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Long term prep for math competitions

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My son is in grade 3. I think he will enjoy math competitions. So far we’ve done MK. We don’t live closer to any test prep centers. I’d love to incorporate a small amount of test prep into our week in the hopes of keeping him on track to do well on the AMC test in the future. I need a plan.

 

My daughter is in 9th grade and took the AMC 10 for the first time. She didn’t do well. While I’m not surprised because so much prep often goes into these tests, I’m hoping not to make the same mistakes with my younger son.

 

So if you don’t live in a major metro, how do you prepare to do well nationally on these math tests?

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I'd get books like this one.  https://www.amazon.com/Contest-Problems-Division-Richard-Kalman/dp/1882144120?SubscriptionId=AKIAILSHYYTFIVPWUY6Q&tag=duckduckgo-d-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=1882144120 This books has past tests to Math olympiads.

 

Math counts provide free math club materials (so i'm told).  https://www.mathcounts.org/

 

Join any math club or math circle in the area. 

 

There area lot of math organizations out there.  Math Kangaroo, mathnasium (although they may or may not have contests), trimathlon, math olympiad, math counts, math circles and I'm sure there's more!  I think if you google math circle that they provide free materials to start a math circle.

 

It's not easy.  Hope this helps.  Will be following.  Can always learn more!

 

The mom of Let's Play Math (Denise Gaskins) has a link and blog(?) about math circle and I think how to set one up. 

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If you just  go on the AoPS sequence, the textbooks will continue to thread in increasingly difficult competitive math problems which should serve you well by the time your son starts trying the AMC8. I don't  think you necessarily need to do anything more yet just keep moving through the curriculum. When you've reached PA/Algebra it might be time to reevaluate assuming there is still interest.

 

But Math Circles are great anyway even if you're not competitive and if you can find or start one in your area that would certainly work well.  I think finding math peers and cultivating a sense of joy/passion is just as important in the long run.

 

[Got the wrong poster originally]

Edited by seaben
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Art of Problem Solving has a two volume set of books that is focused on problem solving and there is also the competition math for middle school book by Jason Batterson that is recommended by AOPS.

 

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I brought about half of the math club I was leading in 5th grade to try it out for the first time (they were all doing a 7th grade curriculum in school so it was reasonable from a leveling perspective). It's a bit tricky since it must be administered by a teacher in a school setting, That year  I lucked out and had a friend arranging it with extra test packets.  So assuming you can find space I'd say after reaching the 6th grade curriculum.  You can always try a practice version and see if you're scoring high enough for it to be a positive experience and waiting until actual 6th grade is perfectly fine too.

 

 

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Our first math competition was the Primary Maths Challenge in the UK. http://www.primarymathschallenge.org.uk/ Similar to Math Kangaroo I believe. Sample tests are online so throw those into the prep pile. ;)

 

Looking back I think much of my kids success in competition math can be attributed to a daily concentration on story problems. We always did a page from Singapore’s Challenging Word Problems. They are challenging, truly, so we generally did the book behind the level of Singapore we were actually in. The aim was to solve whatever the problems of the day independently. We also had the Abeka math sequence which is strong in story problems. Sometimes we just did the story problems.

 

As soon as possible start playing on Alcumus.

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The test prep books from AOPS say to wait until after algebra. We are purposely trying to go slow with subject advancement because I fell into the calculus trap with my oldest, but I don’t want to hold off test prep at all. Have any of you tried to AOPS test prep earlier?

 

Pretty much I want someone to spell out a sequence from 4th-12th grade that tells me where to put all of the non traditional math and the test prep. Any takers? I currently have a 9th header in honors precalc (with the highest grade in her class), with great SAT scores, but an abysmal AMC 10 score. I’m realizing that I didn’t go about it correctly with her (not enough test prep and discreet math) and I don’t want to make the same mistakes twice. So does anyone have a long term plan, you’d recommend for the 3rd grader?

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The test prep books from AOPS say to wait until after algebra. We are purposely trying to go slow with subject advancement because I fell into the calculus trap with my oldest, but I don’t want to hold off test prep at all. Have any of you tried to AOPS test prep earlier?

