Splitting Math into Sub-Topics and Addressing Them

[CrunchyGirl]

First, I'm so thankful to Ruth's post over on the thread discussing why so many threads are math related. I felt like a light bulb went on in my head :)

 

So in theory LegoMan is finishing up SM3 and BA 3. I feel like he's doing well with computation, mental math, and math facts (memorized the multiplication table during SM2 for example). But I have concerns about:

Conceptual math

Problem solving

Reading comprehension (for math word problems, not in general)

 

Granted he's young but I'm feeling compelled to either screech to a dead stop and work on those three or start consciously breaking things up and working on different levels for each sub-topic. That is seriously way easier with LA though.

 

So...I'd love to hear ideas for addressing those three topics directly or for splitting up topics in general (dare to dream?). Starting tomorrow I'm planning to go through SM CWP2 and IP2's challenging problems and just spend the next month going through both...every single problem. I wasn't as good with using the CWP and IP until we got to SM3 but I have them on hand (today we were using CWP3 and it hit me that we have a problem).

 

Any more resources I could look at using if we get to the end of December and I'm not feeling ready to move forward and shift into SM4/BA4?

[lewelma]

Both of my kids have been really good at conceptual math and problem solving, so I have not had to teach them and would not know what to recommend. However, my younger is definitely having trouble with reading comprehension of math books.  So far this is what I have done:

 

1) Have him read the question to himself, and then out loud, and explain it to me. 

2) There are regularly word he does not know from #1, so I define them and make flash cards (because they simply never sink in - like 'quotient', 'factor', ' simplify' etc)

3)  Drill the flash cards 2x per week

4) Have him work through Life of Fred, because it is an easier text style for learning from a book. (Decimals seems to be at just the right reading comprehension level)

 

Next up is to

5) Have him read silently  the 'teaching' section of our current textbook (MEP secondary), and then have him explain it to me.  (I think reading out loud often makes understanding more difficult, because you are doing 2 things at once)

6) Have him read the solutions and learn from them in a similar way as #5.

 

You did not mention teaching a student about writing down answers, but this is the other big problem my younger is having with math.  Big problem.  He does not yet see the difference between what he is actually trying to do vs the method he uses to solve the problem (often mental math).  This is huge in word problems which is mostly what he focuses on.  So I am also currently doing a massive push on how to write down your solutions.  What *exactly* is expected in an answer.  I am making flash cards even for this.  Yesterday when asked something like what 27% of 540 was (but the problem was harder), he just started doing it in his head, and did not know to write down .27x540.  He just does not see it that way.  So we are working on what is the first line of work that must be written down, and some of these things he has to memorize.  Hopefully, that is just for now, and later it will be obvious and intuitive. 

 

Ruth in NZ

 

 

[La Texican]

I remember in school learning the phrase "of means times". I googled to see where the phrase came from. Here's the list:

http://www.cliffsnotes.com/cliffsnotes/math/our-teacher-told-us-to-look-for-clues-in-math-word-problems-what-did-she-mean

[regentrude]

I remember in school learning the phrase "of means times". I googled to see where the phrase came from. Here's the list:

http://www.cliffsnotes.com/cliffsnotes/math/our-teacher-told-us-to-look-for-clues-in-math-word-problems-what-did-she-mean

 

I would be extremely hesitant to have a student memorize this list, because these "clues" only work if the problems are formulated in a  very specific way.

 

"Of" does not have to mean "times" or multiplication: "3 of 5 blocks in the bag are red. What is the probability to pick a red block" You divide.

"Increased" does not have to mean addition. "His weight increased twofold" You multiply.

"reduced" does not simply have to mean subtraction: "The budget was reduced by a factor of 2". You divide.

"total" does not have to mean multiplication. "She spent $5 at the bakery, $10 at the store, $7 at the post office. Her total spending is.." you add.

 

A student who is drilled to watch for "clue words" and memorizes the "action" that goes with the word will have trouble.

