# What's a good topic for a one-hour math lecture?

April 10, 2014 10:24 AM Subscribe

I work as a math tutor at a community college and have the opportunity to spend an hour teaching math to a group of students preparing for a the college's math placement test. Now, I don't know what's on the placement test, but I want to teach something that's more engaging and conceptually accessible than "here's how to multiply (4x+3)(2x+5)", since I can't possibly review all of high-school math in an hour and don't think the students will get much from just another lecture. What are some interesting topics that I can explore that will be accessible and memorable?

Good answers above. I'd add a twist on "how to think about math" - the right attitude/mindset for learning math. Many students think math is a natural talent that you either have or don't have. In reality, math is very much a "practice makes perfect" thing.

Getting that mindset corrected makes all the difference in the world.

So, when I tutor in math, I like to always start with things like this:

- You are not doomed to failure in math because you are "not a math person."

- It's all right to struggle. That's part of the process and helps you understand it.

- The more you do, the better you get.

- Everybody learns differently. Find different explanations of how to do whatever it is you're having trouble learning until one of them clicks.

posted by greenmagnet at 10:36 AM on April 10, 2014 [2 favorites]

Getting that mindset corrected makes all the difference in the world.

So, when I tutor in math, I like to always start with things like this:

- You are not doomed to failure in math because you are "not a math person."

- It's all right to struggle. That's part of the process and helps you understand it.

- The more you do, the better you get.

- Everybody learns differently. Find different explanations of how to do whatever it is you're having trouble learning until one of them clicks.

posted by greenmagnet at 10:36 AM on April 10, 2014 [2 favorites]

I think you're going to get a lot of good answers for "how to do an interesting math lecture" but am I out of line to ask a question? If this hour is for students who are supposed to be prepping for the placement test but you have no idea what's on the test how is this lecture useful for these students?

Is the goal of your talk to get them more excited and/or informed about math or is it to help prepare for the test? The potential topics for the former are many and varied, the suggestions above are good, but if the goal is explicitly and specifically the latter then why are you wasting these kids' time?

posted by Wretch729 at 10:39 AM on April 10, 2014 [3 favorites]

Is the goal of your talk to get them more excited and/or informed about math or is it to help prepare for the test? The potential topics for the former are many and varied, the suggestions above are good, but if the goal is explicitly and specifically the latter then why are you wasting these kids' time?

posted by Wretch729 at 10:39 AM on April 10, 2014 [3 favorites]

*I think you're going to get a lot of good answers for "how to do an interesting math lecture" but am I out of line to ask a question? If this hour is for students who are supposed to be prepping for the placement test but you have no idea what's on the test how is this lecture useful for these students?*

Is the goal of your talk to get them more excited and/or informed about math or is it to help prepare for the test? The potential topics for the former are many and varied, the suggestions above are good, but if the goal is explicitly and specifically the latter then why are you wasting these kids' time?

Is the goal of your talk to get them more excited and/or informed about math or is it to help prepare for the test? The potential topics for the former are many and varied, the suggestions above are good, but if the goal is explicitly and specifically the latter then why are you wasting these kids' time?

I'm definitely not looking to focus on the the "get kids excited about math" part - not that it's a bad goal, but I definitely want to help prepare students for the test. Without knowing the exact contents, I'd like to focus on mathematical problem-solving and how to approach unfamiliar and complicated problems, and I think the best way to do this is with an interesting and distinct example that I can explore in depth. Something like taking a mathematical model and looking at it from a basic level, then going into more detail.

posted by LSK at 10:44 AM on April 10, 2014

simple math problems that everyone can understand, but nobody's ever been able to solve. the goldbach conjecture. perfect cuboids. the riemann conjecture, if you think you can explain the zeta function within a reasonable time.

posted by bruce at 10:44 AM on April 10, 2014

posted by bruce at 10:44 AM on April 10, 2014

As a math tutor, I am guessing that you know well what students at the college commonly have problems with. Can you choose a few common issues and teach different ways to solve that type of problem? If I were one of the students, that would be what I'd want to learn.