 

Pretty much I want someone to spell out a sequence from 4th-12th grade that tells me where to put all of the non traditional math and the test prep. Any takers? I currently have a 9th header in honors precalc (with the highest grade in her class), with great SAT scores, but an abysmal AMC 10 score. I’m realizing that I didn’t go about it correctly with her (not enough test prep and discreet math) and I don’t want to make the same mistakes twice. So does anyone have a long term plan, you’d recommend for the 3rd grader?

 

I'll bite.  This is basically what we did.  You can pick and choose what works for you.  

 

Start with the old MOEMS linked by a PP.  Begin with elementary level exams,  When your student is routinely getting 4-5 correct, then move up to middle school MOEMS.   

 

When middle school MOEMS gets to be too easy (maybe in 5th or 6th grade?) level up to AMC 8's.  AoPS has all the exams on their wiki, with complete solutions for free.  At the same time, take a look at MathCounts.  They post the most recent exams for free on their website, and old exams are for sale at their store.  Look to join a homeschooled team in your area, and if there isn't one, then start one yourself.  (More on this later.)  For fun your student can take the AoPS AMC8/MathCounts prep class.  

 

By 8th grade they can also start practicing AMC 10s, from the same AoPS link as above.  

 

All throughout, your student should be using AoPS curriculum from Beast Academy continuing on in PreAlgebra and on from there.  

 

While you are at it, you'll probably want to build a community of other math lovers.  Do the MOEMS exams together as a group.  Students can complete an exam together in class or as homework.  Together they can take turns discussing their solutions and learning from each other.  With any luck, you'll be cultivating new friendships and more importantly, new members of your MathCounts team, lol!  

 

And don't be too hard on yourself wrt your dd and her performance on the AMC 10s.  Being successful on these exams takes practice, and it isn't too late for her to build up those skills.  Though it is much easier and less discouraging if you start early.  Good luck!  

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My ds is a math competition kid, and will be representing NZ at the IMO for the third time this July.  My son's path is unusual, but this is approximately what he did:

 

4th: AoPS intro algebra

5th: AoPS intro algebra

6th: AoPS intro algebra

7th: AoPS intro geometry, intro number theory, intro combinatorics 

8th: UKMT (intermediate) geometry, AoPS intermediate number theory, intermediate algebra

9th: AoPS intermediate combinatorics, precalculus, olympiad geometry

10th: Calculus, WOOT

 

What is clear from this list is that he learned all of his problem solving skills through the Intro Algebra series.  He did every single problem in the text, with no hints and no help from me. He struggled for hours on some of the problems, and he would work over the period of days for others. He worked on the book for 2 hours a day year round for close to 3 years with no help.  In all honesty, I started to worry that he was just moving so slowly, that he would never get through a standard high school sequence of math at the rate he was moving.  But it was the *problem solving* that he was learning through Art of Problem Solving. The content was easy. The exams are all about problem solving, especially the proof based ones like the USAMTS exam.  It is the problem solving that is the difference between a competition and the SAT.

 

Happy to answer questions,

 

Ruth in NZ 

 

 

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Ruth in NZ,

 

I  :wub: that you took the time to type out what your son did. I feel reassured now. I have from time to time been second guessing the meandering path we are on right now. I am doing very little instruction and allowing my son to work through JA on his own and stepping in to help guide only when he gets stuck. My plan is to let pre-A (JA, AOPS and other math resources) and algebra (Jacobs and AOPS) take as long as it takes to work through with no rush to complete it in any set time frame.  

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Ruth and daijobu, thank you so much for “biting.†This is super, super helpful.

I’m trying to figure out how to start a math team, but once homeschooling expands beyond the instruction in my home, I get intimidated.

 

Ruth, I have a couple of questions. Has your son surpassed your math abilities? If so, when did that happen? When he is stumped, to whom does he turn? Also did he embrace the two hours a day of work even at the youngest age? Did you split the time up within the day or work a solid block? Was he determined to finish the problems on his own or did you just force the point? Also did you do pre-algebra with AOPS?

 

Thanks for all your help, moms!

