Wednesday, February 08, 2006

Chess, Factoring Quadratic Trinomials, and My Math Family


Playing chess is a very humbling experience. Always has been, probably always will be. I just don't get the strategy! It's one of those games that I wish I got, unlike football, which I wish no one got. . .

Chess is a very intricate game of strategy and great for building thinking skills. Unfortunately my poor widdle brain just can't handle it! Every time I play I end up just scratching my blond hairs in confusion. My strategy in chess is nonexistant, zilch, nada, nil. I had a 5 year old girl put me in stale mate a few months ago. Granted this was a smart 5 year old, but still!

Hannah and I just finished a game of chess (shock, she won), and I just feel like my brain oozed out of my head. It took so much mental effort. Maybe this is what most people feel when they do math.

Hehe. I got to teach factoring to my Algebra I class today. I love factoring! To me it's like a puzzle; you see the end result, you just move the pieces around until it fits. Factoring is therapeutic; seriously. Mother Dear was telling me that she remembers when she was taking Ben through Algebra I, and they got to the part on factoring; she hadn't factored in years, and she thought it was so fun that she sat down and did all 40 homework problems for fun :). Isn't my mother fun-loving?

My students were enjoying factoring until we got to the second or third example with a leading coefficient other than 1. They weren't fond of checking all the different possibilities, although they did lighten up after I explained why we only had to OI to check instead of FOIL to check :). One of my students came up with saying it that way, and I found it pretty amusing, so it stuck.

Anyway, so yes, they thought I was a bit strange for loving factoring so much. They really did understand how to factor, they just thought it was time-consuming, which of course it is when you first learn. But I had to explain to them that to me math is nostalgic. When I do math I think of my family, because that's a lot of what we did together growing up. We played math games, we talked about math, we laughed about math, we made conjectures about math. . . and contrary to what some may believe, we did have real lives too.

The headmaster of the homeschool program for which I teach seems to take a secret delight in introducing me to people at informational meetings. We've known him and his family for years, as we were in the same home school group, had many mutual friends, and went to sister churches for a while. At informational meetings for new people interested in Heritage, he introduces each of the staff in turn to the parents and gives a little background. With most of the staff he says: "And this is Mr./Mrs./Miss ______, who has taught ______ for us for Heritage for __ years. The kids love him/her, etc."

For me he says, "And this is Miss Garrison, who teaches Algebra I and Geometry. She comes from a math family." After a pause for emphasis, "Some of you may never have heard of such a thing; I hadn't either until I met her family." After another pause, still addressing the parents at the meeting, "Did you all used to tell your students bedtime stories when they were little?" Parents then nod heads. "Well, her parents told bedtime stories, but they also did bedtime math problems!" The reactions to this are truly hilarious :).

We really did have bedtime math problems, by the way. It was all in good fun, mind you! It wasn't like we weren't allowed to turn out the light until we had finished factoring our trinomials. Nothing like that. When we were preschool age or so, my dad would ask us simple, oral arithmetic problems. The most memorable were akin to this: "Okay, Hannah, if I have 20 bunnies and you take 5 of my bunnies, how many bunnies do I have left?" After our bedtime math problems, we would snuggle into bed thinking about math and bunny thieves. Sweet dreams.


Adrian C. Keister said...

The problem with chess books is that they're either beginner books that call rooks "castles" *shudder*, or are written by an Expert for the edification of other great Experts, and are so esoteric as to leave the ordinary reader as befogged as before.

One exception to this rule is the book The Logical Approach to Chess, written by Max Euwe (world chess champion) and Frances A. Davis (an amateur). I would highly recommend this book to someone who knows how the pieces move, but doesn't have an over-arching strategy. It's also inexpensive, being a Dover book (yay!).

