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Next year I volunteered to lead the math class for a group of 6th graders (ages 11 - 12). Here are the pertinent details:

  • About 5 - 8 (U.S.) students, for about 45 minutes, 3 days a week (they'll meet with the regular teacher the other 2).
  • These are the "advanced" students. This year, as 5th graders, they are in the 6th grade math class. The school (small, private) only goes up to 6th grade, so taking math with the 7th graders isn't really an option.
  • All (or almost all) of them have completed Khan Academy's 6th grade math curriculum, and most have already made significant progress through Khan Academy's 7th grade math curriculum. (This is probably what they'll continue to work on during the two "off" days.)
  • In addition to Khan (mainly as homework), their current teacher uses a lot of inquiry-based and group-work approaches in the classroom, so they should already be relatively comfortable with loosely structured lessons that involve exploration. In general the school uses the Singapore/Eureka Math curriculum.
  • The minimal goal would be to prepare these students to enter Algebra 1 in their 7th grade. But since a lot of them are close already, it seems like an opportunity to do more.
  • I am a college math professor, but I don't have any Math-Ed experience/training at this level.
  • Yes, my son is one of the kids. And if my daughter continues her trajectory, I'll be doing this again in 2 years.

So here are the main questions: What would you do? What topics would you cover? Is there a collection/book of interesting problems/topics we could work through? Any other advice?

A couple of notes:

  • While one or two ideas of what to do for a day or week are appreciated, I'm more concerned about having/creating enough material to last 3 days a week for the whole year. I'm looking for a larger resource or coherent theme that can generate a wealth of math topics.

  • One idea that's been suggested by a colleague is prepping for and doing various math competitions for this age group. Most of them do compete on the school's math team. But, prep specifically in this direction is usually considered an after-school activity and probably wouldn't be appropriate. Perhaps, though, the topics for such competitions might be a good starting place for ideas.

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  • $\begingroup$ Perhap not a full answer, but Art of Problem Solving (AoPS) is a program focused on younger gifted children. I've used their text book at some summer camps for 7th-8th graders. For your age group, they have Pre-Algebra, Algebra I, Problem Solving Basics. For a topic not really shown in 'regular high school,' they also have a Intro to Number Theory book. The books draw questions from AMC, and AMIE style competitions $\endgroup$ – ruferd May 1 at 15:25
  • $\begingroup$ There are likely some math educators at your university that can help, just a thought... $\endgroup$ – jfkoehler May 9 at 21:50
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Beast Academy is a new(ish) curriculum, meant for math-loving students, from the Art of Problem Solving folks. It has 4 levels for each 'grade' (from 2nd to 5th), and each level has a Guidebook and a Practice book. But don't believe the grade levels, they can be challenging for much older students.

Although your students are advanced 6th graders, I believe the level 5 will still be challenging, and Beast Academy is a lot of fun. You can use the books or do it online. If you do it online, they can do lower levels too.

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Basic content:

If you expect them to get into Algebra 1 in 7th grade, you need to cover pre-algebra,now. This is essentially one equation with one unknown. I would make sure you cover this very solidly as there become a lot of problems later on when kids lack the ability to manipulate sides of an equality. It is important that they get some solid practice with mechanically "doing the same thing to both sides of the equation" E.g. adding to both sides, not "throwing it over from one side to another and then reversing the sign". You need to take the time and give them lots of drill.

Assuming too much brains/knowledge:

In general, you need to be cautious about assuming your level of knowledge or even brains in kids with much less experience and whose brains are not physically mature. I see this problem all the time (expert blindness). I'm not saying not to progress the kids. Just to be sensitive to your likely blind spot and to watch for it.

Learning what you will teach:

It is also good that you recognize your level of ignorance of the content. Math prof is fine, but you need to get yourself up to speed on the content for this course. A question on SE is not adequate to educate yourself. IOW, you need more detail than my first para here. But at least you recognize your gap.

Go get some competing textbooks and read them (maybe outline them in topics covered, not saying read word for word) so that you have some basic feel for typical pre-algebra content and how much it may vary.