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Here's an old getting started with a Math Club post I put together: http://mymathclub.blogspot.com/p/how-to-get-started.html.  I think when starting its important to clarify your goals. There is an interesting quiz I linked to from natural math that was good that way. Once decided upon then yes advertise based on your vision.

 

Beyond that its also good to know your potential target audience. Third grade is still pretty young for anything intense and you're less likely to find others who want to go that way.  Also after working with a lot of 4th and 5th graders, I'm going to throw it out there that on average they don't have long attention spans for challenging work. There are outliers but I'd plan on no more than 20-30 minutes of focus from a group as a whole at the earliest ages and its equally important to think about making it fun at the same time so kids keep coming back.

 

[Also one other thing to keep in mind about AMC10 or any other contest is that there is a large processing speed component to them. There is very limited time to do the questions and you have to either think quickly or quickly recognize the problem structure to even finish at all. This doesn't mirror mathematics in the real world.  Its often useful to separate whether given  unlimited time you can solve the problems from the practice tests (and learn from them) vs. can you solve them in 75 minutes etc.  While practice can improve performance, you may find it plateaus out just due to that processing speed constraint.  Its usually good to be clear eyed about  this and focus on goals that serve you long term if you're not lucky enough to be "super fast".]

Edited by seaben
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Has your son surpassed your math abilities?

Haha. That would be a definite yes!!

 

If so, when did that happen?

At the age of 12. I did a massive push with him in 7th grade (see x-post below) to prepare him for the camp-selection problems (like the USAMTS). That year he got into the the IMO camp and that was the last year that I helped him in any way at all. I am a math tutor up to calculus, but as I said in my earlier post, the content is easy; its the problem solving that I can't help him with.

 

When he is stumped, to whom does he turn?

We had him start taking AoPS classes, so when he was stumped, he asked the other kids or the instructors for hints. Some of the kids organized a online study time so they could work together to solve the challengers. I looked for a math mentor, and found none. There was no club in my city.

 

Also did he embrace the two hours a day of work even at the youngest age? Did you split the time up within the day or work a solid block?

He did. But I required him to stop if there were tears. Back then he was scarily focused on math. And over the years, he would have spent way more on math if I had allowed it. As I remember, he did it all in one block, but I was not in the room so not sure. It was his choice to do that much. I would never have required more than 45 minutes in primary/middle school, and an hour a day in high school.

 

Was he determined to finish the problems on his own or did you just force the point?

He was determined. Teaching was cheating in his eyes. I never would have forced him to work on crazy hard problem solving if he had not wanted to. But there have been a lot of discussions on this board on how to teach, guide, facilitate AoPS so that problem solving can be enjoyable for kids who find it tough to learn on their own. Maybe someone can link you to these threads.

 

Also did you do pre-algebra with AOPS?

There was no PreA when ds went through AoPS. The first 5 chapters of Intro Algebra acted like his preA and took him a full year to complete. Now, most people say that if you have done PreA, the first 5 chapters are crazy easy. The general feeling on the board has been that to do it well, PreA+IntroA will take 3 years in total. My ds just did 3 years of introA.

 

++++++

 

 

This post from 5 years ago discusses how I taught him in the last year that I could help. Notice that I was not a teacher of content.  In fact, I was co-learning, not actually teaching, as I did not have the problem solving knowledge. We were using the Art and Craft of Problem Solving (NOT an AoPS book).

 

X-Post from 2013!

Yes, that is the book. My son is 12. We are currently able to understand only 30% of it. It is a University math majors textbook. The author states that you should read each chapter until you don't understand, then move to the next chapter. When you finish the first pass of the book, you start again. This approach allows you to work at your personal level in each topic, and allows your ability in all topics and problem solving to be increased concurrently.

 

There is NO way that my son could work with this book independently. We work on each problem together and then read through the proofs together. If the problem is easier, we each separately investigate it and write up a formal proof and then compare. My goal is to find ideas in each problem that will be generalizable to other problems. We keep a list, and I quiz him every day about the different generalizable skills we have learned. For example, what kinds of problems are would likely be helped by the extreme principal? or what kind of problems suggest a proof by induction? How can you recognize parity in geometry problems? These types of questions are not directly answered in the text -- they are more of a way for us to really internalize what we are reading and categorize all the ideas. Plus, it helps us review esoteric ideas by recalling specific problems that reflect them. We've decided that if there are 20 different tactics that are possible, and we can recognize that 4 are good candidates for a certain problem, we can try those four. If one works, great, if none work, then at least we have gotten our hands dirty and have a much better understanding of the problem and can go from there.

