Identifying Problems...ok Math Opportunities

Metacognition (thinking about thinking) is the feedback loop or the "little voice in your head that you hear when you do Math -- such as add 4 to each side and divide both sides by 2".

Self-awareness of knowledge and skills can be achieved by categorizing Math problems into types of problems.  The ability to identify problem types can refine learning and bring clarity while increasing the enjoyment and flow of Math opportunities.  This is especially important in Math as gauging the level of challenge can help students know what to study and how to invest their time and energy under peak perfromance coniditions (tests).

It is a problem that they call them problems --  so how about Math opportunities?

Math can Build Non-Cognitive Skills too!

Studying Math may seem like a purely academic endeavor but it improves focus, persistence and self-advocacy which are takeaways that are "life skills".  This article quotes Dan Pink author of Drive on parents focusing on academics at the expense of "life skills" but school can also fuel these skills and talents that can then be applied to any endeavor whether academic, athletic or otherwise.
New York Times on Determination and Deliberate Practice

Planning for Success in Math and Life

A planner is vastly different than a calendar.  A calendar keeps track of appointments and scheduling but a planner focuses on prioritization and short- and long-term planning!

The Personal Digital Assistant (PDA) has become a common tool in school and business and many people use their phone to store their calendar and appointments.  While the Treo phone has a very basic calendar --I went back to the low-tech paper version of Franklin Covey Planners -- the Weekly pocket format.

The planner inspires vision and goals which leads to thinking about the Important but Not Urgent tasks such as studying for next week's exam, filing your taxes or scheduling an annual checkup.  In addition to feeling more inspired and organized, perusing your paper planner is more socially correct than glancing at your phone.  A zipperable planner protects your plans from the elements (like a water bottle!) and offers a place to store a pen or pencil. Zippered Planner Binders

Franklin Covey offers Plan Plus Online which can be reached from any web browser -- planning on paper or on-line can raise productivity and motivation to stay focused and reach goals.

March 2010 Brain Teaser Solution

Amanda went to the mall to buy supplies. She spent 1/2 of what she had plus $2.00 in the first store. Then she went to the second store and spent 1/2 of what she had left plus $1.00. In the third store, she spent 1/2 of what she had left plus $1.00. In the fourth store and last, she spent 1/2 of what she had left. After all of her purchases, she was left with only $3.00. How much money did she start with and how much did she spend in each store?

Amanda started with $64
she spent $34 in store 1
$16 in store 2
$8 is store 3
$3 in store 4

she spent a total of 34 + 16 + 8 + 3 = 61
therefore she has $3 left


After store 1 she has x - (1/2x + 2) which becomes 1/2x -2

then store 2
1/2 of answer 1 - 1

so 1/2(1/2x - 2) - 1

1/4x - 1- 1
so after store 2: 1/4x - 2


then store 3
1/2(1/4x-2) - 1

1/8x - 1- 1

so after store 3:1/8x - 2

then store 4:

1/2(1/8x - 2)

1/16x - 1

this is = 3

1/16x - 1 = 3

add 1 to both sides

1/16x = 4

x = 64

After store 1 she has 1/2(64)-2 = 30
so after store 2: 1/4x - 2 = 1/4(64) - 2 = 14
so after store 3:1/8x - 2 = 1/8(64) -2 = 6
then store 4: 6/2 = 3

How Far Can Math and Patience Take Kids?

Patience is a virtue!!  Math builds space telescopes and also life skills such as persistence and endurance.

Washington Post article on Math and Hubble -- the sky is the limit! has some great quotes from Neil deGrasse Tyson, director of the Hayden Planetarium in New York, "who gets to peer into the starry great beyond for clues to the origin of the universe. "

"Tyson earned a bachelor's degree in physics from Harvard and a doctorate in astrophysics from Columbia, but it was at the Bronx High School of Science in New York where he learned to not to be deterred when the going gets rough. " 
"I remember the transition from algebra to calculus and thinking: 'I will never in my life figure this out. I better try something else.' How many people do we lose because they don't think they are getting it as fast as they should? What I did was take a little bit at a time. Over the months, it was [as] though a misty fog began to dissipate and I was slowly emerging with a fluency in the new and powerful symbols of calculus."

