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I've been assigning algebra textbook and worksheet problems (from the publishers and my own) that look like this:

Simplify the following expressions.

  1. $x^{- 3} y^2$
  2. $c^2 d^{-5}$
  3. $\dfrac{x^{-2}}{y^{-4}}$
  4. $\dfrac{5x^2}{y^{-2}}$

I don't feel that my students (who come from low income families) are getting the materials. In three weeks the district wants to know if I am teaching the students this content. What is ridiculous is their suggestion to cover "negative integer exponents in 1 day" followed by "rules of exponents in 3 days." The next week they are theoretically supposed to be on "quadratic equations." I want to laugh at the clueless people who made this scheduling and question whether they've ever taught at an inner city school. How do I teach this material in a culturally relevant and engaging way? What teaching practices and materials could I use? I don't know what kind of curriculum is out there for me to use, this is so challenging! I need student engagement and comprehension of the materials.

When I call out random students what happens next at each step I get resentful looks. I've tried appealing to their number sense intuition by looking at patterns, but it only works for some not all students. Obviously something is not working.

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My experience tutoring is that the kids are weak on the material from the year before and the year before that, but nobody is willing to admit that. I tried to tutor my neighbor's middle school kid, for free I might add. Middle school algebra, distributive law. He had trouble with adding and multiplying whole numbers by hand. You cannot show how algebra encapsulates patterns that work for all integers, if they cannot manipulate integers in the first place. Sigh. –  Will Jagy Jan 11 at 1:49
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I'm sure you're already familiar with it, but "Stand and Deliver" was a great movie and touched on this topic a bit. Some of the teaching techniques that are most effective transcend the material, but also require a measure of teacher-student rapport. That's so much platitude to say that you have a difficult job, but it is definitely worth the effort! –  abiessu Jan 11 at 1:58
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@WillJagy you are 100% correct -- they can't do algebra because they don't know arithmetic and the problem does not stop there. I also tutored a student who was failing in algebra, and I had to back up all the way to multiplication before we could start moving forward. I did make her put away her calculator, even for algebra. Students in college classes have the same pattern -- I was trying to help one with multivariable calculus, but he didn't know h.s. geometry. –  Betty Mock Jan 11 at 2:05
    
Is it practical to get them working together in small groups? A lot of embarrassment is avoiding by working in small groups. You could assign several small groups different problems, and have one person in the group present what the group has found. If someone is wrong, then it's a group error, and doesn't fall on one person. People can be paralyzed by fear and peer issues. I suspect this may not work so well for you at this level, but it does at higher levels. –  T.A.E. Jan 11 at 6:16
    
I recommend asking this question at mathematicsteachingcommunity.math.uga.edu, where I feel there are more qualified people to answer it. –  Joel Reyes Noche Jan 12 at 2:23

2 Answers 2

I completely believe that your kids do not understand x and y, let alone exponents, let alone negative exponents. And the amount of time it takes to make up this ground is considerable. Of course you can't do it in the time allowed.

However, in terms of getting more relevant, one thing they all like is sports. You might poll them about which sports engage them the most (at least they will pay attention while you do that). Say it is basketball. Suppose someone needs to take 1000 practice free throws. Suppose the first day they take 5 throws, the 2nd day they double that, the 3rd day they double down again, etc? How many days to get to 1000 free throws? (And how much better will they be after that? Maybe the needed number is 5000 or 10,000 -- what do they think?). I'm sure you can invent many other problems. Perhaps negative exponents can be expressed as penalties?

Another thing that interests them is money. You might talk about scams. We all get scammed, even those of us who know a lot of math, if only because the worst scammers manage to lobby their way into laws that enable or even require the scams. It is easier here to discuss percentages than exponents, but I'll bet you can imagine some financial scenarios, legitimate or otherwise.

I've passed along your question to a friend who has substantial experience teaching math to inner city students. If she has any suggestions, she or I will enter them here.

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As promised, I asked this question to someone more knowledgeable, and here is the answer:

I taught math for 6 years in inner-city schools and definitely feel your pain! IMO the issues are systemic and way outside the scope or control of the individual teacher. All you can do is to do what you must to protect your career interests while giving the best instruction you can to your students. It's unfortunate that this presents a conflict but sometimes that's the reality.

Depending on how strict your environment is, you may be able to spend a little more time where it's needed and find something to skip later, and/or teach the pre-skills that the kids don't know while aiming for the assigned topic. If anyone asks you are "addressing the common core standards" while "using a spiral curriculum approach to reinforce pre-skills," "differentiating your instruction," "providing accommodations to support all learners in your classroom," etc..

Kids who have struggled with math often assume that they will never do anything correctly and have shut down. However my experience is that even if they're putting up a front of apathy, they do care and appreciate chances to be successful. They benefit from lots of small opportunities to engage, learn, and succeed. I've found these strategies helpful:

Try a daily warm-up problem that focuses on pre-skills for that day's lessons or on a past topic that they didn't get. Give them credit for completing this.

Break procedures into small steps and give written descriptions of each in as simple language as possible. I like to write descriptions off to the side right next to each step of the math.

You can spend lots of time on sub steps and even if you cannot reach full mastery for all students in the allotted time frame, you are teaching what you were told to teach and they are learning something. For example, if your topic is solving quadratic equations, you might have mini-lessons on any of the following:

Writing factor lists of the constant terms. So they're practicing factoring of numbers and multiplication. Find factor pairs that combine to the middle term (for leading coefficients of 1). Now they're practicing combining negative and positive numbers. Give them the factorizations and have them set each factor to zero and solve. Now they're working on solving two step equations.

Try to talk for no more than 5 minutes at a time as much as possible. Do one or two steps of an example, and then have them repeat those steps on a parallel problem. You can walk around and give some individual attention to those who need it. (This is a "formative assessment" btw.)

You can also put them in small groups so you can help a few kids at a time. You might want to carry around a small white board for this. You can try "grouping heterogeneously" by grouping a kid who gets it with one or two who don't.

Try writing and distributing your your notes in advance but leave blanks for them to fill in. This helps them tune in as they'e looking for what goes in each blank. Again, I would award credit.

When you ask questions, start with really simple requests that you know for sure the particular kid can handle. i.e. simple arithmetic or reading the next step in the notes out loud. Give enthusiastic praise or thanks. What you're really acknowledging is the kid's contribution and engagement. And you can build to harder questions as the kids' trust and confidence grows.

Another way to minimize lecture time is activities that aim to have them discover properties for themselves. For instance, have them solve some problems like $x^3*x^4$ by expanding out and counting the x's. Hopefully after their hand cramps up from all the writing they'll figure out the shortcut!

Make two versions of each assessment by changing the numbers in the problems and give one as practice the day before. This way the kids will know exactly what to expect and what they will need to do.

You may want to give them a quiz on each topic that provides written instructions for each step. Then even if they're not quite getting the big picture, they are learning some of the pre-skills necessary and getting rewarded for this.

Give credit for lots of little things just by walking around and checking, maybe have a daily class participation grade. Don't take every little thing home or you'll drive yourself nuts. Kids like this kind of instantaneous reward anyway.

Hope this helps!!!

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