posted by snorkmaiden at 10:45 AM on April 10, 2014

posted by snorkmaiden at 10:45 AM on April 10, 2014

Ah, if I might make a suggestion, as someone who spent over a decade as a math tutor and test-prepper (amongst other things), what you want them to know reflexively are

3-4-5

5-12-13

8-15-17

7-24-25

20-21-29

9-40-41

... with the last two having only been present a couple of times on those tests in all of my experience. It will not take too long for them to memorize these sequences, hopefully. They should be able to recognize these sequences and their more obvious multiples. The payoff is generally two or three questions, which isn't bad for a little work.

posted by adipocere at 10:45 AM on April 10, 2014 [3 favorites]

**Pythagorean Triples**. They show up all over ACTs and SATs. I have only ever seen multiples of, in descending order of likeliness:3-4-5

5-12-13

8-15-17

7-24-25

20-21-29

9-40-41

... with the last two having only been present a couple of times on those tests in all of my experience. It will not take too long for them to memorize these sequences, hopefully. They should be able to recognize these sequences and their more obvious multiples. The payoff is generally two or three questions, which isn't bad for a little work.

posted by adipocere at 10:45 AM on April 10, 2014 [3 favorites]

If I were a student who signed up for a hour worth of test prep, I would expect to get some prep on the content of the test, not an hour on why math is interesting or formulas which may or may not have any relevance to what's on the test. Do a quick hand's up poll at the beginning of the hour to identify problem areas, if necessary group the students into a small number of workgroups, and teach the concepts they are struggling with.

Is this a standardized test? There's *always* an outline somewhere of what any standardized test covers. Usually there's previous year's test questions released online by the test developer too. Study those to prep for the scope of what to teach.

posted by jamaro at 10:48 AM on April 10, 2014 [8 favorites]

*Without knowing the exact contents*Is this a standardized test? There's *always* an outline somewhere of what any standardized test covers. Usually there's previous year's test questions released online by the test developer too. Study those to prep for the scope of what to teach.

posted by jamaro at 10:48 AM on April 10, 2014 [8 favorites]

When I administer math placement tests, I notice a lot of the students struggle with reading comprehension, and it affects their ability to do even simple word problems.

For example, in one problem they're supposed to figure out how many dollars per hour Joe makes. I frequently--FREQUENTLY--get answers like "$475." So...what's the likelihood Joe makes $475/hr?

Or in a word problem that asks them to figure out how to increase the yield of a cookie recipe and find out how many cups of flour they need for 3 dozen cookies, they'll answer "85 cups." Really? 85 cups of flour for 36 cookies?? Come on!

Obviously neither of these answers makes sense, so that should be a clue that they've done the math wrong. Maybe getting the students to practice reading comprehension with word problems would be a good idea.

posted by hurdy gurdy girl at 11:06 AM on April 10, 2014 [2 favorites]

For example, in one problem they're supposed to figure out how many dollars per hour Joe makes. I frequently--FREQUENTLY--get answers like "$475." So...what's the likelihood Joe makes $475/hr?

Or in a word problem that asks them to figure out how to increase the yield of a cookie recipe and find out how many cups of flour they need for 3 dozen cookies, they'll answer "85 cups." Really? 85 cups of flour for 36 cookies?? Come on!

Obviously neither of these answers makes sense, so that should be a clue that they've done the math wrong. Maybe getting the students to practice reading comprehension with word problems would be a good idea.

posted by hurdy gurdy girl at 11:06 AM on April 10, 2014 [2 favorites]

If the test is anything like the big standardized tests where time is an issue and you want to save your time/energy for tougher problems, going over mental math tricks and tips for recognizing problems that you can use them on seems very useful. This was what helped me a lot preparing for the GRE math section because I tend to dig in and slog through a problem the hardest way possible because I don't have much practice/don't trust using intuition with numbers.

Like rounding to get ballpark numbers and then eliminating wrong answers.

Or if they will have geometry questions with figures on the test, identifying angles/sides that are equivalent to missing values, so you may be able to avoid using formulas.

Working with powers of ten quickly.

...

posted by dahliachewswell at 11:11 AM on April 10, 2014 [1 favorite]

Like rounding to get ballpark numbers and then eliminating wrong answers.

