Why Math? What Math?
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[edit] Research Division
[edit] Math Attitudes Survey
See HERI reports
[edit] Why do so many people (students) hate math?
Hypotheses:
1. Because so much of what is taught is not applicable in most real-life activities.
2. It takes more thinking than doing. By which I mean: writing you can think about while working, math takes a lot of sitting and contemplation.
3. To some people, math is like a language. It makes you feel like you have to transcribe it in order to get anything done.
4. Math is such a huge concept. As the universe is limitless so is math. The size of the universe is absolutely terrifying. Perhaps it isn't a hatred of math but a fear of it.
5. Since there is a "correct" answer in math problems, there is less wiggle-room and you feel trapped in one process or way of doing it.
6. Since math is connected to the social idea of intelligence, it can make people feel like it is a greater feat then it actually is. Thus, the sense of failure increases.
7. Math is not really dynamic the way History or Biology or even a foreign language is. From a young age students are taught multiplication tables and learn to take for granted certain mathematical functions. Mathematics without context is about as fun as computing José's fence area when he could clearly just measure it. By using and discovering mathematics in real life, maybe this subject won't be so dry, lifeless, and hated.
8. Math is abstract. It deals with totally foreign, alien concepts like numbers and graphs that usually have no obvious bearing on the real world. With other subjects we can relate to things and in the process become interested: in English we can relate to the characters in the stories, in history we can relate to the old stories of other people, in social sciences we can relate to it because it deals with ourselves in large part, and even in science we can relate to factoids as they deal with real life. But in math, so much of it is so abstract, and attempts to make it "applicable to real life" are usually laughably bad. The old "if two trains leave different stations at the same time . . ." problem is not something which we will ever realistically have to solve. While mathematics can be applied more easily to certain fields, most of us do not go into those fields, making the whole subject seem pointless, unnecessary, and confusing. The fault here lies in part on the teachers (for sticking to the arbitrary problems of math instead of branching out into the real world) and on the subject, which is, after all, more abstract than other subjects.
9. Perhaps a reason for the mass math phobia is that it stacks on top of itself. In mathematics, you can't even sleep through one year, or you won't be able to understand anything in the following years. This applies to an extent to other subjects, but none to the extreme of math. Everything branches out from the basics, and things are constantly touched upon briefly that come back later as critical, so that if you are confused at any point or forget one thing, the entire subject will become an even worse struggle later. This branching is not so prevalent in other subjects: English can generally be taken book-for-book or poem-for-poem, and while themes may exist between them it is not so critical to understanding to see them; science has some intermingling of subjects, but generally you don't need to remember a thing from "physics" to get by in "chemistry;" history can easily be taken on a step-by-step basis (though it is enhanced if intermingling themes are seen in it). The only major subject that really shares this attribute is foreign language, which also requires that every little thing is remembered.
10. Too much of math education is based on raw memorization of facts. Nobody wants to have to sit at home and study the times tables or remember the quadratic formula. Nobody wants to do fifty problems, all in the exact same way, to get the technique engraved in their skulls. Often thought is discouraged in math, and we are forced to just memorize and regurgitate ideas that seem irrelevant to anything except the subject itself. In other subjects we are usually encouraged to think about things and be creative, or to give our opinions. It is unfortunate that math is often taught as the ultimate anti-opinion course, where the only colors are black and white and the only homework is monotonous repetition. Math as a subject has plenty of room for flexibility, creativity, and free thought. It is the fault of the way math is currently taught that these possibilities are not seized upon.
11. Sometimes math classes are taught too fast that a student who needs more time to learn a concept falls behind and can never catch up to the rest of the class, making the entire math class a struggle. Also, math does not exactly have a clear story, like history, that is enjoyable to follow. Finally, math seems to not allow a lot of creativity to make the subject fun.
12. Math is something that has a foundation of basic things one needs to learn (such as elementary school math) to be able to build upon. If one is missing that basic information such as the times tables and adding and subtracting, it becomes really hard to incorporate those things into a harder math problem.
13. Math is a completely different language than any other subject. It's full of numbers and rules and theories that you have to keep in mind while trying to solve a problem. There are many rules that are incorporated into a problem that you have to follow.
14. Where is the debate? math carries no arguable subject matter until the high school level. Kids who are upstarts (many) will have trouble identifying with the subject because there are very few arithmetic teachers that will entertain a discussion about the whys and nuances of the subject. The upstarts and those who would otherwise be interested lose interest and become disillusioned with the subject because it is not allowed to reach its abstract potential until it is too late.
15. Math and Science are two subjects that people use to signify how smart you are. If you're not good in neither, people assume you're not very smart. Therefore it's intimidating to take the lead in volunteering for problems, for fear of being wrong and embarrassed.
16. One factor that plays a huge role in why so many people hate math is that the people who tend excel in math are stereo typed to be very intelligent. This can make math a very intimidating subject to learn because you are constantly surrounded by such intelligent people.