Author Courtland Milloy encourages schools and parents to inspire students by showing an interest in Math and Science ;)

Academic Support Is Helpful ;)

At Xavier, Nun Works Out Players' Academic Side

Many students can benefit from this type of support.


It is great to see an article on academic coaching even if the main focus is on sports.

Robin Schwartz

Founder, www.mathconfidence.com

Author, Build Math Confidence e-newsletter

Helping Students Know What They Don't Know

This is in response to Willingham Helping Students Know What They Know in the Washington Post's Answer Sheet column with guest columnist Daniel Willingham.

Test taking is a skill that can be developed -- especially if one focuses on thinking about their thinking processes (metacognition).
As a Math peak performance coach (and former engineer / MBA), I help students to know what they know and know what they don't...to know where the traps are and what could go wrong. Often students do know the material better than their test scores show -- points can be lost due to not reading/answering the questions carefully!!

Engineering school taught us this attention to detail --please click on this link to my mathconfidence blog:

http://mathconfidence.blogspot.com/search/label/metacognition

Robin Schwartz
Founder, www.mathconfidence.com
Author, Build Math Confidence monthly e-newsletter

Core Standards Team Members...add Industry and GED

The Math Core Standards Team Members includes many Math educators from colleges, K-12 teachers and supervisors at the district level.  Also included are people from the College Board and Achieve.  From the academic perspective, GED experts would add to the discussion.

It would be also be interesting to add people from industry/corporate to see what employers would like to see in employees.

Common Core Standards Draft Released

The Common Core Standards are an initiative to standardize American public education.
Each state has had its own disparate (sometimes a very long list) standards.

The comments are open to the public until April 2nd.
In New York, the link is: Toolkit for Common Core Standards NY
To post comments: http://www.forms2.nysed.gov/emsc/ocis/ccssm.cfm

Do Not Pass Go, Do Not Collect $200 (Math as a gatekeeper)

COMPASS is used by CUNY and many other colleges for Math and English placement. 
COMPASS Placement Test Pre-Algebra and Algebra provides sample questions and info about the test.
Practicing for this placement test will help students potentially avoid remedial classes saving time and money and keep them on track to their educational and career goals.

Near(ly) Perfect Squares

Perfect squares are great landmarks for Mental Math. Math has changed since 19XX as calculators have changed the way that Math is taught and learned and tested. Increasing Mental Math ability increases confidence, empowerment and self-reliance.

Nearly Perfect Squares
Perfect squares (like 4^2 = 16 and 5^2 = 25) can help people find close facts like 3 x5 and 4 x 6 (answers are both one less than the perfect squares) .
This will work for:
9 x 11 (99) = 1 less than 10^2 (100)
19 x 21 (399) = 1 less than 20^2 (400)
29 x 31 (899) = 1 less than 30^2 (900)
and for any number!!
(x-1)(x+1) = x^2 - 1 always one less than x^2

Somewhat Nearly Perfect Squares
Perfect squares (like 4^2 = 16 and 5^2 = 25) can help people find somewhat close facts like 2 x 6 and 3 x 7 (answers are both four less than the perfect squares) .
This will work for:
8 x 12 (96) = 4 less than 10^2 (100)
18 x 22 (396) = 4 less than 20^2 (400)
28 x 32 (899) = 4 less than 30^2 (900)
and for any number!!
(x-2)(x+3) = x^2 - 4 always four less than x^2

February 2010 Brain Teaser answer and solution

Solve for a, b, c, d, and e.

a (b + c + d + e) = 128
b (a + c + d + e) = 155
c (a + b + d + e) = 203
d (a + b + c + e) = 243
e (a + b + c + d) = 275