Or if they will have geometry questions with figures on the test, identifying angles/sides that are equivalent to missing values, so you may be able to avoid using formulas.

Working with powers of ten quickly.

...

posted by dahliachewswell at 11:11 AM on April 10, 2014 [1 favorite]

Agree entirely with

- teach to the test as much as possible

- pythagorean triples are everywhere

- rounding, ballparking, reality checking

I also found it really useful and shorthand to be able to look at a number and tell if it was divisible by: 2, 3, 5 or 9 immediately (and the other numbers with a bit more guesswork) Felt like cheating but it was also math!

posted by jessamyn at 11:57 AM on April 10, 2014

- teach to the test as much as possible

- pythagorean triples are everywhere

- rounding, ballparking, reality checking

I also found it really useful and shorthand to be able to look at a number and tell if it was divisible by: 2, 3, 5 or 9 immediately (and the other numbers with a bit more guesswork) Felt like cheating but it was also math!

posted by jessamyn at 11:57 AM on April 10, 2014

I would try to find the last three (or more) versions of the test and find similar questions (esp if some have higher point values) that reappear multiple times. Go through those problems. If that's not possible then do 'test taking strategies' (ie eliminating unlikely multiple choice answers,and/or substituting in available answers to determine which is correct etc).Calculator tricks/knowledge if they are all using the same calculators- ie where is 'x' button, exponent button, and so on....

Honestly know your audience...it is unlikley they want any sort of abstract math lecture or 'fun' topic- they want to prepare for this exam. Honor that.

posted by bquarters at 11:58 AM on April 10, 2014 [1 favorite]

Honestly know your audience...it is unlikley they want any sort of abstract math lecture or 'fun' topic- they want to prepare for this exam. Honor that.

posted by bquarters at 11:58 AM on April 10, 2014 [1 favorite]

My first thought was to think of Vi Hart--which is to say, trying to find some angle on this that would be educational but also fun and maybe something in the way of a confidence-builder before the exam? A few things to show that this isn't something to be too afraid of. An hour is not nearly enough time to cover any significant portion of the material that's actually on the exam if they aren't actually prepared for it, but it is enough time to motivate them to be able to actually perform up to their abilities.

posted by Sequence at 11:59 AM on April 10, 2014

posted by Sequence at 11:59 AM on April 10, 2014

Word problems and algebra. I used to teach math at the university level, and I was surprised at how many people still had trouble with those topics. They had many mnemonics (like SACATOA or something) and formulas but no idea why it all worked; I would work out the algebra leaving out no steps.

posted by phliar at 12:04 PM on April 10, 2014

posted by phliar at 12:04 PM on April 10, 2014

Yeah, Pythagorean triples are good.

if you're test prepping, do some teaching about tests. They're not measures of intelligence or even mathematical ability - they're more like...belt tests (use an example your class would relate to), where you show that you can recognize a bunch of question types and perform all of them.

"Cool math things" is not what people signed up for here, but you can find opportunity to give that talk at any variety of children's enrichment groups.

posted by batter_my_heart at 12:15 PM on April 10, 2014 [1 favorite]

if you're test prepping, do some teaching about tests. They're not measures of intelligence or even mathematical ability - they're more like...belt tests (use an example your class would relate to), where you show that you can recognize a bunch of question types and perform all of them.

"Cool math things" is not what people signed up for here, but you can find opportunity to give that talk at any variety of children's enrichment groups.

posted by batter_my_heart at 12:15 PM on April 10, 2014 [1 favorite]

Units. The key to word problems is to combine terms so the result has the right units, e. g. mph.

posted by SemiSalt at 12:20 PM on April 10, 2014

posted by SemiSalt at 12:20 PM on April 10, 2014

I would talk about test taking strategies and also how to handle issues like test anxiety. But particularly test taking strategies. Like, if it's multiple choice test, how to make an educated guess, etc.

If it's at the community college level? You're going to get students who can't add, all the way up to those who took Calculus, but they have to take the placement test as a technicality.