Ok, my family may include a lot of geeks (me, Dad, Arne (brother), Uncle Brad, and Grandpa Keister), but we did not have math problems right before bedtime. That is ultimate geek. Speaking of which, have you taken the nerdity test? Just search for that on Yahoo, and see how you come out. I think I'm about 64. I'd be interested, if you should ever choose to waste your time on it, to see how you fare. The thing is, you don't have the experience with physics I do. That might hurt your score a bit (assuming you're trying for a high score). Have you experience programming computers? If not, that'll hurt, too.

Well, I'm glad you love math. Far too few people in this country love math. For me, it reflects the glory of God and His unchanging nature.

In Christ.

Susan said...

You must have a book recommendation ready for every subject possible ;). I do love recommendations, though, so please keep them coming.

Hehe, you think bedtime math problems is ultimate geek? Do I have stories I could share. . . That anecdote barely scratches the surface.

Did you see the math clock I posted to my blog sometime in December? We were awfully proud of that creation :-D. My family of five once sat in all possible 120 permutations on our couch, just for fun one night. On our last road trip we played "try to find the highest perfect square" and also looked for Fibonacci numbers in succession. My mom and I take practice SAT math sections for fun. Of course you witnessed Hannah's and Ben's online debate as to whether 144 or 8128 was cooler :). My dad taught my brother to estimate logarithms when he was about 7. . .

I could go on, but won't :). Some families play sports together, we did math together (and other things).

Thanks for the nerdity test link. Now I feel normal :). Oh wait, I hate normality - the modern sense of normality, that is. I guess I mean that I feel less nerdy after taking the test.

Sister Dear and I both took the nerdity test and scored pretty low :). Hannah's score was around a 23 and mine was about a 30. I think my limited (and distant) background in physics and lack of computer geekiness really helped me with that low score ;). I've never programmed; I leave that up to Brother Dear, who has a Master's in Computer Science.

Every nerd or geek test I've taken has so many questions on computer assembly, computer programming, computer operating systems, role-playing games, Star Trek - all things to which I do not relate. . . Many of the nerdity questions on knowledge I knew in highschool or early college, but have since forgotten. That's ok; I'm alright with a low nerd score :).

Well, I'm glad you love math. Far too few people in this country love math. For me, it reflects the glory of God and His unchanging nature.

That's why I love math as well :). It's so concrete, so set, and so organized. God is a god of order, not confusion, and mathematics perfectly reflects that. Just look at something like the golden ratio in nature. That's just awe-inspiring!

When I was student-teaching Algebra II last year, I had a student stop me in the middle of a lesson and ask me "who came up with these rules," to the effect that mathematical rules must be a made-up human invention for arbitrary reasons. This during a lesson in which I was actually explaining the reasoning behind what we were doing!

His question just kind of stopped me short; I kind of paused and said, "God made the rules. Math isn't arbitrary."

Observing and teaching a the public schools was a real eye-opener for me. I didn't realize that math was taught so rotely in most classrooms.

I watched one teacher teach exponent rules with absolutely no explanation behind them. I sure would be confused if I was told to add exponents when we were multiplying two monomials, unless I was given an explanation! When students would ask the teacher why such-and-such a rule worked, her answer was "the book says so." No shock that the students struggled with exponents for the rest of the semester! It really makes me sad how many kids have no idea the beauty or order of math, instead seeing it as arbitrary and drudgery :(.

Adrian C. Keister said...

Yes, I saw the "horrid" math clock. Hmm. Nerdy and geeky just don't go far enough here. I'll have to dream up something else. The 120 permutations is hilarious. SAT math sections for fun; that's just silly. It's too easy. Estimating logarithms would actually be quite a useful thing to know how to do. Too many people just punch it into the computer or calculater, and assume the answer is correct. The issue is, computers make fast, very accurate... mistakes. There's a section in one calculus book I have that has the title, "Lies My Calculater Told Me." It's quite good; a fantastic tour-de-force of why you can't rely totally on the computer. You simply must have some idea of what you're going to get.

My score on the nerdity test was something like 54% nerd.