Check out the prime factors of each of the numbers.
155 = 5 x 31...therefore b = 5
203 = 7 x 29...therefore c = 7
243 = 3 x 81...therefore d = 3
275 = 11 x 25...therefore e = 11

a (b + c + d + e) = 128
a(5 + 7 + 3 + 11) = hey this doesn't work

ok let's try 243 = 9 x 27 so d = 9
a(5 + 7 + 9 + 11) = a ( 32) therefore a = 4
4(5 + 7 + 9 + 11) = 128

Check:
5(4 + 7 + 9 + 11) = 5(31) = 155
7(4 + 5 + 9 + 11) = 7(29) = 203

9(4 + 5 + 7 + 11) = 9(27) = 243

11(4 + 5 + 7 + 9) = 11(25) = 275

so: a = 4,b = 5, c = 7, d = 3, e = 11

GED as a Possible Standard

http://voices.washingtonpost.com/class-struggle/2010/02/crawling_toward_national_tests.html

How about using the GED as a high school standard?According to the ACE that administers the GED, "Only 60% of graduating high school seniors would pass the GED Tests on their first attempt". http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_Fact_Sheet_v1_2010(3).pdf

Since institutions already accept the GED as an established standard, it would be interesting to consider the GED as an exit exam rather than defining new ones.
For lower grades, SAT or ACT (or placement tests like Accuplacer or COMPASS) could be used as goals (whether or not these exams cover what is needed, they are already an accepted standard).

Math Helps People Think Better

Seth Godin writes:
Can you factor this?
If you're like most people, you get a little queasy at the thought. And when you were in tenth grade, you surely wondered why they were bothering you.
(the answer is (x-2) times (x-2), in case you were curious.)
It turns out that the real reason you needed to do this work was to be able to play with numbers in your head. Abstract numerical thought is an important skill among educated people.

My response:
Great analogy...except no queasiness ;)

Why Take Math comment on about.com

http://math.about.com/b/2010/02/08/why-take-math.htm#gB3

Instilling Core Values with the Life Skill and Discipline of Math

Info for Parents on Math Ed

http://www.wheresthemath.com/Pages/informationforparents.aspx

This advocacy group based in Seattle has been a strong proponent of parental involvement and curriculum choice.

Checking Up on Student Understanding

http://www.denverpost.com/education/ci_14350149

In this the article, the reference is to POP (Proof of Purchase) -- some call them exit slips. Sometimes I call them checkpoints. A short quiz at the end of class or at the end of a lesson (within a class) can help both students and teachers assess what they know and what they still need to learn.

The GED is a Common Standard

http://www.acenet.edu/Content/NavigationMenu/ged/test/math.htm

A Common Core accepted standard is the GED.

Kids Need Work to Do

http://voices.washingtonpost.com/answer-sheet/homework/give-kids-homework-while-schoo.html?referrer=emaillinkpg
With beforeschooling and afterschooling, just add snowschooling ;)

Letters on Playing to Learn

http://www.nytimes.com/2010/02/08/opinion/l08teach.html?ref=opinion

Two of the letter writers would like to see elementary Math education to go beyond the four operations.
"In addition, in any mathematics curriculum, including early childhood, children are capable of learning much more than the four basic operations. Where are geometry and early algebra? What about logic, measurement and estimation?"

The same letter writer as quoted above also points out the lack of social studies in Engel's ideal early schooling.

What should a 12 year old know?

http://www.nytimes.com/2010/02/02/opinion/02engel.html?ref=opinion

Reading out loud is a terrific skill to develop!

However, by age 12, other Math concepts can be added to the four operations -- especially the middle school merry-go-round of fraction/decimal/percent.