In addition to learning what topics are covered, you should practice a homework problem or few; work through some of the examples, etc. Don't just assume you are smartypants math prof. Make sure you can do all the manipulations. And also, it puts you in some "walking in their moccasins" so that you get the feel of what the students must learn. After all, your own experience will be in dim past.

In addition, glance over the content in the year before pre-algebra (I can't even recall what that was) and of algebra itself. This is so that you have sufficient battlespace situational awareness that you don't give the kids a gap. For the year before and after, I think just looking at their past year book and likely next year book is sufficient (don't need to look at competing texts). You don't need to work any problems here either.

Once you have done all that (maybe 2-3 long evenings), you will be able to at least converse about the content with some baseline. At that point, I recommend interviewing a couple teachers (you will have generated some questions from the task I gave you). Go over content coverage, likely hard/easy parts, and ask for a few tricks. Do this with real teachers face to face.

This site is mostly junior college pre/calculus teachers. It has weak coverage of K-12. There are also blogs, forums etc. in the greater web (not SE) where you have middle school teachers. But I would try for some face to face. But at least an electronic exchange with them will be better than at MESE. In addition, do your "task" first, rather than reaching out before you have educated yourself.

Level

Note, that I have a little confusion as to their level. In the dark ages, Algebra 1 was stereotypically 9th grade. Pre-algebra was 8th. Kids who were one year advanced covered Algebra 1 in 8th. Of course these kids may be a couple years ahead. And there has been some movement to push 8th grade algebra for all (a failure). But certainly the most advanced kids may be able to handle Algebra in 7th. The point I am making is just to make sure that you know their real level (this is a key thing to assess) and don't miss out on some grade 5-8 content that they need to be getting.

Offspring

Treat your boy similarly to the other students (no familiarity or references to family/home life) and ask him to call you Mr. Umptifratz. Don't be harsh with him. But just have a normal teacher/student mode of engagement. No favoritism or the converse. Talk to him ahead of time, so he understands the need for this and is actively supporting this policy.

Class time

Use a book/workbook. Do not just invent what you want to talk about (same applies for college courses...just pick a book as a scaffold...it may not be perfect but nothing is, including your mishmash).

Try to keep it active, with some games, drill, solve and pass papers, etc. But do not make it math contest focused because then when do they learn basic content. Teach a standard pre-algebra course.

Mesh with other 2 days

This is actually kind of a puzzle to me. How do they learn all the stuff they need for her class, with less time. how does your stuff work, when they don't have full year of her stuff. Etc. But at least we know it's a puzzle. Baseline, I assume that she will be covering stuff from standard 6th or 7th (whatever that is, advanced arithmetic?) and you will cover pre-algebra, which is stereotypically 8th? But I am not sure if this is correct.

You should at a minimum review what content will be covered in their regular course, so you know it. I guess if the class is structured so that they just spend a lot of time drilling arithmetic, perhaps your smart kids can just do with less drill (there) and simultaneously learn pre-algebra on 3 days per week. Possible maybe. But keep your finger on the pulse and see how things are going. Ideally the other teach covers major principles on the 2 days she has the kids and uses the other 3 for more practice. (I imagine she has a bigger class and you are selecting out the top kids for a few days/week?)

She also may know a lot about basic middle school math, so you should consult her as one of your face to face interviews. (Not just how you mesh together, but she may have advice for you on your own 3 days/week. She is an SME.) After doing the "task" so you are educated enough to ask better questions and learn more.

This whole thing sounds tricky in and of itself, so it is important not to have any rivalry with the other teach (one more straw on the donkey). Be down to earth and talk to her as a colleague and win her over.

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    $\begingroup$ This response contains many assertions. Since you have used a new guest account with no associated information, it is difficult to discern whether these assertions are based on actual practice or research or experience or second-hand advice or [etc]. So: Could you give some indication as to the source of your ideas? Are/were you a practicing K-12 math teacher? You mention MESE has "weak coverage of K-12" and, irrespective of whether this is true, I am wondering what your advanced-6th-grader advice is based upon. $\endgroup$ – Benjamin Dickman May 1 at 1:15
  • $\begingroup$ I would really like to upvote this, but as @BenjaminDickman wrote above, it is unclear what the information is based on. $\endgroup$ – Tommi Brander May 10 at 9:03

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