Did you actually say that, "God made the rules" in a public school? That's gutsy! It also might not have been the wisest thing ever. You can get thrown out of school for milder things. Though, I would hasten to add, you were 100% correct. Not 99.99%, though you would be 99.99999(bar)% correct. ;-)

I think one of the biggy reasons so many students don't like math is because they see no real-life application for it. And even supposing you do have a teacher who understands some of the applications, they're probably not terribly interesting ones. The secularists have no explanation for, as one person put it, "The unreasonable effectiveness of mathematics in modeling the physical world." (Inexact quote). We Christians have quite an acceptable answer, don't we? Praise God for it, and not our own understanding.

I rather object to the pure mathematicians snobbishness about the real world. It's gnostic, I think. Now there's nothing wrong with pure mathematics per se, but I think ultimately, the mathematician should seek to find the order in creation, not in his own fallen mind.

Speaking of great books and recommendations, try Mathematics: Is God Silent?, by James Nickel. This is a fantastic start on a Christian philosophy of mathematics. You also might find a little essay by my father interesting. You can find it on the Trinity Foundation website:

Go to Review Archives on the left. Dad's article is the September 1982 one, entitled Math and the Bible. Interestingly, James Nickel has a footnote on page 263 which refers to Dad's article. Nickel doesn't think much of it, though. He says it is "naive...simplistic." Dad thinks not, of course. I think Dad thinks Nickel is misunderstanding him.

Well, time to turn in. No doubt, tomorrow I'll have a whole slew of new Susan comments to which to reply. That will be your fault.

In Christ.

Samara said...

Susan, this is the most charming post I've read from you yet. I think you feel about math the way I feel about linguistics- that it's a beautiful and fascinating part of God's perfect, ordered Creation. I'm now going to look forward to telling some "bedtime math problems" someday :)

helen said...

I love the post! I just finished teaching my sister how to factor trinomials. I'd forgotten how FUN it is!

My sister, brother, and I love working out math problems just for entertainment too. Anything to do with triangles is our favorite. :-)

Can't agree with you on chess though... We used to spend every recess and lunch break at school playing chess. :-)

Susan said...


Okay, I think you're on Mother Dear's bad side now ;). After reading your comment on our cherished math clock, her exact words were, "I'm crushed." She said I should tell you that, too.

Calculators definitely have their use, but it pains me to see how much they are abused by most math students. My students don't get the luxury of a calculator, except in rare circumstances :). Calculators can be deceiving in many ways. Trig ratios, for example, or area under a curve. Plus, mental arithmetic is just plain fun! There are all sorts of wonderful shortcuts to mental arithmetic.

It was a rural school in the Bible belt. Most of the school was probably nominally Christian; in fact the principal was a sweet, Southern Baptist man. I was a student-teacher, so the worst that could have happened would have been a tap on the wrist :). My dad has given his evolution/millions-of-years talk (and passed out books and flyers) in his public school classroom many times, and he still has a job, though he has been called to the office at least once. . .

The math department at the school for which I student-taught was glaringly un-Christian in comparison to the rest of the school. I endured more filth during lunch that semester than I did the whole rest of college, and I am not exaggerating.

I definitely want to read your dad's article. It sounds interesting :). I'm rushing to finish my blogger "homework" this morning before a busy 2-3 days, though, so I will bookmark it and come back to it probably on Monday. I'll let you know what I think.


Yay, a convert to bedtime math problems! :) They really were great fun. My sister is like-minded with you regarding linguistics. Languages fascinate her; she's majoring in French (and Education) and minoring in Spanish and ESL.


Triangles are so much fun! One of my geometry students told me that he decided that every proof we've done this year relates back to triangles in some way, which is close to true :). Even most proofs with circles use triangles.