Division with Fractions 1 and 3/4 divided by 1/2

This is an example from Liping Ma's book:

Using Decimals
How much is 1.75 divided by .5?
1.75/.5 = 3.5


Using Fractions
1 and 3/4 divided by 1/2
1 and 3/4 = 7/4
7/4 divided by 1/2
How many half cups are in 7/4 cups?
1 half cup = 1/2
2 half cups = 2/2 = 1
3 half cups = 3/2
4 half cups = 4/2 = 2 -- this is too much

7/4 divided by 1/2
multiply 7/4 by the reciprocal of 1/2
7/4 x 2/1 = 14/4 = 7/2 = 3 and 1/2

Division with Fractions is "a topic at the summit of arithmetic". In the introduction, she asks a division with fractions question: 13/4 divided by 1/2 and offers three additional problem-solving methodologies (besides Keep, Change, Flip) -- Dividing Using Decimals, Applying the Distributive Law and You Don't Have to Multiply.

Checking Multiplication with Casting Out Nines

Multiplication can be checked using Casting Out Nines. (rather than long division)

By studying the digits in the problem and comparing them to the digits in the answer, we can gain confidence that we have done the problem correctly.

Here are some examples:
12 x 12 = 144
The digits in 12 add up to 3 (1+2)
The digits in the other 12 add up to 3 (1+ 2)
3 x 3 = 9 (144 adds up to 9)

13 x 13 = 169
The digits in 13 add up to 4 (1+3)
The digits in the other 13 add up to 4 (1+ 3)
4 x 4 = 16 (169 adds up to 16)
We could also add up the digits in the 16 of 4 x 4 and get 7
and get 7 in the answer by casting out the 9 in the 169 so we are left with a 16 that add up to 7.

125 x 4 = 500
The digits in 125 add up to 8 (1+2+5)
The 4 is just a 4
8 x 4 = 32 and the digits in 32 add up to 5
The answer 500 also adds up to 5.

What You Know About Math?

Great and enthusiastic fun video about the TI-84
http://www.youtube.com/watch?v=Ooa8nHKPZ5k

Learning Math Takes Patience

Feature on an award-winning Calc teacher in North Carolina who emphasizes practice for improvement and likens the process to bettering athletic ability. The article also talks about how Math attitude affects students and performance.

Personal Finance Classes in High School

This is such a needed app for Math and Life!!

Economics is also terrific but can be theoretical rather than practical.

Math provides the foundation for processing and understanding personal finance and economic terms to increase savviness and savings while reducing debt.

Singapore Math Success

Singapore Math in Focus is hailed by students and teachers.
http://www.kentucky.com/142/story/1109176.html

ACCUPLACER: College Placement Exam

The ACCUPLACER is used by many colleges for placement into Math and English.
Passing these tests is important in order to avoid non-credit remediation classes.
The title link goes to a page with a pdf of sample questions for both Math and English.

Tips for the ACCUPLACER:
http://www.collegeboard.com/student/testing/accuplacer/accuplacer-tips.html

Where is the GED?

While states are spending money and resources on exit exams, it would be interesting to think about using the GED as a standard. According to this document, only 60% of graduating high school seniors would pass the GED Tests on their first attempt:
http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_FactSheet_20092.pdf

GED sample questions:
http://www.acenet.edu/Content/NavigationMenu/ged/test/prep/sample_questions.htm

Math Show for Preschoolers

This new Nickelodeon preschool show will debut on January 25th.
Web site of show
http://www.nickjr.com/team-umizoomi/


http://www.nickjr.com/family-entertainment/kids-books/nickjr-quick-picks/best-math-books-for-kids.html

Math Quiz by Arthur Benjamin in the NY Times

http://www.nytimes.com/2010/01/03/education/edlife/03quiz-t.html?ref=edlife

E-Newsletter Brain Teaser December 2009

Ann went from Point A to Point B.

Simultaneously Peter went from B to A.
In six hours they met and in another three hours Peter reached A.
How many hours did Ann travel from A to B?