17. Perhaps another reason why so many people hate math is because there is really only one answer to every problem. Math is taught in such a way that the student is attempting to solve a problem that has already been solved. This teaching style does not make for a tremendous amount of motivation to discover an answer that is already known.
18. Another thing that adds to the common dislike of math could be that it is not very easy to relate to the subject. In English and history, one can relate many of the characters or events to their own lives but it is very difficult to find something in common with a number!
19. Geometry has no shame.
20. Math is a lot like broccoli, when you're forced to have it as a child, you really can't appreciate it until you're older. By that I mean most people only do it as children because they have to. It all seems very practical at first and the life applications make sense because how else are you going to describe every day things like if there are buying gas or counting how many apples can fit in a basket, whatever. As the math you study becomes more advanced the applications get smaller and more focused (i would draw a graph, but this is a wiki) so as purpose leaves, the person is less willing to do it. Anyone would tell you addition subtraction multiplication and division are all required to live in our society, but when you get into geometry and calculus it doesn't make sense. It is only later in life that you can ever really have any hindsight about it and whether it was worth it.
21. People may not like math because it can all only be done one way, and the answer is usually just "because that's how it is." 2 + 2 will never equal 5 and that can frustrate some people.
22. Everybody learns differently, when we are in grade school we probably all heard about how some learn better visually, some through listening, and some just from reading bare facts. When you have a classroom filled with all these different "learners" and one teacher there can be problems. Most of the time, it just takes one thing to really make everything click for a person in a certain math problem, and that can be hard to establish thirty times over. Whether or not this theory of different learners is true, it is pretty obvious that there are different rates of learning math. That is why most schools have "advanced math" and "regular math" which can also be a problem for self esteem with those not in advanced. To sum it up, some people don't like math because it can be harder for them to learn it and may not have the best teacher for them personally.
23. Math can be rigid and surfaced. It leaves little room for people who are bursting with creative energy. Math is often taught with emphasis on the mind; while other subjects are taught with emphasis on the heart (i.e. art). People are often emotionally driven.
24. Math often installs fear and intimidation. People speak in words; not numbers. People like to be good at what they are doing (and right away). Math teachers often don't recognize student's fear of math and speaking in a language of numbers. Students are intimated further and give up on it.
25. Culture emphasis. It is cool to grab a guitar and make catchy tunes. You won't be in the magazines for solving a math problem unless its on a huge scale.
26. There's no room to make mistakes. There is only one right answer.
27. So much of what we're being taught in math classes is useless unless you want to be a mathematician, and it's frustrating for students to spend time learning material that has no real impact on their lives.
28. It takes someone that's passionate about any subject to get students bubbling with excitement about it, and if more math teachers had such a passion for their subject, perhaps there would be a much larger crop of mathematicians springing up in the world.
29. People hate math because, unlike other mediums where you can spit out something completely absurd or unitelligible and have it considered brilliant and unconventional, math has a very "set in stone" feeling about it. Many people feel creativity is discouraged.
30. Math is kind of like the shell-shocked/Vietanm-vet uncle in a family of hippies (everyone avoids him at Thanksgiving and Christmas).
31. The pyramid theory: you can't progress in math until you know EVERYTHING about the level that you're currently stuck at. Well, what if that level really sucks?
32. It is normal, perhaps even trendy to say "I'm not that good at math" in an apologetic tone of voice, whether one is capable with math or not. Thus, the middle range of people who are competent are hiding in shame, making everyone feel even more insecure about the subject, and unsure of who, if anyone, actually knows the stuff.
33. It is not until high school (or middle school in some cases) that many students get a teacher who is genuinely fired up about math. Often, elementary and middle school teachers are just as uncomfortable with the subject as their students, because they feel they don't really understand the concepts themselves, and their insecurities only make their teaching worse. The cycle then continues, producing another generation of teachers who lack confidence in their math abilities.
34. There is no sense of math as a living field, full of unanswered questions and possibilities, until either a Bennington education, or studying math in grad school elsewhere. It all seems dead and resolved, lacking only the toil of re-computation by the next generation.
35. because it is exceptionally nerdy to love math or to be good at math, more so than with other subjects
36. because of high tech calculators math is about "how you do it" so there isn't much creativity left.
37. math teachers are rarely able to explain why math works
38. Math is something associated with geeks who wear large, round, thick-framed glasses and pocket protectors. No movie has ever portrayed math as "cool". No one really knows the names of "rich and famous" mathematicians. To people for whom that is important, math may be unappealing.
39. Math is a language. And like any other language, math requires practice, memorization and constant use to maintain familiarity. People who don't love it, or have a job in which they use it frequently, may have a hard time keeping up.
40. Math is harder than most other subjects to teach to one's self. With history or English, you can just pick up a book, read it, learn something new. Math is something that must be taught; first the basics, and then what follows. If the teacher is bad, or too fast, or teaches in a different style than the student is used to, it is easy to become discouraged and bitter.
41. Like anything else, it's possible to have a negative experience with math which turns you off to the subject entirely. That might be kind of a no-brainer but it could account for some percentage of math-haters.