I want to love chess, but it's hard to love something that is so hard for me :). The main problem is that I've never really played much chess. I've played about 10 (or fewer) games in the last 6 months, and I was about 10 years old when I played before that. Chess is a game that takes time and dedication to master. Hannah and I are hoping to try at least weekly chess games, since neither of us are very good at it, and she wants to see if our library has the book Adrian recommended.

Susan said...


Since my weekend trip was postponed, I got a chance to read your dad's article today instead of Monday. After reading the article, I see where you got your love of mathematics :). Thank you for sending me the link. I noticed your dad has a doctorate. What discipline is his degree?

Interesting that your dad noted the mention of pi in I Kings; that passage is oft used by atheists and others to discredit the Bible, but your dad did a nice job of addressing it. Incidentally, in the late 19th century a bill was attempted in the Indiana legislature to officially set the value of pi as 3. It unanimously passed the house, but failed in the senate.

Pi has always had a certain fascination for me. One of my brother's friends used to list as one of his hobbies, "memorizing digits of pi." My aunt got my family a "pi plate" for Christmas; it has a giant pi symbol in the middle and pi written out to many, many digits wrapping all around the rim. Is that as horrid as the math clock ;).

I loved the different axioms of arithmetic that your dad pulled out of scripture. I never would have noticed those myself, but it was neat. It's amazing what one can find in scripture.

Like I said before, so many people think mathematical laws (even things as simple as the axioms of arithmetics) were man-created. Of course that makes no sense when you even begin to think about it. I can't imagine making up my own system like mathematics without constantly running into contradictions and other nonsense. Mathematics is just to complex and integrated to be man-created.

The article was deep enough to stay interesting, yet simple enough to be read by non-technical people - a nice balance. It makes me wish I would have had access to the article when one of my Algebra I students wanted to know when he's ever going to use the distributive property :).

David said...


Bedtime stories are the best =) I remember bedtime Peretti Novels, Tolkien novels, Orc and Goblin stories, and math story-problems, too :)

Such good times =D

And then of course there were the times when we found ourselves waiting at restaurants and my dad would try to stretch each of us kids to the limits of our math knowledge either through word problems or through sequential calculations spouted off in rapid succession until only one sibling was still calculating (a vertiable mathematician's version of Simon-says). Yes - the joys of parenting!

My younger brother and I shared a bunkbed all growing up and since I always got the bottom (tricked him into thinking the top was better, I did :) (yes....reverse psychology WORKS! at least on younger siblings) Anyway, having the bottom meant that I could post all sorts of things from times-tables to much more interesting things on the bottom of the top bunk from my earliest years. (Gosh...bedtime and math seem to be awfully related ;)

You teach math and I teach Chess. And we both enjoy it very muchly =)

The desire to love it is all that's needed. So, let me know when you'd like to have your first lesson. My rates are very....accomodating...oh yeah, they're free :D

I think it's (almost....not quite) a sin to have someone pay you for Chess lessons. It's too much fun! =D

Your family 'pi plate' sparked another memory. At West Point it is a freshman's duty at meal times (all meals are family style) to do a number of very important things; including the cutting of all cakes and pies. There are ten seats at a table....but every meal can yield a different number of people actually sitting at the table. Plus, not everyone sitting at the table may want a piece of the pie. Therefore, it is incumbent on the lowly freshman plebe to be ready to cut the pie in any number of configurations, quickly and efficiently. Of course, the upperclassmen actually decide how many pieces are to be cut, so if seven people want pie they can determine that they really want fourteen pieces cut (two per person) or 15 (two per person plus one for the server ;) Of course....there is always a great deal riding on the proper cutting of said dessert because the standard-rule is that the smallest piece always goes to the highest ranking cadet at the table (who will certainly compare the size of his piece to the lower-ranking cadet sitting next to him and (very effectively) fein mock anger if he detects even the slightest irregularity in the aforesaid cutting. Now, new plebes are not allowed to use a template, but once you've goofed up the cake cutting enough times, sometimes the upperclassmen will require you to make your very own "pi template" and check at every meal to ensure that you have it with you, just in case the dessert happens to be one that requires cutting.

