Borland Educational News and Views

Wednesday, July 01, 2015

Math Exploration Station

Playing with particular objects in particular ways is the best way to learn early math concepts and develop instinctive number sense crucial to success in the study of mathematics.

Building a “Math Exploration Station” at home is a great way to help children hone critical math skills while playing! All you need is a small table and bookcase, manipulatives and other math-centric toys like Tinker Toys, blocks, Legos, etc.

Don’t forget good ol’ paper, pencils, felt pens, and crayons for drawing and designing. We had a family friend who was an early computer scientist, and I remember going through reams of surplus wide-format dot-matrix printer paper as a young child in the early 1960’s on which I happily drew everything from complex forts to rockets to abstract free-form doodles.

The best place for early learning is in the home, and the best way is when the mind is opened through play.

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borlandeducational.com

Monday, June 01, 2015

Math Makes Sense with Manipulatives

Mathletes and early computer scientists had recently won World War II, Soviet scientists were threatening to militarize Earth orbit after Sputnik in 1957, and so the goal was set in the late 1950's that the United States would aim to quickly boost the quality of mathematics education.

Emphasis was shifted from wrote memorization of “facts and formulas” to discovery-based experiential learning. The goal was for K-16 students to understand deeply the math they were learning, rather than merely repeating facts or algorithms robotically without knowing why. Grade school math homework now involved mathematical theory in addition to traditional drills in basic operations. Parents were left scratching their heads at homework that involved the abstractions of set theory rather than simple, unadorned arithmetic. In answer to the question “Why does 2 plus 2 equal 4?,” it was no longer acceptable to respond with an exasperated “BECAUSE!”

New Math was designed to literally “make sense” to young students by involving their senses and whole brains as they learned mathematics rather than mentally photographing and filing pages of facts “just because.” Objects were counted and distances measured when learning to add and subtract. Rods of equal length were arranged in rectangles to prove multiplication facts.

“No doubt about it: 2+2 does equal 4; five two's are in fact ten."

Students learned not only to memorize facts of arithmetic, but to understand arithmetic processes themselves. And this new comprehension was viscerally anchored, which meant it was deeply understood, and could be more easily and productively connected to other knowledge the student had (or would later have).

Physical objects used to reify numbers and clarify mathematical concepts and processes later came to be called Math Manipulatives. Manipulatives are still are the best way to teach young children basic arithmetic and early mathematics. The result of manipulative-based learning is an indispensable instinctive “feel” for numbers called “number sense.” *Legitimate criticisms of "New Math" notwithstanding, I simply can’t imagine learning arithmetic any other way.

In addition to traditional physical math manipulatives, screen-based "virtual manipulates" are now available for use on computers and other devices to aid in teaching and learning early math. These on-screen versions are superior to physical math manipulatives in many respects. Virtual manipulatives are easier to use, harder to lose, don't need to be picked up and put away after use, they go anywhere a tablet device goes, and can save tons of money and space.

Though virtual manipulatives shouldn't completely replace traditional physical manipulatives at home or school (especially during the first stages of a child's introduction to numbers and mathematical ideas, when sensory information involved in handling physical manipulatives is such an important aspect of developing critical early number sense), virtual manipulatives are well worth considering as an adjunct to traditional manipulatives.

For parents eager to set up a Math Exploration Station at home, I’ve listed below what I believe to be the most generally useful math manipulatives and virtual manipulatives along with selected guidebooks on how to use them in teaching math at home:

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Physical Manipulatives

Colored Plasticine

Cuisenaire Rods

Cuisenaire Rod Track

Jumbo Cuisenaire Rods

Centimeter Gram Cubes

Centimeter Snap Cubes

2cm Creative Color Cubes

Inchworms

EAI Master Fraction Ruler

Measuring Tapes, Tape Measure: 30m/100ft

Animal Counters, Dinosaur Counters, Family Counters, Transportation Counters

Two-Color Bean Counters

10 Frames

Hundred Numbers Boards

Hundreds Pocket Chart with 100 Number Cards

Place Value Disks

Play Money

Square Color Tiles

Wooden Pattern Blocks

Fraction Toys, Aids, and Activities

Tangram Toys, Aids, and Activities

Pentomino Toys, Aids, and Activities

Wooden Geometric Solids

Fillable Geometric Solids

AngLegs: 72 Piece Set

Math Dice, Polyhedral Dice: Set of 7 (D&D)

5-Bead Soroban Abacus, Guide Book

Algebraic XYZ Bosse Tiles Set

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Virtual Manipulatives

National Library of Virtual Manipulatives

Matti Math

BrainingCamp Virtual Manipulatives

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Guidebooks and Resources

Why Teach Math With Manipulatives?

Manipulative Glossary

Activity Math: Using Manipulatives in the Classroom

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* Parents today are experiencing a similar frustration with "Common Core," which could be characterized as "New Math 2." There's good reason for this: For most students, "Discovery-Based Math Instruction" only works well when closely paired with traditional algorithm-based "Direct Instruction." Although currently out of fashion, memorization, algorithms, drills and other traditional approaches to math instruction are at least as important and useful to most students as the "New Math" methods in vogue since the Math Standards movement picked up steam in the 1990's.

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Contact Chris

borlandeducational.com

Friday, May 01, 2015

The Junior College Transfer Option

Why pay full-fare for four years?

Transferring to the in-state flagship school after living at home and taking JC courses achieves the same credential for half the cost.

For low and middle-income families, the junior college transfer option is looking better each year. Although students taking this path forgo the "real college experience" for a couple of years and may feel a prestige hit, the drastically reduced financial burden could more than make up for these rather insubstantial benefits.

Junior colleges often have transfer agreements with particular state universities that make it easier for successful JC students to attend a top state school. For instance, Santa Rosa Junior College, our local JC, has a transfer agreement with U.C. Berkeley, arguably the best public school in the nation.

Our daughter graduated high school in 2011, took a gap year, and then matriculated at pricey Wesleyan University in Connecticut, graduating in 2016 with a double major in math and computer science. Wesleyan seemed like a good idea at the time, considering she had originally planned to major in English ... but given the STEM degree she ultimately earned at Wesleyan, she would actually have been better off transferring from SRJC and graduating with a math/compsci degree from UCB, one of the most highly regarded STEM schools in the world.

She did fine. Our daughter was offered a good scholarship to attend Wesleyan, and though her liberal arts math/compsci degree offered her fewer opportunities than the same degree from UCB would have afforded, she landed a great job soon after graduation as a software engineer at Amadeus North America in Boston.

One significant disadvantage of the JC transfer option is the lower-quality student body JC's typically attract. Although JC instruction is often excellent, top students who attend JC's won't find the same high level of intellectual interaction with peers as those who attend good four-year schools.

But if money is a family's biggest consideration, the JC transfer option could make very good sense, even if the student involved is capable enough to gain admission to big-name schools.

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Contact Chris

borlandeducational.com

Wednesday, April 01, 2015

Top Lower-Income Students Should Aim High

While it’s normally true that elite private colleges and universities cost families far more than state schools, this isn’t always the case.

When family income is below certain limits, schools like MIT, Harvard, and Stanford (and even public institutions like UCB) will waive all tuition for admitted students. Excellent students from families of modest means will often get an admissions boost and pay less for a diploma from an elite college than for a similar credential from a less prestigious in-state public university – sometimes far less.

Many poor families erroneously assume that top-flight schools are beyond their financial reach, and that the only realistic option is junior college followed by a transfer to a state university. In fact, for low-income students sharp enough to gain admission, attending an elite school can often be their least expensive option.

Click here for an article listing schools offering free rides and “no-loans grant-only” aid to top students from lower-income families.

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Contact Chris

borlandeducational.com