 

To help in proof writing, I drill him on specific phrases like "This specific case is generalizable because the only special feature of 11 that we used is that it is odd." (yes, I am memorizing all this too, so that just popped out of my brain). This drill has really helped him not only with the language of math, but also helped him realize different approaches he could use to prove a conjecture. For example, the above case showed us that you can use an example as your proof in many cases of parity. This is very important to know, because most proofs do not allow this. Our overall goal is to get as many tools in our tool box as we can, and then remember what tools we have in there!

 

All this is really working. I cannot believe how far we have come in 2 months.

 

I told someone last week that I could only go through this process once because what I am giving my son is not a knowledgeable tutor, but rather a skilled learner who is at his exact level in math. If I ever go through this material again with a student, I would be much much more knowledgeable and I would loose the confusion that has been so critical in helping him battle through this material. What I am finding is that because I don't know the answers and I cannot teach him how to do it, I am instead teaching him how to learn problem solving -- what questions to ask, what answer to hunt for, how to compare problems, how to really interact with this material. No tutor who knows the material well could do this as well as I can, because once you have the knowledge, it would be virtually impossible to relive the confusion.

 

But then I realized that because my memory is so shaky, I could probably do it one more time.  :001_smile:

 

 

Edited by lewelma

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[Also one other thing to keep in mind about AMC10 or any other contest is that there is a large processing speed component to them. There is very limited time to do the questions and you have to either think quickly or quickly recognize the problem structure to even finish at all. This doesn't mirror mathematics in the real world.  Its often useful to separate whether given  unlimited time you can solve the problems from the practice tests (and learn from them) vs. can you solve them in 75 minutes etc.  While practice can improve performance, you may find it plateaus out just due to that processing speed constraint.  Its usually good to be clear eyed about  this and focus on goals that serve you long term if you're not lucky enough to be "super fast".]

 

Here in NZ we do not have any types of competitions like this.  All exams are proof based exams with 4 problems to be solved with a full written proof in 4 hours (like the USAMO).  Yes, you have to be crazy fast, and ds does have a very very high processing speed.  However, the US does have at least one competition that is not speed based -- the USAMTS which is a take home 1-month exam.  

Edited by lewelma

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Hmmmm... processing speed. This is excellent and new information for me. We do not have fast processing speeds in our family, though we love challenging math. Should I abandon the pursuit of competition success?

 

My 9th grade daughter loves math and enjoys hard problem solving problems, but left a significant portion of the AMC10 blank because of time constraints. Granted she was going in blind; however, with focused effort how much can she improve with a slower than average processing speed? She hopes to major in math at a “mathy†school. From reading literature of some test prep centers, I was under the impression that a good AMC score is all but required to get into MIT and the likes. She was planning on dedicating serious time this summer to test prep, but I’m wondering if there might be more worthwhile goals to make her (with her slower than average processing speed) an attractive candidate for a competitive math college.

 

How can you demonstrate excellence in math in high school with a slowish processing speed?

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Daijobu, did you start a math club? Do you have a pointers? Should I advertise it as fun primarily or challenging?

 

Ultimately, I didn't start a math club per se.  I just felt it was too time consuming to come up with great ideas and activities.  Much easier was to start a MOEMS team.  Even though we were a team, each student competes as an individual, but really, it was fun because the students would learn from each other.  And there was a nice structure with materials provided by MOEMS including pdf's of the exams, an easy way to enter the scores, and certificates, pins, patches, and trophies at the end of the season.  The only trouble is it's expensive.  You can probably replicate the season by printing your own certificates and using their old exams that they publish.  

 

Where I am, when activities are presented as being "fun math" it's often more for activities that make use of hands on manipulatives or maybe arts and crafts.  I'm thinking of activities like creating tesselation designs, knitting 3D shapes, using ropes to demonstrate knots.  These are great activities, but it wasn't what I was offering.  It was too much work for me, and it was also being offered by local math circles and other teachers.  