Peter’s total travel time was 9 hours.
Assume both travel at a constant speed:
Let’s pick a speed for Peter…60 miles per hour so Peter will travel 540 miles altogether (as will Ann). He travelled 360 miles in the first 6 hours and 180 miles in the last 3 hours for a total of 540 miles.

after 6 hours, they were both much closer to A than to B


A----------------X---------------------------------B

If Ann took 6 hours to travel her 180 miles (540-360), she was only travelling 30 mph.
So it will take Ann 18 hours to travel from A to B. (540/30)

If we pick another speed, let’s say 100 mph for Peter
So he travelled 600 miles in the first 6 hours and 300 miles in the last 3 hours for a total of 900 miles.

If Ann took 6 hours to travel her 300 miles, therefore she was only travelling 50 mph.
So it will take Ann 18 hours to travel from A to B. (900/18)

Many apologies for a typo, the original problem in the e-newsletter said:
In six hours they met and in another three hours Peter reached B.

Adding It Up on WNYC

http://blogs.wnyc.org/news/category/education/adding-it-up/

Adding It Up multi-part series from WNYC on remedial Math experiences at LaGuardia Community College

Wired for Math

http://www.nytimes.com/2009/12/21/health/research/21brain.html?_r=1&hp=&pagewanted=all

Brain researchers in cognitive neuroscience are finding that young children can learn Math in preschool. This changes the idea that students need to be at least 5 until their brains are ready for Math.

SAT Skills Insight Pinpoints Strategies

http://www.collegeboard.com/testing/sat/skillsmap/select-interval-mathematics.html

This link connects to SAT Skills Insight that helps students find and developstrategies based on their current score.

COMPASS

http://www.act.org/compass/sample/pdf/numerical.pdf

Elementary Math is Misleading

A retired engineer tutors his 4th grade granddaughter in Math and finds that the standard algorithms have been upstaged by regrouping, estimated and calculator Math.

http://suburbanjournals.stltoday.com/articles/2009/12/19/stcharles/opinion/1220stc-opsh0.txt

This Is Your Brain on a Test

http://blog.newsweek.com/blogs/nurtureshock/archive/2009/12/15/this-is-your-brain-on-a-test.aspx

Carol Dweck, researcher at Stanford (formerly at Columbia), wrote about the Growth and Fixed mindset in her terrific book Mindset http://www.mindsetonline.com./

In the study mentioned on the Nurture Shock blog on Newsweek.com, Po Bronson renames the Growth mindset Knowledge-Hungry and the Fixed mindset Grade-Hungry. The Knowledge-Hungry learners were open to learning from their mistakes. Developing this perspective can help students and their teachers and parents to address the "non-instruction" part of learning and teaching.

The Ten Commandments of Mathematics

http://www.doe.virginia.gov/Div/Winchester/jhhs/math/humor/tencommd.html

The Ten Commandments of Mathematics for Students...LOL

Why Do I Need To Know This?

A great piece on the why question!

http://www.examiner.com/x-29491-Topeka-K12-Examiner~y2009m12d8-Why-do-I-need-to-know-this

Math Scores Do Not Show Much Progress

http://s.wsj.net/public/resources/documents/st_math1208_20091208.html



Based on NAEP

This Wall Street Journal on-line resource includes a sortable table of cities, 4th grade scores, 8th grade scores, etc to compare and contrast results.

Math's Double Standard from Achieve

http://www.achieve.org/files/Achieve-MathWorks-FactSheetDoubleStandard.pdf

While people understand and emphasize Reading and Writing, many see Math is a different light. Math Works is an Achieve program -- Achieve is an educational reform organization founded in 1996 by corporate leaders and state governors. Some of its goals is to create common standards, to increase high school diplomas and their worthiness and to advocate for better prepared college students and workers. Click here for more info on Achieve http://www.achieve.org/AboutAchieve.

