I'm working one-on-one with a student who is part of a sponsored refugee family. He's bright and a good learner, but has had a lot of interruptions to his education. No indication of any learning disability, and language is an issue, but not a challenging one.

The family is hoping to get him working at grade level (grade 9, from about a grade 5 level) as soon as possible.

My question is this: is it a better strategy to:

  1. go full-tilt on one topic (for example, fractions) from start to finish, then tackle the next topic, and the next, and so on

OR

  1. follow standard curricula - cover all of grade 5, then 6, etc.

I realize this is a bit open-ended and opinion based, but I'm looking for suggestions based on people's experience and best practice recommendations.

  • My guess would be to use whatever materials are convenient, meaning books with problems and answers. If you can find a "review" book, that might be the best approach in that it will be a bit slimmed down. See here: google.com/… But you could use standard grade books and just try to move through the stuff with some sort of skimming or selection process. You will have to see how he responds to see how fast you can go but I would hold some hope since age-related intelligence gains occur for kids. – guest Dec 3 at 18:43
  • In my opinion, there is very little happening in MS in terms of math: algebra starts in 9th grade in most states, and most necessary prerequisites for algebra are taught by the end of elementary school. Considering that American high-schoolers use graphing calculator to solve a simple system of two linear equations, he is not much behind. Just make sure he feels at ease doing standard arithmetic operations, knows times table, can do stacked addition/multiplication, can perform mental computations using distributive property, knows fractions, correctly applies sign when removing parentheses... – Rusty Core Dec 3 at 20:23
  • 2
    "standard curricula" - that's a good one. – Rusty Core Dec 3 at 20:26
  • Thanks - appreciate the thoughts! – Stidgeon Dec 5 at 1:12

Do you have a favorite curriculum? If you don't, and he likes math, he might enjoy the Beast Academy curriculum. Be aware that their level 3 feels like it's for older than 3rd grade (etc). They have books for grades 2 through 5, which I think is more like grades 3 through 8. Definitely all that's needed before algebra.

If I were working with him, I'd try to structure the time in a way that encourages interest. Which parts does he find most interesting? What motivates him in math? Beast has 12 chapters per grade level, and I don't think you have to do them in order.

If you're not using something that goes by grade level, just keep it connected from one session to the next, and focus on what he can figure out. (I tutored a very mathematically inclined boy for a few years. He did multi-digit multiplication totally backwards from the standard algorithm. It worked for us.)

  • I suppose, the comic strip look of these books is an unfortunate result of many kids being unable to read after completing 1st grade, possibly because of whole language snake oil. So the math books do a second job of teaching reading, with colloquial language to boot. Another strike against them in my view is that they are made in the customary for the U.S. workbook format, not proper textbooks. Anything that requires to fill in the blanks is an immediate turn off to me. The right way is a textbook and a blank notebook, preferably squared. Students must copy and complete the exercises in full. – Rusty Core Dec 6 at 17:50
  • Sounds like you have some strong opinions. The folks who made this curriculum have worked for many years with gifted kids who enter the math contests, at national and international levels. They know what kids enjoy, and are interested in sucking kids in. It is not about problems with reading. I have no idea why you think a "proper textbook" is important for elementary math. – Sue VanHattum Dec 7 at 21:18
  • I do not discount the technical correctness or hallmarks of the exercises, but getting through the pictures and banter will get boring quickly. Cute pictures only slow down the kids who are really interested in math. But maybe I am wrong, this is elementary curriculum after all. Also, I hate workbooks and worksheets no matter how interesting the exercises are. – Rusty Core Dec 7 at 22:14

If you have the luxury of ignoring what's going on in math class in school, do so.

If you want a student to make big progress, you need to focus on common bottlenecks that span multiple grades, not the entire content of each individual grade. Students rarely cry or give up on their intellect because they don't understand volume. Many students will cry or give up on their intellect because they don't understand fractions.

So, focus exclusively on:

  • Whole number sense. That's place value, the operations, relationships between the operations, estimates, math facts (e.g. times table such as $9 \times 8=72 $), and extended math facts ($900\times80 = 72000)$.
  • Extended whole number sense to fractional sense. Ensure the student can place any set of any rational number on a number line. Make sure they can intelligently compare and contrast whole number arithmetic and fractional arithmetic.
  • Introductory algebra. That means solving and checking simple linear equations (e.g. $5x+2=3x+28$), then using that knowledge to, say, determine, check, and use formulae for Visual Patterns, or other simple word problems. Representing relationships in graphs, tables, equations, words, drawings, etc.
  • "extended math facts (900×80=72000)" - could you elaborate what do you mean by "extended math fact"? To me, your example is about place value, commutativity and associativity: 9*100*8*10 = 9*8*100*10 = 72*1000 = 72000. – Rusty Core Dec 5 at 20:05
  • That's pretty much what extended math facts are. Eventually, when the student takes on rational number arithmetic, they will more easily understand that 70% of 9 is (0.7)(9) which is an extended fact of (7)(9) = 63, 70% of 9 is 6.3. – WeCanLearnAnything Dec 7 at 1:14
  • Interesting. I could not find a definition of "extended math facts". Maybe I am reading the word "fact" not the way math teachers mean it , but "(0.7)(9) which is an extended fact of (7)(9)" rubs me the wrong way. Anyway, thanks. – Rusty Core Dec 7 at 3:07

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