Discomfort and Learning

People love patterns and categorizations. Students laugh when I say "this problem is exactly like the last one but completely different." A good example of overgeneralization is the equation of a straight line y = mx + b where m = slope and b = y-intercept.

Everything is cool and groovy with y = 2x + 5 (slope 2 and y-intercept 5)
or y = 4x+ 8 (slope 4 and y-intercept 8)

but what about y = x (where slope 1 is invisible as is y-intercept 0)?

This New York Times article "How Nonsense Sharpens the Intellect" has research and ideas about promoting learning and creative thinking through novelty and anomalies.

SAT Tips from the College Board

SAT Tips from the College Board


Below are some tips that will help you do your best on test day.
Before Test Day
Get organized:
Make sure you have two No. 2 pencils and a soft eraser. Pens and mechanical pencils are not allowed.
Have your SAT Admission Ticket and acceptable photo ID ready.
Check your calculator and put fresh batteries in it.
Bring a watch to time yourself. Use a watch that has no audible alarm—separate timers are not allowed.
Prepare snacks to take. A healthy snack will help keep you alert during the test.
Prepare yourself like an athlete:
Get plenty of sleep the night before the test. Your brain will work better if you are rested.
Eat a good breakfast that morning.
On Test Day
Leave your cell phone at home. If your phone rings during testing, it could cost you your scores!
We strongly advise you not to bring a cell phone or any other prohibited electronic device to the test center. If your electronic device makes any noise, or you are seen using it at any time—including breaks—you may be dismissed immediately, your scores may be canceled, and the device may be confiscated.
This policy applies to any prohibited digital and/or electronic device such as a BlackBerry®, pager, iPod®, MP3 player, camera or other photographic equipment, or separate timers of any kind.
Check to see if your test center is open.
Tune in to your local media, like you do for school closing announcements.
Check online for a list of test center closings.
Leave early. Get to the test center no later than 7:45 a.m., unless otherwise noted on your Admission Ticket.
Go to the center listed on your Admission Ticket.
Even if it's not your first choice, you are only guaranteed admission to the test center on your Admission Ticket.
You will be charged an extra fee if you go to a different test center, and a seat may not be available for you.
Arrange your ride home ahead of time. Your testing may end a little before or after the times listed below. If you are testing with extended time, ask the supervisor for approximate finish times.
For the SAT, plan on being picked up at approximately 12:45 p.m.
For SAT Subject Tests™, plan on being picked up at the following approximate times:- 9:45 a.m. for one test- 11:15 a.m. for two tests- 12:30 p.m. for three tests
Taking the Test
Make sure you use a No. 2 pencil. Follow the instructions on your answer sheet when filling it out.
Keep focused:
Use breaks to eat or drink any snacks you have brought with you.
Pace yourself. Each question counts the same. Don't spend too much time on any one question.

Answer to Sudoku question from 9/29/09

There are 5 numbers missing and they are 1, 2, 5, 7, 8

Once you choose the first one (out of five), there are four left to choose from
Once you choose the second one (out of the remaining four), there are three left to choose from
Once you choose the third one (out of the remaining three), there are two left to choose from
Once you choose the fourth one (out of the remaining two), there is only one left

For example, if you first choose the 7 then remaining is 1, 2, 5, 8
Then if you choose 1, then remaining is 2,5,8
Then if you choose the 8, remaining is 2 and 5
Then if you choose the 2, the 5 is left over by default.

So the choices are: 5 x 4 x 3 x 2 x 1 = 120 different numbers that can be possible answers to
"a nine digit non-repeating number that ends in 6349"

Sudoku...how many possible numbers?

This cartoon shows a man asking a woman,
"What's a nine-digit nonrepeating number that ends in 6349?"

How can we figure out how many possible answers there are that would fit this criteria?
(without listing them all)...

Answer will be posted tomorrow (Weds 9/30/09)

Flow, Long-Term Goals and Stress Management

While being immersed in any kind of flow state (where time evaporates) is desirable, those with long-term goals seem to be the most fulfilling. Studying technical content like Math can be so absorbing that time and mind disappear making the 'problem at hand' more pressing and pleasing than any other problem one may have.

It would be interesting for mental health professionals to recommend brain fitness exercises as a stress management strategy.

New York Times Magazine on Education

Interesting perspectives from Geoffrey Canada (Harlem Children's Zone), Diane Ravitch and others on How To Remake Education.

Math = Awesomeness

This are examples of Teach Back posters made by students in College Algebra ;)

Core Standards for Math

http://www.corestandards.org/

This is an interesting initiative supported by many governors, the College Board and Achieve in a quest to form national standards.

Motivation in the Math Classroom

http://www.nctm.org/resources/content.aspx?id=16481
Tips for teachers (and parents and students) from the National Council of Teachers of Mathematics (NCTM) for motivation including goal setting, focusing on effort and by encouraging cooperation.

SAT as a Predictor

While success can be based on many factors, some fields of study use the SAT as a measure of 'keeping up with the Joneses'. Engineering schools want high Math scores (to follow along with profs who write a dozen equations on the board); likewise, journalism schools want high verbal scores.
Because grades are subjective, the SAT is a broader indicator. Due to the absence of a national curriculum, we can think of the SAT as a unifier for a reasonable body of knowledge for high schoolers.
As a Math peak performance coach, I have found that studying for the SAT can be challenging and entertaining while promoting brain fitness at any age. Although I graduated from college in 19XX, this October 10th I will take the SAT to gain perspective, to have fun, and to boost mental fitness.

Click here for the SAT Question of the Day http://apps.collegeboard.com/qotd/question.do

Click here for related blogging on the SATs
http://mathconfidence.blogspot.com/search/label/SAT

What Do the Scores Mean?