 

Challenging is a better word for what I did.  But what was most helpful was to present examples of the work students would be doing.  For example, for math olympiad, I would link to this sample exam provided from the organizations website.  That way parents know exactly what we will be doing.  

 

I agree with a PP that 3rd grade may be a bit too young for MOEMS.  I've even hand parents of second graders ask if they can participate.  In response I tell them my (true) story of a young student who cried after not getting all the problems correct.  I needed to call the mom's cell phone to come console him.  You definitely don't want a young child to have a poor experience with math, and sometimes they just aren't mature enough to participate in a group setting away from their parents.  It's better for them to try (and sometimes fail) in a safe supportive environment at home.  That always convinces them to wait a year or two.  

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How can you demonstrate excellence in math in high school with a slowish processing speed?

 

My son hates tests like the AMC.  There are a couple of them here - the Auckland Maths Competition is one of them.  And my ds won't take them.  He does proof-based exams only.  

 

Seems to me that you could do math camps, AoPS crowd research, USAMTS, dual enrollment, etc.  Maths in real life is not about speed, it is about complexity of thinking.

 

I would suggest you PM Kathy in Richmond and ask her to join this conversation as she is very knowledgeable in this area.  

 

Ruth in NZ

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Hmmmm... processing speed. This is excellent and new information for me. We do not have fast processing speeds in our family, though we love challenging math. Should I abandon the pursuit of competition success?

 

My 9th grade daughter loves math and enjoys hard problem solving problems, but left a significant portion of the AMC10 blank because of time constraints. Granted she was going in blind; however, with focused effort how much can she improve with a slower than average processing speed? She hopes to major in math at a “mathy†school. From reading literature of some test prep centers, I was under the impression that a good AMC score is all but required to get into MIT and the likes. She was planning on dedicating serious time this summer to test prep, but I’m wondering if there might be more worthwhile goals to make her (with her slower than average processing speed) an attractive candidate for a competitive math college.

 

How can you demonstrate excellence in math in high school with a slowish processing speed?

 

I agree with the PP that as you improve in problem solving, higher scores on the AMCs does require some amount of fast processing speeds for further improvement.  But I don't think that should negate the value of learning to solve these sorts of problems.  Qualifying for AIME on the AMC 10 requires answering 18-20 problems correct, so a student  wouldn't even need to tackle the dreaded "final five."  The student just needs to be certain of not being wrong on those first questions.  

 

Even if your student isn't an AIME qualifier, having a respectable score on the AMCs is helpful, not only on its face for college admissions, but those skills are really helpful if your student wants to pursue engineering-related fields.  And it will just make her a smarter person.  :-D   But test prep need not be time consuming.  If she just takes a practice test maybe once or twice a week, and studies the problems, she should improve quickly.  

 

But certainly there are many other ways of demonstrating math proficiency and interest.  AoPS offers opportunities to participate in real math research, which is fantastic, especially if your student wants to pursue pure math in college.  

 

I was chatting with the mom if a student I tutor.  She asked me a similar question about participating in math competitions because she asserted that success will only come with a great deal of time devoted to prep.  I argued that when students decide to play on the school basketball team, it's rarely with the intent of being the best player and ultimately playing pro.  But just because you aren't committed to becoming a professional basketball player, does that mean you shouldn't play at all?  There are other benefits:  exercise, making friends, doing a fun activity.  

 

I argue math competitions offer the same benefits:  exercise (for the brain), making (smart, mathy) friends, doing a fun activity.  Plus you'll develop skills that will actually come in handy in her academic and professional life.  

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Hmmmm... processing speed. This is excellent and new information for me. We do not have fast processing speeds in our family, though we love challenging math. Should I abandon the pursuit of competition success?

 

My 9th grade daughter loves math and enjoys hard problem solving problems, but left a significant portion of the AMC10 blank because of time constraints. Granted she was going in blind; however, with focused effort how much can she improve with a slower than average processing speed? She hopes to major in math at a “mathy†school. From reading literature of some test prep centers, I was under the impression that a good AMC score is all but required to get into MIT and the likes. She was planning on dedicating serious time this summer to test prep, but I’m wondering if there might be more worthwhile goals to make her (with her slower than average processing speed) an attractive candidate for a competitive math college.