Oh the joys of being a cadet again! :-D =D

BTW, look for a blog post on Chess and Bridge and Dancing and Set coming soon,


Susan said...


Wow, you had intense stories for bedtimes. . . Did you have frequent nightmares? :)

I'm glad others got good-naturedly drilled in math by their parents :).

Times-tables brings back memories. My brother had a times table in his bedroom for years and my sister and I had an addition table. A great way to learn without trying :).

Heh, yeah, I kind of have to charge for teaching math ;). I feel the way you do about teaching sewing, though. It's just too much fun to charge to teach people sewing. I do it more for me than for them.

Ooh, is that Set as in the super-fun card game of patterns? That is addicting. . . And dancing - goodie, goodie. My sister and I learned some basic square dancing last fall and it was so fun.

Adrian C. Keister said...

Reply to Susan.

Well, there's a difference between enjoying math and wallowing in it. Hehe. You'll forgive if I come to some of my own conclusions...

I'm impressed with that public school. It sounds a bit like the public school Lane and I went to for our first three grades. (We were both homeschooled 4-12, oddly enough since we are twins.)

Dad's degree is in experimental low-temperature solid-state physics. He did his thesis on superconducting (you probably already know this, but it's the phenomenon of, when you cool certain materials below a threshold temperature, it develops zero resistance to electricity.) But Dad has never used that research since he did it. He has done mostly math since then, teaching at Covenant College for 14 years, then doing mathematical modeling for Alcon Labs in Fort Worth, TX, and finally mathematical modeling for 3M up there in the Twin Cities. He's my hero. :-)

I always knew Indiana was messed up.

No, the pie plate is not as horrid, because there's a pun on the word "pie" for one thing, plus there's only one very narrow theme for the entire object, in contrast with the math clock.

I'm glad you liked Dad's article; maybe someone will enlarge on it some day, and really get to the bottom of a Christian philosophy of mathematics. Whoever did it would have to take Godel into account.

In Christ.

Susan said...

Well, I may forgive your comment, but my mother may not. . . ;)

And now you say you always knew "Indiana was messed up"? That's another chalk against you. *shakes head sadly* That was not the correct response to that story. Perhaps I should have warned you that I was born in Indianapolis, as were my parents (who were also raised there) and Brother Dear. We're loyal Indiana Hoosiers. The legislature may have had issues a few centuries ago, but it's still the greatest state in the Union ;).

So now we're all confused. You were homeschooled for 4-12? I thought you went to a classical school in high school.

Ah, so your math and physics sides are explained. It's neat to follow in your parents' footsteps, isn't it? I think it thrills my dad that I'm teaching math like him :).

Susan said...

I said:
We're loyal Indiana Hoosiers.

Mother Dear thinks a clarification of this is necessary. There are two types of hoosiers. Hoosiers can generally refer to folks from Indiana (that would be us) and hoosiers can refer to IU folk. We're not IU people, just from the state of Indiana. . .

Adrian C. Keister said...

I think any state that decides that not only will the state not follow Daylight Savings time (if for no other reason than to be in sync with the rest of America, and the world) but only part of the state will not follow Daylight Savings, while the rest will, has got to have something wrong with it. That's all.

I do have relatives in Indiana; very nice ones. And, considering present company, I'd have to conclude that roses can grow out of the mud. Now, about this extreme geekiness so universally found in your family...

Ok, let me clear up the education question. I was in public school for grades 1-3. It was quite a good school as public schools go. Prayers over the PA system, corporal punishment, and they taught us to read in first grade using phonics. But then along came Ross Perot, and messed up the entire Texas public school system. So Mom and Dad pulled us out and began homeschooling. Now in relation to the classical form of education, I will say this: I think both Mom and Dad had read Wilson's Recovering the Lost Tools of Learning. They implemented some of that, especially in the grammar and dialectic traditions. The rhetoric was a trifle weak, in my opinion, but so few people these days have good dialectic, that I've found that almost to be more useful. They go together in the long run, of course. I really don't know how self-consciously Mom and Dad were doing classical ed. All I know is that what I got was great, really great. Sure, it could have been even better, but that's a given with any education. So does that clear that up? ;-)

In Christ.