[quark]

So in theory LegoMan is finishing up SM3 and BA 3. I feel like he's doing well with computation, mental math, and math facts (memorized the multiplication table during SM2 for example). But I have concerns about:

Conceptual math

Problem solving

Reading comprehension (for math word problems, not in general)

 

Granted he's young but I'm feeling compelled to either screech to a dead stop and work on those three or start consciously breaking things up and working on different levels for each sub-topic. That is seriously way easier with LA though.

 

So...I'd love to hear ideas for addressing those three topics directly or for splitting up topics in general (dare to dream?). Starting tomorrow I'm planning to go through SM CWP2 and IP2's challenging problems and just spend the next month going through both...every single problem. I wasn't as good with using the CWP and IP until we got to SM3 but I have them on hand (today we were using CWP3 and it hit me that we have a problem).

 

Any more resources I could look at using if we get to the end of December and I'm not feeling ready to move forward and shift into SM4/BA4?

You don't have to come to a dead stop. What we did was to break math up into 2 or 3 and sometimes 4 different strands in a day, and spent anything from 10-40 minutes per strand depending on how much time was needed and how much interest kiddo had at that particular moment of that particular day. We also made math as fun as possible so he did quite a bit of it on his own.

 

One strand was always above level conceptual stuff either using curriculum meant for older grades or living math books. We sometimes had another strand that touched on mathematicians (again living math style, but through documentaries as well as books). One more strand (the shortest one among all strands) to practice computation skills. Then we did a problem solving strand that included understanding word problems. We addressed that with the question "what exactly is this problem about?" and we drew lots of pictures (once, we did a "how many legs?" sort of problem by drawing out all the cats and dogs that the problem stipulated...it was fun lol), underlined key words in the word problems, or actually carried out reasonably accurate word problem experiments or left them for another day if we couldn't solve them immediately. One time, we actually tossed coins for almost an hour and a half!

 

How much time are you willing to spend on math? For me, the priority wasn't so much an extremely well-rounded kid. It was to have a kid who loved math so I didn't feel very bad about ditching formal history or language arts to achieve this.

 

Three books (apart from the regular curriculum) that we liked at that age:

Good Questions for Math Teaching

The MOEMS book by Lenchner (Volume 1)

Family Math

 

ETA: just in case anyone was wondering, the how many legs problem was a cats, dogs + chickens problem lol. I can't remember which book it was from but it was pretty fun for him at that age.

[acurtis75]

You don't have to come to a dead stop. What we did was to break math up into 2 or 3 and sometimes 4 different strands in a day, and spent anything from 10-40 minutes per strand depending on how much time was needed and how much interest kiddo had at that particular moment of that particular day. We also made math as fun as possible so he did quite a bit of it on his own.

 

One strand was always above level conceptual stuff either using curriculum meant for older grades or living math books. We sometimes had another strand that touched on mathematicians (again living math style, but through documentaries as well as books). One more strand (the shortest one among all strands) to practice computation skills. Then we did a problem solving strand that included understanding word problems. We addressed that with the question "what exactly is this problem about?" and we drew lots of pictures (once, we did a "how many legs?" sort of problem by drawing out all the cats and dogs that the problem stipulated...it was fun lol), underlined key words in the word problems, or actually carried out reasonably accurate word problem experiments or left them for another day if we couldn't solve them immediately. One time, we actually tossed coins for almost an hour and a half!

 

How much time are you willing to spend on math? For me, the priority wasn't so much an extremely well-rounded kid. It was to have a kid who loved math so I didn't feel very bad about ditching formal history or language arts to achieve this.

 

Three books (apart from the regular curriculum) that we liked at that age:

Good Questions for Math Teaching

The MOEMS book by Lenchner (Volume 1)

Family Math

 

 

Very helpful suggestions. I'm thinking we're going to move to a similar strategy

[EndOfOrdinary]

When my son was beginning arithmetic studies (basic add, subtract, multiply, divide), I would have him do a problem, and then tell me how he did it, and why he did it that way.  Then I'd ask him to tell me another way he could do it.  For each problem he had to give at least 3 different ways he could have solved it. 

 

That would hit all three on your list, and in general show you whether he "gets it" or not.

 

As problem solving as has advanced, we still discuss this area of math (no such thing as one right way), but it becomes a little bit more complicated as the problems get more complicated.