 

How can you demonstrate excellence in math in high school with a slowish processing speed?

 

Rereading this, I want to caution you about these test prep centers which of course are trying to sell you their services.  They are correct that places like CalTech, MIT and CMU explicitly ask for AMC scores.  But they are still optional, and there are many other ways to demonstrate math interest and achievement.  I would view strong AMC scores (not even AIME qualified) as a sort of validation that your student is capable of tackling the classes that you'll see at schools like those.  (They aren't easy classes, lol.)  But your student doesn't need to be an IMO winner by any means.  She can participate in research in math as I mentioned, get involved in computer programming, maybe create some things and post them to git hub.  She can participate in one of the many competitions related to science and technology.  (Winning one would be better, but not necessary.)  Do something she enjoys!  The nice thing about homeschooling is she'll have more time to devote to those endeavors.  

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Thank you, Daijobu, for your insight. I was beginning to feel like maybe it was all a lost cause. I start researching and then feel like all is lost.

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Quark's son got into Berkeley at a very young age having never taken a math competition.  If your child would *like* math competitions, then go that route.  But I would not do it just to impress university admissions.

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I would agree with Daijobu's post above about the value of competing regardless of scores. The AMC problems themselves are quite good and worth looking at and figuring out how to solve no matter whether you even take the real tests.  Checkout mikesmathpage .wordpress.com to see how they can be a really great enrichment activity on their own. And long term if math studies is a goal there is definitely more than one path to success.  AMC scores can help but are not necessary. Take a look at opportunities like http://hcssim.org/ for instance.

 

 

 

 

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My son hates tests like the AMC. There are a couple of them here - the Auckland Maths Competition is one of them. And my ds won't take them. He does proof-based exams only.

 

Seems to me that you could do math camps, AoPS crowd research, USAMTS, dual enrollment, etc. Maths in real life is not about speed, it is about complexity of thinking.

 

I would suggest you PM Kathy in Richmond and ask her to join this conversation as she is very knowledgeable in this area.

 

Ruth in NZ

I tried to pm Kathy, but the computer gave me an error :-/

 

 

Sent from my iPhone using Tapatalk

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I'm linking here to a talk given by Richard Rucszyk a few years ago. Don't worry, the talk is very long (over an hour!) but the link will take you to one particular slide (only a minute or two) and an anecdote that RR tells.

 

“Yeah what’s up?!? You didn’t prepare me for this!â€

The link was for the whole talk for me. Do you have a guess of roughly where the slide is?

 

 

Sent from my iPhone using Tapatalk

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Haha. That would be a definite yes!!

 

At the age of 12. I did a massive push with him in 7th grade (see x-post below) to prepare him for the camp-selection problems (like the USAMTS). That year he got into the the IMO camp and that was the last year that I helped him in any way at all. I am a math tutor up to calculus, but as I said in my earlier post, the content is easy; its the problem solving that I can't help him with.

 

We had him start taking AoPS classes, so when he was stumped, he asked the other kids or the instructors for hints. Some of the kids organized a online study time so they could work together to solve the challengers. I looked for a math mentor, and found none. There was no club in my city.

 

He did. But I required him to stop if there were tears. Back then he was scarily focused on math. And over the years, he would have spent way more on math if I had allowed it. As I remember, he did it all in one block, but I was not in the room so not sure. It was his choice to do that much. I would never have required more than 45 minutes in primary/middle school, and an hour a day in high school.

 

 

He was determined. Teaching was cheating in his eyes. I never would have forced him to work on crazy hard problem solving if he had not wanted to. But there have been a lot of discussions on this board on how to teach, guide, facilitate AoPS so that problem solving can be enjoyable for kids who find it tough to learn on their own. Maybe someone can link you to these threads.

 

There was no PreA when ds went through AoPS. The first 5 chapters of Intro Algebra acted like his preA and took him a full year to complete. Now, most people say that if you have done PreA, the first 5 chapters are crazy easy. The general feeling on the board has been that to do it well, PreA+IntroA will take 3 years in total. My ds just did 3 years of introA.