42. A couple different people have mentioned that math is "for geeks" etc. I think this is because, and this is especially true in America, we find it much more impressive to have natural talent than learned skill. It's difficult for anyone to be "talented" in math; obviously some people are far more predilected towards it than others, but theres no degrees of success in math; either you can do the problem, or you can't; there's no room for impressing people. I think this might be why we regard people who choose to specialize in math as "weird", or "brainy" or "geeky" or whatever term you want to use; why would you be interested in something which has little practical value, no immediately ascertainable aesthetic value, and can't even impress anybody other than your fellow math nerds? It creates an immediate degree of separation between the average person and a "math person".
43. Tying in to the above idea, there's also no personal reward inherent to math. When you spend 10 years playing piano 5 hours a day, at the end you can play a beautiful concerto that's as fun to play as it is to hear. When you spend 10 years doing math problems 5 hours a day, you can solve a complex equation and end up with a string of numbers that nobody except you can understand. Where's the fun in that?
44. It is difficult to have a discussion about Pythagorean' theorems unless you are hanging with math nerds. (i.e. math is something that is difficult to discuss in a normal social context)
45. Math is not personal, its very difficult to write something original in math, unlike literature.
46. Because we're more inclined to use words for communication rather than numbers.
47. They have a preconceived notion of what ‘math’ is from very early on – elementary school teachers may have their own notions about math, that it’s dry and unenjoyable, and even though they may try to hide it, it is translated through to the students in the very nature the class is taught.
48. Just as art appeals to certain people more than others, so does math – it may come easier to some, and certain aspects may be more or less enjoyable than others. However, just like art, math is for everyone – it just needs to be presented in a way that connects with the mathematician’s interests and passions, but all too often math is seen as isolated from the rest of the world, and that connection is rarely made in school.
49. It is difficult to be original and express yourself in math.
50. To many, solving a math problem may not be as rewarding as creating something original.
51. Students get discouraged when they learn math that they would have no use for.
52. For the most part math is taught in an unappealing way. Lecturing about numbers isn't going to get kids excited, it's going to make them tune out.
53. People think it is only for "geeks" and want to stay away from it instead of understanding what it is really about.
54. There is little motivation for math. People see math career options as 'boring' 'paper pushing' jobs usually involved with taxes and other unpopular fields.
55. They don't, they just get frustrated with the PROCESS and PRACTICE of math, they are secretly in love with math, they love their cars, and houses, and toasters, and other such things to do with math.
56. Some people hate that math keeps them up at night, they are lying there trying to get to sleep and they try counting sheep, but that leads them to thinking of numbers in general, and before they know it they are wizzing through the times tables and it's five AM...for instance.
57. They hate math because they feel distanced from it, it is numbers, we talk and think in words...and what they don't realize is that math is absolutely everywhere, because they haven't seen it yet, and no one has bothered to show them.
58. Too many people today are not willing to put in the effort required to grasp a good understanding of Math. Americans especially are accustom to this mind set of seeing results immediately, and anything that requires time and extended amounts of effort to understand is too difficult.
59. In the High School that I attended it was a very competitive setting where everyone had to be in the advanced level classes and had private tutors for the SAT’s and AP exams, along with everyday classes. My Chemistry teacher once said that the majority of the students were really good at regurgitating the information that they were given, but were lacking in independent thought. Many students took advanced level math classes, but for the majority, seemed to struggle in this class above others. Formulas can be memorized, but the independent reasoning and thought that math requires is foreign to those who are used to succeeding by memorizing.
60. It is difficult to relate math to other preconceived knowledge; in regards to the question of “why do I need to learn this?”, but also in the sense of Math being like another language. Math requires abstract thought that can be difficult to fathom and if the student is not willing work for the understanding of it, they will probably not understand it and thus dislike the thing that confuses them.
[edit] Why do so many people love math?
Or, let's admit: all of us love math sometimes. What is it specifically that we are enjoying in those moments?
Hypotheses
1. Jason hit upon something (if I do say so myself) when he wrote the CANINE/BUDGET puzzle on the board. What makes this a fun puzzle is that there is only one answer. The puzzle would be lame if it had two answers; you would lose that "EUREKA!" moment, the "I Found It!" It's only fun to say "I Found It!" when there's an obvious "It" to find. So one of the things that is so frustrating about math - that there's only one answer - is also one of the things that makes it fun (when it is).
2. It's challenging. After all, nothing ventured, nothing gained. There's nothing like the sense of accomplishment when you untangle a complex, seemingly impossible math problem and come out with a simple, perfect answer - the right answer. Yeah, it's hard, yeah, it's seemingly worthless, but the triumph you get when you do it right is all the sweeter because of this.
3. There are some really cool concepts in math. There's more than just the dry "blah blah blah" of it; there's techniques which allow you to tackle problems dealing with infinity, there's brilliant proofs of simple theorems which fill you with awe, there's all sorts of weird "coincidences" where seemingly arbitrary numbers like pi or e show up again and again . . . if you look past the heaps of obnoxious algebra, there's some rewarding and interesting subject matter here.