Math vs. Reading from Math Works

From Achieve's Math Works

Things you never hear about reading and writing
(but often hear about math).
“I’m just not that good at writing, so why bother?”
“When will I actually use reading and writing in the real world?”
“Only nerds like to read and write.”
“I’m just not smart enough for writing.”
“My parents can’t read, so why do I need to learn how to read?”
“It’s just a fact that guys are better at reading than girls are.”
“I’m not a writing person; it doesn’t come naturally to me, so
why should I try?

National Educational Standards...Leadership

http://www.nytimes.com/2009/12/05/opinion/05herbert.html?_r=1&ref=opinion
This Bob Herbert op-ed piece outlines a new Harvard Ph D in Educational Leadership that will emphasize reform, learning and policy. He discusses the challenges of public education in our country with its video game culture and high dropout rate.

Leadership is essential in education at the national, district, school and classroom level. Will add some leadership links later in the month.

Math Works from Achieve

From Achieve's web site:
Far too many students in the U.S. give up on math early because it does not come easy and they believe only students with innate ability can really be “good” at mathematics, a notion that is all too often reinforced by adults who believe the same thing. Yet, in most other countries students accept that mathematics—especially advanced math courses—can be challenging, but know that with enough motivation and perseverance, they can learn difficult material. The uniquely American attitude towards math—the perception that only people who are naturally gifted at math are good at it—leads to a dangerous corollary: that it is ok to be “bad at math.” This is a significant factor in the comparatively low math achievement of students in the U.S., which
limits students’ education and career options and makes it harder for the U.S. to compete.

What's Your Math IQ? (By grade level)

http://www.mathnasium.com/mathiq.htm

Engineers as Role Models (besides athletes and entertainers)

http://www.nytimes.com/2009/11/24/science/24educ.html?_r=1&hpw

The White House is starting a campaign to promote Math and Science ed...maybe this will help STEM (Science, Technology, Engineering and Mathematics) 's PR ;)

Warning from Free Rice

WARNING: This game may make you smarter. It may improve your speaking, writing, thinking, grades, job performance...
www.freerice.com

Checking Homework and Metacognition (Thinking about Thinking)

http://blog.newsweek.com/blogs/nurtureshock/archive/2009/11/18/at-what-age-do-you-no-longer-have-to-check-your-children-s-homework.aspx

This Newsweek article by Po Bronson, author of Nurture Shock, is titled "At What Age Do You No Longer Have to Check Your Children's Homework?". This is a complex question as many middle schoolers are still developing metacognitive skills for self-evaluation (do I get it?) and the maturity for self-advocacy (I should see the teacher).

Free Rice Has Math and Vocab and More!

http://www.freerice.com/subjects.php?t=27627787492

The United Nations World Food Program's Freerice.com raises awareness of world hunger by donating 10 grains of rice for every correct answer. Besides Math, there's Art, Chemistry, English, Geography and Language Learning.

Coolmath's Math Survival Guide

Very witty and funny ;)

Might think of the wording from a different perspective -- like Thrive with Math. or Math Enjoyment Guide!

Her very terrific web site is www.coolmath.com

Algebra II Regents Sampler

http://www.jmap.org/JMAP/RegentsExamsandQuestions/3-AdobePDFs/CompactExams/Algebra2Trigonometry/fall09ExamA2_EV.pdf

The sampler for Alg II includes trig, abs value inequalities, function definition, logs in non-Base 10, trig identities, imaginary numbers, negative exponents, stats, inverse functions, domain of a fucntion, binomial expansion, compounded interest, sequences, Law of Cosines.

As far as informing SAT prep, abs value inequalities, function notation, summation, negative exponents, equation of a circle, and solving algebraic equations.

US Coalition for World Class Math

http://usworldclassmath.webs.com/

Habits of Mind from Studying Math

From The Opportunity Equation:
"Math and science embody habits of mind and methods for discerning meaning that enable students to learn deeply and critically in all areas."