 

++++++

 

 

This post from 5 years ago discusses how I taught him in the last year that I could help. Notice that I was not a teacher of content. In fact, I was co-learning, not actually teaching, as I did not have the problem solving knowledge. We were using the Art and Craft of Problem Solving (NOT an AoPS book).

 

X-Post from 2013!

Yes, that is the book. My son is 12. We are currently able to understand only 30% of it. It is a University math majors textbook. The author states that you should read each chapter until you don't understand, then move to the next chapter. When you finish the first pass of the book, you start again. This approach allows you to work at your personal level in each topic, and allows your ability in all topics and problem solving to be increased concurrently.

 

There is NO way that my son could work with this book independently. We work on each problem together and then read through the proofs together. If the problem is easier, we each separately investigate it and write up a formal proof and then compare. My goal is to find ideas in each problem that will be generalizable to other problems. We keep a list, and I quiz him every day about the different generalizable skills we have learned. For example, what kinds of problems are would likely be helped by the extreme principal? or what kind of problems suggest a proof by induction? How can you recognize parity in geometry problems? These types of questions are not directly answered in the text -- they are more of a way for us to really internalize what we are reading and categorize all the ideas. Plus, it helps us review esoteric ideas by recalling specific problems that reflect them. We've decided that if there are 20 different tactics that are possible, and we can recognize that 4 are good candidates for a certain problem, we can try those four. If one works, great, if none work, then at least we have gotten our hands dirty and have a much better understanding of the problem and can go from there.

 

To help in proof writing, I drill him on specific phrases like "This specific case is generalizable because the only special feature of 11 that we used is that it is odd." (yes, I am memorizing all this too, so that just popped out of my brain). This drill has really helped him not only with the language of math, but also helped him realize different approaches he could use to prove a conjecture. For example, the above case showed us that you can use an example as your proof in many cases of parity. This is very important to know, because most proofs do not allow this. Our overall goal is to get as many tools in our tool box as we can, and then remember what tools we have in there!

 

All this is really working. I cannot believe how far we have come in 2 months.

 

I told someone last week that I could only go through this process once because what I am giving my son is not a knowledgeable tutor, but rather a skilled learner who is at his exact level in math. If I ever go through this material again with a student, I would be much much more knowledgeable and I would loose the confusion that has been so critical in helping him battle through this material. What I am finding is that because I don't know the answers and I cannot teach him how to do it, I am instead teaching him how to learn problem solving -- what questions to ask, what answer to hunt for, how to compare problems, how to really interact with this material. No tutor who knows the material well could do this as well as I can, because once you have the knowledge, it would be virtually impossible to relive the confusion.

 

But then I realized that because my memory is so shaky, I could probably do it one more time. :001_smile:

I could read this post over and over again from 2013. For me this is the essence of homeschooling. I want it to be a sticky.

 

 

Sent from my iPhone using Tapatalk

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The link was for the whole talk for me. Do you have a guess of roughly where the slide is?

 

 

Sent from my iPhone using Tapatalk

Sorry, skip ahead to 6:40 and watch from there for a couple of minutes.  

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We started a math club for middle schoolers and high schoolers in Jan. 2017.  We had a blast.  It is really neat to see how different everyone thinks and where their strengths are.  We all learn from each other.   I ordered the free materials for a math club here for the middle schoolers:  https://www.mathcounts.org/programs/math-club  but we did lots of other things too.  We had a few middle schoolers ask if we could do the MATHCOUNTS competition.  I truly didn't know anything about it but we signed up in November 2017 and dug into the resources they give you.  We did many problems and the kids continued in their math curriculum.  No one was further than the very beginning of Algebra at the time of competition (Feb. 2018) but all the kids love playing with math.  Our team placed 13 out of 17 at our chapter competition and we had one kid place 35th out of 120 competitors.  Not bad for just jumping into it.  We learned so much!  All our 7th graders can't wait to try again next year and now we have a much better idea what to expect.  