4. Math can be found everywhere (specifically what comes to mind is Fibonacci) link
5. Math is like a good puzzle or a mini contest. Finishing a hard problem correctly is like earning a really tasty cookie.
6. Math is another language you can immerse yourself in and get lost in doing a problem. It's a good work out for your brain and many people enjoy the challenge. Plus, if you're just naturally good at math it's a good bragging tool. Math also holds the key to many physics problems that still remain a mystery to us. Math builds upon itself and can create answers to questions we never knew.
7. Math is involved in almost every aspect of our lives as human beings. Time management is math. Humans may appreciate/love math without their awareness of it. You can't create an expressive photograph in the dark room without measuring your chemical equipment.
8. Think about the films: The Beautiful Mind or Good Will Hunting. If you are exceptional in math it gives you (most of the time) a brilliant reputation. It is as if you can speak a language that others can't even start to understand.
9. Math = money. Money can be used to buy big houses, to pay for research to provide clean water to those who do not receive it, and much more. Whether money is being used for honorable purchases or selfish ones... the world revolves around it.
10. I must admit, I have a pretty big crush on Sudoku puzzles. I suppose that's that not really math... Even though I've never been terrific with the concepts of math, I have always found comfort in numbers...literally. I enjoy counting. (Sudoku is definitely math, or at least logic-based!)
11. Puzzles and riddles are wonderful ways of stretching our brains. I personally love math when it relates to what I'm already interested in, regardless of subject lines. There are some days when a good graph is my best friend.
12. Math is like art – it’s for everyone and can be enjoyed by everyone, and what is considered fascinating is unique to each person. Those who love math have found what is fascinating about it to them, just as someone who loves art has fallen in love with a particular aspect of ‘art’ that resonates with in them.
13. Math is comforting in its rigidity. Through my experience, I’ve found that many mathematicians (especially the ones that really get into it) are actually rather insecure. This comes off as foreboding and uncompromising. Math, in a sense, is a refuge for those who feel deeply insecure about the world around them – math is concrete. It is steadfast. You could trust your life with math and rest assured you’d be saved every time. And that’s what they do – they let it control the chaotic world around them. Unfortunately, they are also confining themselves to what is definable, to what can be translated into the language of math. This doesn’t mean you need to be insecure to enjoy math – it means math gives us something sturdy to hold onto, like a walking stick or something to fall back on, like the comfort of leaning against a tree.
14. Math makes things make sense.
15. Who doesn't love to solve problems? Mathematics is always an adventure in finding answers. Definite answers. Do senators ever have definite answers? No.
16. If you ask a girl on a date and she says "maybe" it's awful. The answer to 2+2 or the intersection of y=3x+6 and y= -2x+3 will never be "maybe."
17. It's not something you just make up out of nowhere, it's there, right there, and everywhere, and you just have to tap into it.
18. It is extremely satisfying to know that you are the only one in the class that understands a complicated math problem.
19. There is something about math that is uniquely human. In thinking mathematically we explore, play with, question, and relate to that which can not be touched, seen, proven or objectified. It is a way of thinking unconcerned with objects, but rather with relations.
20. In math one can and does construct a universe out of nothing (the void, the empty set, the null set ... whatever you want to call it), what could be more creative than this?
21. Math is ontology. We may not be able to prove this but it is exciting to think about.
22. Math, like art, is a human language.
[edit] What reasons do teachers give to explain their professional choice of teaching math?
[edit] What reasons do parents give for wanting their children to study math?
They want their children to have a "well rounded education".
[edit] Research on Doing Research
1. Purposes and Methods of Research in Mathematics Education This is a .pdf file.
2. an introduction to survey design
3. avoiding pitfalls when conducting a survey
4. Teppo, Anne, ed. Qualitative Research Methods in Mathematics Education. ISBN-10: 087353459X ISBN-13: 978-0873534598 No clue if this one is worth it or not.
5. whether or not qualitative research is appropriate to your purposes
6. Rachel Wentz has an introductory book on doing research that has a chapter on survey design (and potentially other relevant chapters). She needs it this week (thesis design), but after that we can borrow and photocopy it.
7. Survey and Questionnaire Design Tutorial
8. Basic info on how to go about creating a survey. http://www.statpac.com/surveys/
9. A few tips on survey design -- similar to link 2.
10. Basic overview of psychometrics.
11. Analyzing Quantitative Data - a little verbose?
12. Wordy explanation of how one goes about presenting qualitative data.
13. http://www.surveysystem.com/sdesign.htm
14. http://www.surveysystem.com/sdesign.htm
[edit] Research on Other Schools
Selected Quantitative Literacy Programs in U.S. Colleges and Universities:
This is the .html version, because my computer/firefox is having a lot of difficulty opening the .pdf original. Macalester is on this list, Elon isn't.
(Fun note: I can't format this link with single brackets and the title, perhaps because the link is stupidly long. ~Sasha)
Tip: Use www.tinyurl.com to convert long links to short ones.