Are students more proficient? Is the test the same difficulty level?
Read this NYT article about the score needed to pass the NY state test:
http://www.nytimes.com/2009/09/14/education/14scores.html?_r=1

Brain Fitness for Success Link

Brain Fitness for Success at the College Board Forum 2009
http://www.collegeboard.com/events/forum/2009/homepage/index.html
Forum 2009: Education and the American Future
New York City October 21-23, 2009

While students would like relevant content, they often view the classic high school math curriculum (algebra, geometry, trigonometry) as the least applicable topics of their courses. However, quantitative reasoning can improve metacognition (thinking about thinking) and is an excellent way to boost knowledge and skills. Participants will discuss the concept of brain fitness, with special attention to how math can enhance critical thinking, problem solving and confidence. Participants will develop strategies and identify opportunities to implement the brain fitness perspective to foster student commitment and to improve their college access and success.
Speaker(s): Robin Schwartz, Adjunct Professor, College of Mount Saint Vincent; Founder, Math Confidence, New York

Math in 2009 is different than 19XX -- The Graphing Calc!

The TI-83/4 is an easy-to-use graphing calculator that allows teachers and students to understand, teach and learn Math differently than in 19XX.

While we were asked to do lots of computations and use trig and log tables, today's students are asked to be analytical. Using the calculator on the SAT is actually more of a distractor than a help as the questions posed are reasoning rather than number crunching. Please see the Wall Street Journal (http://online.wsj.com/article/SB125244891686393811.html) for an update on TI's latest N-Spire graphing calculator...many teachers are keeping their 84s due to its ease-of-use -- in half an hour, students can learn enough to be dangerous ;)

Here's the link to mathconfidence's comment: http://online.wsj.com/article/SB125244891686393811.html#articleTabs=comments#comment450823

WSJ Cartoon

Being right is not as important as working on problem-solving ':>)

The Teach Back for Algebra and Prealgebra

This was written in response to the following question:
Can you help me with tips on teaching algebra?
I start next week teaching Algebra and Pre-algebra part time. I may think the gubject is great, but I'm looking for ideas on how to get the kids 'hooked', and help them continue to embrace teh subject with enhusiasm. So I'm looking for ideas and for classroom tools, etc. And I'd like a network to seek input & help as needed throught the fall.


Hi Steve: Best to you on teaching algebra and prealgebra. How long are the blocks? A variety of instruction can work well and keep kids engaged -- lecturing, working in groups on the same worksheet, working with calculators, Power Point, chalk-and-talk, and especially the Teach Back. The Teach Back is working in groups on different content. It is a very effective tool for review and test prep as it engages students to be responsible for their own learning. Working in groups (each with a unique Math opportunity), students solve problems, write solutions and present their findings to the entire class. As each group finishes, they are given the entire packet of problems so that they can learn from one another and maxmimize performance on their exam. By increasing participation and fostering a culture of teamwork, learners improve their skills and test scores while building confidence and camaraderie. Please see the two attached links. Thanks, Robin the Math Lady
Links:
http://mathconfidence.blogspot.com/search/label/Teach%20Back
http://archive.constantcontact.com/fs086/1102574170134/archive/110259616631...

Attention and Learning

Jessica Hagy's Indexed http://www.thisisindexed.com/ uses xy graphs to relate two things to each other.

Graphing Calculator - Top 10 Back-to-School iPhone Applications - TIME

99 cents for a portable graphing calculator -- have not seen it up close but a student said he would download it this week:

Graphing Calculator app on the iphone

Master Teacher Mindset by Robyn Jackson

Jackson outlines strategies for teachers and students to enhance learning and maximize student potential and performance. Her philosophy incorporates key ideas from Mindset by Carol Dweck and The Art and Science of Teaching by Robert Marzano.

Here are her seven principles:

Start where your students are
Know where your students are going
Expect to get your students to their goal
Support your students along the way
Use feedback to help you and your students get better
Focus on quality rather than quantity
Never work harder than your students

Cheat, I mean, Reference Sheets

The slope formula…the distance formula…the midpoint formula – ARGH!
With all those x sub 1s and y sub 2s, these formulas or maybe they’re equations..HMMM…anyway, get all jumbled and misapplied.
As an adjunct Math prof, former engineer and ‘Robin the Math Lady’, I help people to build Math Confidence through metacognitive strategies.

How much does a cheat sheet help? If Math = formulas, then it would indeed be cheating. But problem-solving is so much more. In engineering school, our open book untimed exams with only 3 problems would take 6 or more hours and a ‘C’ would be welcomed with open arms! Some profs allowed just one piece of paper. It took days to craft a crowded cheat sheet chock full of problems (ok, opportunities) with a 0.5mm mechanical pencil. This process helped us know our strengths and weaknesses for maximizing potential on our exams (ok, assessments).

Now as a prof, I encourage homework and classwork on cheat sheets for reference points
so that learners can size up the challenges and tackle them under peak performance conditions (tests). Cheat sheets boost confidence, performance and enjoyment of Math and learning!

Brain Fitness for Success at College Board Forum

Title: Brain Fitness for Success
Description: While students would like relevant content, they often view the classic high school math curriculum (algebra, geometry, trig) as the least applicable topics of their courses. However, quantitative reasoning can improve metacognition (thinking about thinking) and is an excellent way to boost knowledge and skills. Participants will discuss the concept of “brain fitness,” with special attention to how math can enhance critical thinking, problem solving and confidence. Participants will develop strategies and identify opportunities to implement the “brain fitness” perspective to foster student commitment and to improve their college access and success.

Presenter: Robin Schwartz, Adjunct Professor, College of Mount St Vincent; Founder, Math Confidence, New York
Thursday 10/22/09, New York City

College Board's Forum 2009: Education and the American Future
New York City October 21-23, 2009