Susan said...

Okay, agreed that Indiana's decisions on Daylight Savings time are rather odd. . . Do you know they just passed legislation to change that, if I'm not mistaken, so they soon will be in sync with the rest of America.

Okay, okay, my family is extremely geeky? You don't seem so normal yourself. You are the one who had so much "fun in a perverted sort of way" from solving a problem about coconuts. You're the one who felt the need to revenge against me for posting the above said problem. You're the one who's working on a doctorate in Mathematical Physics of all fields. Looks like a case of the pot calling the kettle black. . .

Ah, that explains your educational background. Not sure why I thought you weren't homeschooled before. My education wasn't classical either, though still very good. My mom doesn't understand the idea of tests being a sampling of required information, so she just asks everything - in detail; when I got to college I was rather disappointed how easy the tests were, thanks to her training :). And of course both my parents insured my math background was solid. . .

Adrian C. Keister said...

Well, finally! Indiana is going with the flow. Granted, I actually think Daylight Savings time is silly nowadays, with electric lighting that Benny Frank didn't have. But even sillier was not going along with it.

Now about this geek battle between us. You have to understand that it is as a family that I'm labeling this extreme geekiness. It's your whole family, not just one of you, or even two of you. In my immediate family, there are three geeks out of six. Your family is five-for-five. So, 50% versus 100%... And there's only a few more geeks total in my extended family (which is sizeable.) So overall, I'd say the percentage couldn't be more than 30%.

So in conclusion, geeks are a dime-a-dozen. I'm geek, and proud of it. So I have no issue making fun of them. Incidentally, have you ever visited I think your whole family would like it. Those people understand geeks, because they are geeks themselves! Talk about a sentient website...

In Christ.

Adrian C. Keister said...

Well, finally! Indiana is going with the flow. Granted, I actually think Daylight Savings time is silly nowadays, with electric lighting that Benny Frank didn't have. But even sillier was not going along with it.

Now about this geek battle between us. You have to understand that it is as a family that I'm labeling this extreme geekiness. It's your whole family, not just one of you, or even two of you. In my immediate family, there are three geeks out of six. Your family is five-for-five. So, 50% versus 100%... And there's only a few more geeks total in my extended family (which is sizeable.) So overall, I'd say the percentage couldn't be more than 30%.

So in conclusion, geeks are a dime-a-dozen. I'm geek, and proud of it. So I have no issue making fun of them. Incidentally, have you ever visited I think your whole family would like it. Those people understand geeks, because they are geeks themselves! Talk about a sentient website...

In Christ.

Susan said...

I was thinking, I thought it was Benjamin Franklin who first thought of daylight savings time. I was rather slow to connect him with "Benny Frank" ;).

Well, Sister Dear tries to reject her geekish tendencies and has managed to partially mask them underneath her humanities majors and minors. We're not all 100% geek. . . We each just have an appreciation for math and other various facts :). My extended family (which is also sizeable as my parents each have 5 siblings)doesn't have a great number of geeks either, though we do have a few math and engineering majors mixed in there. . .

Okay, I'll admit that admitting you're geek yourself does give you license to making fun of them. Same reason I freely tell blond jokes :).

Hmmmm, that geek website was. . . interesting. Looks like geeks are a whole separate market for products ;). The games all look interesting.

Adrian C. Keister said...

TOIC? Please see my replies to your comments on my blog for an explanation of this acronym.

In Christ.

Susan said...

Tie-off-it cordially :). *smirk*

Nah, instead I vote that we TIOC.