Macalester's Quantitative Literacy Main Page
I can't find anything interesting about Elon's math department. Has anyone else had more luck?
~Sasha
"Designing Surveys: A Guide to Decisions and Procedures" by Ronald F Czaja
In high school my math program was called "Integrated Math". I found a blog discussing a similar program, so here it is: [1] -Lindsey
Williams College makes math fun! puzzles & and a prize!
http://www.collegenews.org/x5026.xml
On Colorado College's Academic Layout
[edit] Research on Testing/Surveys
Here's where we can put links to testing and theories on surveys and other things.
1. Scantron machine for $450, makes testing a lot simpler Scanner
2. Intro to Survey Methodology and Design
Hi, this is Jordan, here is the website for the advertising company IAG (Intermidiate Advertising Group) and an explanation on what they do:
http://www.iagr.net/au_overview.jsp
3. Hey this is Emma, just did some research on survey design- I am not sure how helpful these sites are but take a look.
Hyman, Survey Design and Analysis, Free Press, New York, 1955. On reserve. Start reading at p. 66; eventually you will phase out and skim. Pay attention again starting from p. 126 to p. 172.
[edit] Curriculum Division
A brainstorm of specific proposals (for discussion in class):
1. Bennington should require all applicants to take the ACT math test. Only the subscore in Pre-Algebra/Elementary Algebra will be considered. This is a subscore based on 24 out of the 60 questions on the ACT math test - specifically, the 24 questions that deal with basic operations using whole numbers, decimals, fractions, and integers; place value; square roots and approximations; the concept of exponents; scientific notation; factors; ratio, proportion, and percent; linear equations in one variable; absolute value and ordering numbers by value; elementary counting techniques and simple probability; data collection, representation, and interpretation; understanding simple descriptive statistics; properties of exponents and square roots, evaluation of algebraic expressions through substitution, using variables to express functional relationships, understanding algebraic operations, and the solution of quadratic equations by factoring. No student will be admitted to Bennington College with a subscore below 11 in Pre-Algebra/Elementary Algebra. (Half of ACT test-takers score below 11 in Pre-Algebra/Elementary Algebra; see ACT's norms.)
2. Along the lines of the visual arts lecture series, there should be a Quantitative Thinking Lecture Series.
3. Along the lines of Joe Holt's "Code Critique" class, Bennington should offer a "Math Critique" class every semester. Students with math-intensive projects could present their work and their questions/problems in class.
4. Along the lines of the writing tutors, Bennington should have math tutors.
5. Bennington faculty from the full range of disciplines should collaborate in the writing of the Bennington Math Manual. The Manual is a textbook for self-study. It skips a lot of the traditional topics (such as trigonometry) which are only useful for specific disciplines (such as physics). Instead, it focuses on ideas and techniques that are powerful and practical for real-world policy discussions. For example: a vocabulary of diagrams, with discussion of what's at stake when we make them; how to use simple math in non-simple ways, such as making order-of-magnitude estimates; the basics of simple and not-so-simple statistical techniques; and pointers to the best resources for further study. The Manual would include questions and problems, with answers provided. It would also include exercises to be done on the Web, in Excel, etc.
6. Every fall, Bennington should offer a Quantitative Thinking class with no maximum enrollment and no prerequisites. The textbook for the course is the Bennington Math Manual.
What are the likely consequences of each proposal? Which consequences are positive? Which negative? What are the financial or budgetary implications? What could be done to "patch up" problems with each? How could a given proposal become a reality? Finally, why should anything be done about this at all?
--
General thought: We want to make it so that whatever we do here responds to the realities in the "hate" section as well as the realities in the "love" section. (Bearing in mind that we don't have any realities yet, just personal intuitions.)
I want to draw two "boxes." Once you draw the boxes, it is easy to think of things that go into each one. The hard part is getting the boxes right in the first place, so that the discussion of what goes into them is a fruitful one. So, here goes:
Box 1: At Bennington, everyone learns...
Box 2: At Bennington, everyone can learn...
The stuff that goes into the first box is stuff that seems so central to living a productive and examined life that we would be comfortable committing to it as a college. Note that when I say "everyone," I mean everyone: not only the students, but also everyone on the faculty! And any interested staff members too. If it's not important enough for everyone in our community, it doesn't belong in the box.
Most of what's in the first box, in fact, will not be "mathematical." I suspect that in Box 1 we will want lots of things such as mediation; improvisation; sketching and diagramming things; speaking in front of others. Interestingly, this will require faculty to learn new things. I don't know anything about mediation...but I would like to! And I would have to, if it goes into Box 1. That's what it means to commit to that.
Box 1 is very different from a "core curriculum." For one thing, it doesn't revolve around course offerings. These capacities will arise in all kinds of contexts - mediation in the context of a theater production, improvisation in the course of giving a science talk. Even the formal teaching structures can be much less formal than a 14-week course. They can be brief 3-week seminars that come and go from time to time...one-off lectures...etc. Also different is that the contents of Box 1 can change. There will be a continual conversation about what we're doing and why. As each cohort of students moves through the College, the needs, priorities, and values will shift. The goal is not for a centralized committee to engrave it on a stone tablet.