Goal; Much Higher Level of Math and Science Learning

http://www.opportunityequation.org/

"The Opportunity Equation: Transforming Mathematics and Science Education for Citizenship and the Global Economy"

The Carnegie Foundation and IAS at Princeton have published a report entitled "The Opportunity Equation" about the importance of Math and Science education. An interesting fact is that most of the authors and advisors are college and corporate level -- classroom teachers and educational administrators may contribute ideas and perspective.

The Lessons of the Good Teacher

http://www.nytimes.com/2009/11/04/opinion/l04teach.html

Bedtime is Book Time, Math in the Morning

This blogger who has a 7 year old and 5 year old muses on the popularity of bedtime stories and would like Math to get its fair share of time ;)
This might also fall into the category of beforeschooling (working on homework with your kids in the morning before school) !! (as opposed to afterschooling -- working on homework with your kids in the evening/afternoon)

Math Learn It Live It Love It

SAT Scores

Math up 40 points since 19XX.
Verbal average up 250 points.
Overall, Critical Reading bested Math by 30 points and Math bested Writing by 60 points.

Math 750 (97th percentile)
Critical Reading 780 (99th percentile)
Writing 690 (95th percentile)

Before the test, when I walked into the room,a teen asked "Are you the proctor?". My response "No...I'm on the other side!". The test is long...the snacks and breaks really helped. Did not get a Math section until the 5th section! The essay will be up on line on 11/3 -- mine included "Little House on the Prairie", M*A*S*H, World War II and The Pink Panther II to answer if humor helps people through rough times.

http://www.collegeboard.com/student/testing/sat/scores/understanding/percentiles.html

Now, when is the SAT II given? The ACT?

Confusion vs Information

http://thisisindexed.com/2009/10/needles-and-haystacks-and-such/

Do you see a connection between Math and peak performance?

Posted on Linked In by Math Confidence:
Do you see a connection between Math and peak performance?


Responses to Math and peak performance question:

Math is one of several activities that build confidence. Math is unique, however, in stimulating the ability to take a creative initiative in thinking. This ability carries over into many facets of personal and professional life.


Math has giving me so more confidence in other areas as well. This is why I am trying very hard on getting my son to love math for what it is. It makes you think in many differenct directions.

Farm Questions on State Tests

Can downstaters relate to corn stalks and farm animals?
;)

The Numbers Game

This is a brain training exercise

http://books.google.com/books?id=Me5yLtWRamcC&pg=PA79&lpg=PA79&dq=the+numbers+game+kroehnert&source=bl&ots=k7w_Lt0AaB&sig=LzcCEPqFipiETeZxBhiA6W-Al3o&hl=en&ei=Hi3fSpLaEs_clAe-puSnAw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAsQ6AEwAA#v=onepage&q=&f=false

Marvin Gardner Math Puzzler Extraordinaire

The last line says it all, it's the EUREKA!!!

"When you figure out the answer, you know you’ve found something that is indisputably true anywhere, anytime. For a brief moment, the universe makes perfect sense. "

International Test Math Problems

Click on the link to see Washington Post's Jay Mathews education column containing (PISA Programme for International Student Assessment) questions.

Comparison of NY with National Exams

From http://documents.nytimes.com/state-and-federal-mathematics-tests#p=7
"Results of federal math tests released Wednesday showed little or no progress by the country's fourth and eighth graders since 2007, the last time the tests were given. New York State's students fared much worse than they did on the state's own standardized tests: while 87 percent of the state's fourth graders and 80 percent of eighth graders were considered proficient on state tests, only 40 percent of fourth graders and 34 percent of eighth graders met that standard on federal tests."

Click on the title to see the 4th and 8th grade 2009 NY Math tests plus a link to NAEP sample questions.

Are the state tests too easy?

Today's New York Times' cover reads "U.S. Math Tests Find Scant Gains Across New York: Scores Renew Criticism that Albany Testing is Just Too Easy".