I've been in math placement test 'classes' like this, but they were two hours long. They also used copies of this book: Chart Your Success on the COMPASS Test. What they did was quiz each student as to what they felt their math level was at, and then gave them practice sets from the book. Once they 'mastered' it, they moved up to the next level, etc. (I found the book to be inaccurate when it came to the Trigonometry, but the non-Trig elements were pretty on par with what I saw when I took the COMPASS last year. I placed into PreCalculus.)

posted by spinifex23 at 12:52 PM on April 10, 2014

If it's at the community college level? You're going to get students who can't add, all the way up to those who took Calculus, but they have to take the placement test as a technicality.

I've been in math placement test 'classes' like this, but they were two hours long. They also used copies of this book: Chart Your Success on the COMPASS Test. What they did was quiz each student as to what they felt their math level was at, and then gave them practice sets from the book. Once they 'mastered' it, they moved up to the next level, etc. (I found the book to be inaccurate when it came to the Trigonometry, but the non-Trig elements were pretty on par with what I saw when I took the COMPASS last year. I placed into PreCalculus.)

posted by spinifex23 at 12:52 PM on April 10, 2014

I'm not sure about the skill levels of the students, but another topic is how to take test: when to skip a question, how to check answers, which questions to tackle first, how to figure out what the question is asking, etc.

posted by applesurf at 5:24 PM on April 10, 2014 [1 favorite]

posted by applesurf at 5:24 PM on April 10, 2014 [1 favorite]

Is there a reason you can't call the department/college and ask them what sort of stuff is likely to be on the placement test?

I know there are some study materials available for Accuplacer and ALEKS. But being able to tell students that, e.g., it's an adaptive test that will start with basic arithmetic and get harder from there if you get things right, up to standard pre calculus and trigonometry (or whatever) should be non-problematic. Giving examples of the types of problems (eg, Accuplacer is multiple choice, Aleks is short-answer) would also be nice. Getting this information should be doable and is not cheating or giving undue help---I'm surprised there isn't a link to study materials available from the college.

posted by leahwrenn at 9:08 PM on April 10, 2014 [1 favorite]

I know there are some study materials available for Accuplacer and ALEKS. But being able to tell students that, e.g., it's an adaptive test that will start with basic arithmetic and get harder from there if you get things right, up to standard pre calculus and trigonometry (or whatever) should be non-problematic. Giving examples of the types of problems (eg, Accuplacer is multiple choice, Aleks is short-answer) would also be nice. Getting this information should be doable and is not cheating or giving undue help---I'm surprised there isn't a link to study materials available from the college.

posted by leahwrenn at 9:08 PM on April 10, 2014 [1 favorite]

For what it's worth, I don't think Pythagorean triples are likely to show up on a math placement test---unfortunately, there's not typically much geometry on those. Sometimes they come up in the nested inverse trig function of a trig function problems (e.g. , what's arctan(cos(4/5)) ), but a placement test isn't likely to ask those.

FWIW, I am a math prof, and the only Pythagorean triples I know off-hand are 3-4-5, 5-12-13, and 7-24-25.

posted by leahwrenn at 9:11 PM on April 10, 2014 [1 favorite]

FWIW, I am a math prof, and the only Pythagorean triples I know off-hand are 3-4-5, 5-12-13, and 7-24-25.

posted by leahwrenn at 9:11 PM on April 10, 2014 [1 favorite]

Only other thing I can think of is to find out what kind of calculator is allowed for use on the placement exam - and then be able to answer questions about that. I've known a couple of people get blindsided because they wanted to use the calculator app on their smartphone, just to find out that it's forbidden by the proctors.

None? Graphing allowed? Non graphing only? What makes and models are allowed and/or banned? Students can't bring their own calc in at all - they have to use one provided by the proctors? I considered that an essential part of test prep, so when I went in, I knew that my option was only the built in one on the Windows computers.

posted by spinifex23 at 10:36 PM on April 10, 2014

None? Graphing allowed? Non graphing only? What makes and models are allowed and/or banned? Students can't bring their own calc in at all - they have to use one provided by the proctors? I considered that an essential part of test prep, so when I went in, I knew that my option was only the built in one on the Windows computers.

posted by spinifex23 at 10:36 PM on April 10, 2014

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How to answer test problems (gather the facts, what data is relevant)?

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posted by St. Peepsburg at 10:27 AM on April 10, 2014