The stuff that goes into the second box is stuff that some people may from time to time need to have, in order to further their work. To say that everyone can learn it means that we have built the kinds of institutions that make this possible: Course offerings, mini-courses, curriculum materials, reference books, a cadre of people who have done it before, etc.
Some guesses as to what might go in the boxes:
- At Bennington, everyone learns:
- About logic, bad logic, hidden assumptions, rhetoric, and propaganda
- Analyzing graphs
- Basic graph comprehension (decoding graphs, unpacking their message)
- Mature graph comprehension (Where did this data come from? By what methods was it collected? What is the agenda behind it/ why are we being shown it?)
- What it means to make rational decisions in complex situations
- How to summarize complicated data/situations/arguments, and what is gained and lost by doing so
- A sense of large numbers, estimating orders of magnitude (from AMC)
- How to use spreadsheets, web programming, and desktop publishing tools
- Basic ideas of causality as captured in the notion of relative risk and 2x2 tables
- At Bennington, everyone can learn:
- How to design experiments (n.b., we have an existing course in the curriculum)
- Qualitative research methods (ditto)
- Advanced methods of data analysis (factor analysis, multiple regression,
- Epidemiological research methods
- GIS research methods
Box 1 is a WHAT question. Box 2 is a HOW/WHO question.
To try to work through these questions without respect specifically to math, please go to General Bennington Curriculum.
Alan Shoenfeld's article, "Purposes and Methods of Research in Mathematics Education", Notices of the AMS, June/July 200
Sample bit of curriculum for A Vocabulary of Diagrams
1. Make a network showing who in your circle of close friends is close friends with whom; or who in Darfur is killing whom; or which countries export oil to which countries; or etc.
2. Think of a situation in your life where you had to make a difficult decision with real consequences. You could be in this situation now, or if you’re not, put yourself back in the situation you were in then. What made the decision difficult? A lot of options? A lot of uncertainty? A lot of consequence? A lot of ignorance? Differing value systems among the decision-makers? All of these? What else?
Try to write a dispassionate cost-benefit analysis for your situation.
- What is the basic decision to be made?
- What are the factors to consider?
- What are all the available options?
- What don’t you know that you ought to know before making the decision?
- What do you do if you want to maximize upside potential? What do you do if you want to minimize downside risk?
Think about using a 2×2 matrix, a flow-chart, a collection of brief scenarios describing possible outcomes, or some other diagramming tool to help you think about the situation.
It may help to adopt the viewpoint that you are not the person who is actually in the situation, but that you work for this person—like they are a big CEO, and they have to make the call, and you are the advisor who has to give them what they need to do it.
3. Make a list of all the teachers you have ever had - but give them code names, or serial numbers, to maintain anonymity. Organize them into a 2x2 matrix according to the Skill/Will dichotomies.
4. In the file [[4]],
- Describe the verbal score data (mean, range)
- Describe the math score data (mean, range)
- Make a scatter plot. Fix the scales on the axes so that you can see what is going on.
- Summarize the trend, i.e. how do a state's verbal and math scores generally relate?
- Describe the outliers
Look at Phil Daro's great scatter plot; sort of a 2-by-3 table.
Look at the poker cheating scatter plot.
From Sasha: Engage the Brain: Graphic Organizers and Other Visual Strategies, on Amazon.com This is a teacher book for using graphic tools to help kids learn. This is the Kindergarten one, but there's links on that page to grades 1-8. In 6-8 books, it's by subject... I wonder how good these books are.
[edit] Dialogue Division
[edit] Next Visitor
Who? When? Where? What should we do to prepare ourselves? What should we do to prepare our guest?
- This is Emily, I found this guy, Mike Byster, who is on a mission to make math fun. He's wants to tour the country sharing his ideas. Here's a link to a 20/20 article on him and his website:
http://abcnews.go.com/2020/Story?id=2690724&page=1
- Ron Cohen: Faculty Member in Psychology
- Oceana Wilson: Director of the Library
- Ken Himmelman: Dean of Admissions
- Dina Janis: Faculty Member (Drama)
- Susan Sgorbati: Faculty Member (Dance)
- Robert Moses: Founder of the Algebra Project
- Laura Zimmer: My sister, teaches 4th grade in San Diego, CA private catholic school
- Ann Shaw, JRZ's mother-in-law, 7th grade math teacher in Irvine, CA
- Joe Holt: Programmer, Bennington Professor
- Whoever's behind this website(Check it out)
- Patricia Martin, author of the The RenGen.
- Dan Kunkle, trigonometry teacher, and Headmaster of the Gould Academy, A prep school in Maine.
- Bill Quirk, adviser of NYC HOLD http://www.nychold.com/
- Betsy Sherman, to speak on genetics and learning
[edit] Joe Holt - Faculty Member, Computing
Joe has agreed to meet with the class on Thursday the 27th. Please use this space to draft some questions we may want to ask him.