Another homeschool MATHCOUNTS team in a different city that just won the team state competition for our state has been giving us pointers.  They sent us a copy of the MATHCOUNTS "Bible".  I also chatted with the winning teams coaches at competition.  Their kids have done much higher math than mine had (many already through algebra 2 and geometry).  My 7th graders all have goals to get further in their curriculum while working through the MATHCOUNTS resources that we didn't get too.  The top coaches also have their kids working through countdown problems in a countdown setting over and over again for practice so not just knowledge but speed.  The website has problems for each round from years past plus these coaches have all the previous years problems too.

We also found these really helpful too:  https://www.mathcounts.org/resources/video-library  My kids would watch these at home while work on the MATHCOUNTS toolkit.

I started this for my mathy kid who I wanted to "slow" down in math.  Didn't want the calculus trap and this allows us to really understand the why?  as well as dig into fun math topics-binary, octal, Pascal's triangle, Sirpinski's Triangle, interior angles or polygon, fractals, factorials, pi, etc....

That said I am looking for ways to get my younger kids ready for these competitions earlier too.  Starting Math Olympiad group was suggested as the best way to start.  These books were recommend from a top coach:  http://store.moems.org/mm5/merchant.mvc?Screen=PROD&Product_Code=4131 and http://store.moems.org/mm5/merchant.mvc?Screen=PROD&Store_Code=MOEMS&Product_Code=4120

I am hoping to start a MOEMS team soon.

My 12 year old currently is working through AOPS Algebra while doing Geometry at Aleks.com.   We will continue to work through the AOPS sequence and following other math interests.  When he was younger he used Saxon and Singapore.  Some of our team plans to take these classes too:  https://artofproblemsolving.com/school/course/mathcounts-basics and some qualified for the advanced one.

I hope that kind of answers your questions.  I am enjoying everyone's thoughts on this too.

 

 

 

 

 

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On 3/18/2018 at 1:59 PM, seaben said:

Here's an old getting started with a Math Club post I put together: http://mymathclub.blogspot.com/p/how-to-get-started.html.  I think when starting its important to clarify your goals. There is an interesting quiz I linked to from natural math that was good that way. Once decided upon then yes advertise based on your vision.

 

Beyond that its also good to know your potential target audience. Third grade is still pretty young for anything intense and you're less likely to find others who want to go that way.  Also after working with a lot of 4th and 5th graders, I'm going to throw it out there that on average they don't have long attention spans for challenging work. There are outliers but I'd plan on no more than 20-30 minutes of focus from a group as a whole at the earliest ages and its equally important to think about making it fun at the same time so kids keep coming back.

 

[Also one other thing to keep in mind about AMC10 or any other contest is that there is a large processing speed component to them. There is very limited time to do the questions and you have to either think quickly or quickly recognize the problem structure to even finish at all. This doesn't mirror mathematics in the real world.  Its often useful to separate whether given  unlimited time you can solve the problems from the practice tests (and learn from them) vs. can you solve them in 75 minutes etc.  While practice can improve performance, you may find it plateaus out just due to that processing speed constraint.  Its usually good to be clear eyed about  this and focus on goals that serve you long term if you're not lucky enough to be "super fast".]

Seaben, 

My math club prep is taking shape, and I am revisiting your blog.  It's amazing!!!!   I am blown away by the wealth of knowledge you have shared.  

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My ds started a math club last year, and convinced one of the other top competition kids to help him run it.  They have a class of 12.  They are doing 9 weeks on each of the competition topics - algebra, geometry, combinatorics, number theory.  My son lectures on the new content while the other boy works with the subset of kids that already know the content to solve problems.  Then after the lecture, the kids in the lecture group start in on the problems.  They work in groups of 3 mostly self-sorted into skill level for that particular topic, and the two older boys wander around helping them solve the problems on the worksheet that they had prepared earlier in the week.  Over the course of 9 weeks, they try to get through most of the basic content in each subject area.  In ds's final 2 weeks, they are going to focus on *how* to write up proofs.  The whole experience has been excellent for both the kids in the class and the two older boys leading it.  My son and his friend have put this class on their university applications and on their resume.  DS is considering running one of these classes in Boston for pay now that he has a year's experience, knows what he is doing, and has references.  I think he could charge a decent amount to help him fund his university education.  

 

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