The state tests appear to be too easy compared to the national tests:

Grade 4 Samples of NAEP (National Assessment of Educational Progress): http://nationsreportcard.gov/math_2009/sample_quest.asp

Grade 8 Samples: http://nationsreportcard.gov/math_2009/sample_quest.asp?tab_id=tab2&subtab_id=Tab_1#chart

Number Puzzles from the Science Times

Still working on this one ;)

Multitasking and Studying

This title links to a Science Times piece on multitasking and studying. The research is not conclusive but the article is thought-provoking and personal as the author includes her own adolescent and young adult children's work and study habits.

A Sample of GED Math

The title of this posting links to the NY Times article on the GED in New York State.

Please click here for sample Math questions fromt he GED's web site:
http://www.acenet.edu/Content/NavigationMenu/ged/test/math.htm

Practice questions from educational publisher Steck Vaughn:
http://steckvaughnadult.hmhco.com/en/gedtestmenu.htm

Calculation Nation Games from NCTM

These can be accessed by non-NCTM members by using a guest pass.

The SAT Essay

Two more days until the SAT. The Little House on the Prairie books will hopefully help as the Ingalls family endures many hardships that will answer prompts such as:

You have twenty-five minutes to write an essay on the topic assigned below.

Think carefully about the issue presented in the following excerpt and the assignment below.
Many persons believe that to move up the ladder of success and achievement, they must forget the past, repress it, and relinquish it. But others have just the opposite view. They see old memories as a chance to reckon with the past and integrate past and present.
—Adapted from Sara Lawrence-Lightfoot, I've Known Rivers: Lives of Loss and Liberation

Assignment: Do memories hinder or help people in their effort to learn from the past and succeed in the present? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

Goals for Math Classes: Reasoning and Sense Making

This brand new NCTM (National Council of Teachers of Mathematics) guidebook Focus in High School Mathematics: Reasoning and Sense Making highlights reasoning opportunities in five specific content areas of the high school mathematics curriculum.

Reasoning with Numbers and Measurements
Reasoning with Algebraic Symbols
Reasoning with Functions
Reasoning with Geometry
Reasoning with Statistics and Probability

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

Confidence and Knowledge

Came across this link through an ACT article in the Wall Street Journal.
Confidence and knowledge and learning go hand in hand ;)

The Original Article
http://online.wsj.com/article/SB125065253283242295.html#articleTabs%3Darticle


The Poster's Comments (includes the Knoweldge Factor link)
http://online.wsj.com/article/SB125065253283242295.html#articleTabs=comments#comment394900

34 = 65

This article by Diane Ravitch highlights the curve of Regents exams. On the Regents administered yesterday 30/87 (34%) results in a passing score of 65. With higher standards and clearer meaning of scores in grades 3- 8, expectations and learning will improve.

Here's the link to the article: http://www.nypost.com/seven/08132009/postopinion/opedcolumnists/toughen_the_tests_184289.htm

Taking the SAT 10/10/09...long time since 19XX

Sue Shellenbarger's article was inspirational -- only 8 more weeks until the SAT.

http://online.wsj.com/article/SB124337711110856009.html#articleTabs=comments#comment199886

http://digg.com/educational/WSJ_com_High_School_Senior_I_Took_the_SAT_Again_After_41

http://mathconfidence.blogspot.com/2009/05/would-you-ever-retake-sat.html

Take Away the Stress, Multiply the Fun, Divide and Conquer

The print ad says "Add KENKEN, Take Away the Stress, Multiply the Fun, Divide and Conquer

Brain Fitness for $9.95 ;)
http://www.kenken.com/

Teach Back example

This student-made poster was based on Teach Back questions on Unit Conversion and was a key part of the Teach Back process.

The Benefits of the Teach Back method

The Benefits of the Teach Back method

The Upside of Test Prep: The Teach Back

The Teach Back method uses sample assessment questions for learning and teaching in the classroom.