Some questions we may want to ask could deal with his math experience throughout his life and whether he thinks it affected his like or dislike for math.
1. Does he believe that if he was bad at math throughout his schooling would he still have developed an interest in Computing?
2. What are the basics of computers formed upon?
3. If you breakdown the inside of a computer, how much of it deals with math or is math?
4. Do computers read only in math?
5. Is the basis of every computer language math?
6. How important is it for students to have a basic understanding of math in order to use a computer?
7. How do you feel about math/computing at a liberal art college as opposed to say Harvard, Stanford, etc. ?
8. How did Joe Holt become interested in computing? Was it through something else? When did he become interested?
9. Is math simply a tool through which he works, or is it something which is inspiring in and of itself, like art?
10. What is the curriculum model for the code critique class or classes that are similar to it?
[edit] Ken Himmelman - Dean of Admissions
Ken will be coming on Monday the 24th. He is co-teaching the design lab Rethinking Education with Liz Coleman, which I believe is the basis for the invite. What do we want to ask Ken?
1. How does one become dean of admissions?
2. How do statistics play into his job and the math that goes along with them?
3. What are his views on math in higher education, especially here at Bennington, but also what he thinks about it's place in other colleges and universities.
his background
his role as dean of admissions
role sitting on lots of data; what has he studied on that? involve students? they know the business.... interviews lots of prospective students; generalizations? science/math students at BC here also for X? do we have affirmative action or math/science here? is it a priority of his to increase enrollments in science classes? how does SAT-optional policy affect that mission? how does he explain math at bennington to prospective students
his role in teaching design lab
does he feel like he's learned anything from this yet?
his role as father of school-age children
sent jz an email once asking what jz thought about the math program at his kids' school where do they go? what grades? does he or does she help them with math? could they?
Gordon, Kane research from the Brookings Institution on how to identify effective teachers (and how you can't) here
[edit] Previous Visitors
Ryan Moran, his site
Where did you get the skills required for this work?
Came with design skills, some stuff learned on own
Wanted to make alarm clock in flash Picked up a book about flash and did it in two weeks
Physical computing - learned microprocessing to get a project done
Once you figure out one mode of logic, or one language, easier to get more
Learned lots of languages
Each successive language is the inventor's take on what the previous languages lack
- Partially style-driven, individual thinking style
- Partially problem-driven, existing languagues don't work well for some purpose
On learning a new programming language/skill:
- "Sit down with the documentation", with a specific project in mind - the project needs drive your path through the documentation
These projects in computing have informed his thinking about all subjects - literature, art, math, even physics - their ways of thinking.
"Thinking like a computer is not so much thinking like a computer, but thinking like the series of people who have developed these languages." Perhaps this is what math could be more like: thinking the thoughts of the people who have developed the ideas.
The satisfaction of finding an algorithm that works, that accomplishes what you want.
Referred to Tufte's ideas about the satisfaction involved in solution to an information design problem.
Kind of a thrill to think like a robot sometimes!
Hypothesis about why people's feelings about math are what they are: (1) The key events are early in one's education; (2) It's due to the teaching methods, which make people computers or in any case don't engage people in rich thoughts - organic thoughts - thoughts that help people make sense of their life and world - not necessarily concrete or practical thoughts.
Enjoys abstraction, systems, axiomatic systems, with a unifying, philosophical bent.
Look for video showing in Kinoteca at end of term
Working on the virtual graffiti board/shelter in the Sonoran desert, linked to website
[edit] News and Agendas
END OF TERM PAPERS. Must be at least 10 full pages, double-spaced, 12-point Times New Roman, 1-inch margins, 8.5-by-11 inch paper. (Diagrams welcomed! But they must be in an appendix, and the appendix will not count towards the ten pages.)
On Thursday 11/8, come to class with an outline for your paper - or at least some typed-up initial thoughts (at least a page).
Paper topics:
I. Visitors to our class included Ryan Moran, Joe Holt, Ken Himmelman, Ethan/Suzanne/Jess, and [soon] a couple of students from the Rethinking Public Education Design Lab. What did each person have to say? What did you learn from each person - whether they talked about it or not? What do their examples & stories have to teach us about math at Bennington or a Bennington education generally? Feel free to add the instructor to the list of people you discuss.
II. "At Bennington, everyone learns...". What topics, skills, capacities, powers, etc., would you put in this category? For each item, explain why the item is important enough to belong there. Do you think that under the system we have now, most students at Bennington gain these powers as a matter of course during their time here? If not, how would you make sure that everyone does? As part of your investigation, interview three professors; ask them what _they_ would put in this category (and why); and ask them if _they_ think that most students at Bennington already gain these powers as a matter of course during their time here.
III. Whenever we draw a diagram, map, table, scatter-plot, flow-chart, or the like, in response to a real-world conflict/disaster/dilemma, we inevitably summarize...simplify...reduce...abstract...and distance ourselves from the situation. Is this OK? Is this worthwhile? Do we do more harm than good when we do this? Explain with reference to examples.
