the students and they do ask questions of each other. The students also ask me questions and I give them hints and tell them to ask their group members.

    For your equation example, have you tried setting up a chart such as

    x 3x + 5 My answer 17

    The students can plug in values for x and see how close they are to seventeen.

  4. David Wees

    April 20, 2014 at 8:16 pm

    This is a common problem in the classes in which I coach teachers, so I have a few suggestions, none of which will work perfectly well, but which may help.

    1. Make everyone’s thinking more visible, where possible.

    For example, if you use rich math tasks where the objective is to spend more time explaining your reasoning AND which are “ramped” tasks (they start below grade level and move up to grade level by the end of the task) then you have a better idea of where each kid is at. Examples:

    Also, the use of counting circles and/or number talks will benefit a lot of your students, even the ones who are more proficient (they may be proficient at the mathematics, but not at explaining themselves to others, or in using a variety of approaches). See and

    2. Decide on individual goals for your students, and find assignments which all of your students can do, but which are applicable to many different goals for different students. This means you have one assignment to explain and assign to students, and one goal for the main mathematics you want all students to learn, but you have many different areas for different students to focus their growth edge on during the assignment. It is pretty important that this assignment be approachable with a variety of different solutions, and that you circulate around the room (along with the other adults — who must be bought into this approach) to check for understanding with each of your students during the activity. See “Teaching Problems and the Problems of Teaching” for a very careful description of this process in detail.

    3. Phil Daro had a great slide about this exact issue in his presentation at NCTM. Look at slides 84 through 88 in this presentation:

    Slides 88 is especially important. Your goal with these kids isn’t so much to get all of them with the same understandings, your goal is to reduce the differences in what they understand while moving all of them forward. I know that this doesn’t actually help address this issue, but it helps me conceptualize what I’m working toward each day when I’m teaching.

  5. Dane

    April 21, 2014 at 9:53 am

    I’ve been thinking about this a lot lately and created a page with a bunch of resources ( for the topics that I have most commonly noticed. I’m trying to figure out the best way to implement the resources though. I’d love to hear how you and others might approach this. It’s a huge issue in the schools I’ve been in.

  6. dawndup

    April 21, 2014 at 7:47 pm

    I really appreciate the conversation and resources, and I will use them. It is a big issue. I believe in heterogeneous classes, I am actually coping all right with the large amount of standards in the class, and many students of mixed ability grow just fine in my classes. But I get really wrapped up in the kids who come into the grade level with pretty severe academic gaps. The problem will eat you alive if you let it.

    For today’s lesson, I identified the kids who had the most trouble on our most recent test (the ones who couldn’t even independently start the problems), and I sent them to work with a para for 30 minutes of class. I told them if they got to a point that they could solve the basic problems independently, they could work up to a “2” on the assessment. At least one kid really did fix his issues with surface area and volume, and he’ll pass the assessment just fine. The rest are still struggling, but I need to come to peace with this being a slow march and just don’t give up on them.

    Thanks for the resources and help – I will review this week and will update you all on the process…

  7. @malynmawby

    April 21, 2014 at 8:16 pm

    A lot have already contributed. It’s great that you know what students are deficient on – problems with place value is more common than you think! (depressingly so). and it rears its head in unusual ways including, for example, when learning about binary and hexadecimal systems in computing (which I now teach).

    With equations, I found teaching ‘big-picture’ style helped. Here’s a reflective post on working with equations and some links to useful resources. Also, one struggling class opened my eyes to the question of why we need to isolate x when solving for it. I thought it was obvious but for some, it wasn’t.

    With strugglers, I found that having a ‘hero’ helped and we found one in Polya (read about it here).

    Teaching strugglers has opened up my eyes on a lot of things. So much so that now, I’m doing my Masters in Special Ed. I’ve just started but I can see why some of the things I did worked – or not! I devised a ‘token system’ that cut back on the ‘hiding/escaping’ strategies, promoted a sense of community (of learners).

    Anyway, I wish you well on your endeavours. You’ve got a lot of support around you – I felt I didn’t even need to respond! But obviously, I changed my mind…because I empathise! (if nothing else, there’s that). 🙂



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