IV. What does it mean - and what does it take - to make a complex decision _rationally_? When (i.e. for what sorts of decisions) is it important to be rational, and why? Does being rational about a complex decision require us to put our humanity aside - or does it actually require that we bring our full humanity to bear? (What constitutes our humanity anyway?) As a starting point for this topic, read my blog post "So Far, So Good." Ground your arguments in particular examples of complex, fraught, awful decisions from real life. I can give you suggestions if you want.
V. "The New Initiative" at Bennington. (1) What is "the New Initiative"? Use a variety of sources to address this question, and cite them. (2) In what ways is the New Initiative a continuation/extension/articulation of Bennington's core values, past and present? To address (2), you will have to describe Bennington's core values past and present. Use a variety of sources to research this point, and cite them. (3) In what ways is the New Initiative in conflict with (or in tension with) Bennington's core values, past and present? (4) What are the most important challenges facing the New Initiative, how should they be addressed, and how/why would the actions you suggest be effective in surmounting the challenges? Another possible theme to pursue: What impact will the New Initiative have on Bennington over the next five years? (Help me flesh this out better.)
Next term, Kerry Woods is teaching a 2-unit class on the visual display of information - sounds great!
I will be teaching a class about summarizing information, drawing inferences from data, and proving your point. This class will continue some of the themes we are on now, while also covering various statistical methods. My class and Kerry's class would be a nice combination. :)
Agenda for 2007-10-29:
- Announcements
- Can someone from Rethinking Education present to us
- SEPC
- Paper due at end of term (see topics above)
- Lewis Carroll's syllogisms in Steve Martin's reminiscence
Puzzle # 1
(a) All babies are illogical.
(b) Nobody is despised who can manage a crocodile.
(c) Illogical persons are despised.
Puzzle # 3
(a) No interesting poems are unpopular among people of real taste.
(b) No modern poetry is free from affectation.
(c) All your poems are on the subject of soap-bubbles.
(d) No affected poetry is popular among people of real taste.
(e) No ancient poem is on the subject of soap-bubbles.
Agenda for 2007-09-20:
- Debrief on Ryan Moran's visit
- Discuss next visitor and to-do's associated with that
- Collect and discuss sample surveys
- Discuss & record themes among the hypotheses
- Relate to what Hyman says about this kind of work
- List survey design resources people have found; discuss sources; use Schoenfeld as example
- Decide action items for Monday
- Read selections from Hyman noted above, also ...?
- Read Ericsson stuff
- Ideas on delivery method, populations, etc.
- Disuss the two suggested "boxes" (see above under Curriculum Division)
- Discuss idea of having a debate
Agenda for 2007-09-17:
- Take attendance
- Ryan Moran
- Debrief on talk "The Silent Campus: Why Academia is Irrelevant to America"
- HERI
- Became a conversation on the nature of the liberal arts; if interested, see "Risky Business", jz's blog entry
- List survey design resources people have found; discuss sources; use Schoenfeld as example
- Discuss & record themes among the hypotheses
- Make agenda for JH's visit
- Send for JH's approval
- Other visits
- Decide action items for Thursday
- Read selections from Hyman noted above, also ...?
- Each group to read selected survey design materials and create 2-page sample survey - 3 groups on students, 2 groups on teachers, 1 group on parents
- Ideas on delivery method, populations, etc.
- Disuss the two suggested "boxes" (see above under Curriculum Division)
- Discuss idea of having a debate
[edit] Math Zone
Lewis Carroll puzzle:
The only animals in this house are cats. Every animal is suitable for a pet, that loves to gaze at the moon. When I detest an animal, I avoid it. No animals are carnivorous, unless they prowl at night. No cat fails to kill mice. No animals ever take to me, except what are in this house. Kangaroos are not suitable for pets. None but carnivora kill mice. I detest animals that do not take to me. Animals, that prowl at night, always love to gaze at the moon.
Here's a neat website that I found interesting. The Mathematics of Love
This is Sasha. I heard a few people asking for puzzles, riddles, etc. last class, so I thought I'd post these two sites. One is an online game (uses flash), sort of a cross between a maze and a rubiks cube, the other is a huge compilation of riddles of all kinds, including lots of math ones. Happy hunting!
http://www.flashgames24.net/games/3dogic.html
http://www.ocf.berkeley.edu/~wwu/riddles/hard.shtml
Jason's 9/10/2007 blog post makes a conjecture about prime numbers.
Ivar Peterson's Math Trek Archives Strange blog-esque articles of all kinds. Sadly, he seems to have stopped in December, 2003, but there's still quite a few articles, and lots of matter to mull over.
Just testing the new mathematical typing capabilities that Joe Holt added: 
Calvin and Hobbes dealing with math religiously +1
An interpretation of the algorithm outlined by Joe Holt, the number guessing one, in a program written by Matt Nunes (In C++): Number Guessing Program
[edit] Groups
[edit] Background Info.
Older stuff, boilerplate, brainstorming...all at WMWM Background
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