Bellevue Math Mom

Pearson grades the WASL and sells TERC

bellevuemathmom — Sun, 22 Apr 2007 08:50:11 +0000

An interesting (if somewhat long) article from a business perspective on testing companies. They mention Pearson which grades our WASL. The article talks about the scoring errors that testing companies make, says they often bid with very low profit margins on the NCLB test (like our WASL) they do for states, and make up the profits on test prep materials. Very interestingly, the article says that often the companies bid on the not very lucrative NCLB tests so they can sell other products within the state. I don’t know if our schools buy any WASL test prep materials, but I know that Pearson also publishes TERC Investigations.

For test companies, pitching schools to buy preparation materials after receiving a No Child contract is routine,says Robert Schaeffer, public education director at the National Center for Fair & Open Testing, a Cambridge, Massachusetts–based nonprofit group. “It’s standard business practice,the equivalent of razor companies’ giving away razors sothey can make money selling blades,” he says. “It’s where thereal profits are.”Profit margins in test preparation are as much as seven timeshigher than they are for No Child tests, partly because there areno requirements for high-quality questions on practice exams.States leave it to schools and school districts to decide whetherthe test preparation materials they’re buying are sound.

The article also says that some testing companies pay scorers about $10 per hour and are not very careful about checking their resumes to make sure they actually do have the bachelor’s degree required to score tests. The article has a sidebar on the WASL. http://www.bloomberg.com/news/marketsmag/education.pdf

Elementary math the Singapore way

bellevuemathmom — Sun, 22 Apr 2007 08:42:53 +0000

I am enjoying (really) a slim textbook that was written to teach math to elementary teachers. It just gives a basic (but deep) understanding of what it is that should be communicated to the kids. I am using it to help me with my tutoring of my own son. It’s not that adults don’t know this math; it’s that we often know it so well that we don’t see where the difficulties may lie for kids, and we no longer see how profound the concepts behind elementary math really are.

The book is: Elementary Mathematics for Teachers,by Thomas H. Parker and Scott J. Baldridge. It is available from Singaporemath.com and draws on examples from the Singapore Primary Mathematics, U.S. Edition series.

It is meant to be the basis for a one semester mathematics course for elementary teachers, and it is very slim and manageable for self-study. It does not teach pedagogy, but rather elementary mathematics from a teacher’s perspective. It covers place value, arithmetic, mental math, word problems, algorithms, prealgebra, factors, primes, fractions, ratios, percentages, rates, negative numbers, integers, decimals, rational and real numbers.

They say that there is a second strand of elementary math which centers on measurement and geometry. This will be covered in a sequel. I hope they come out with it soon!

Singapore math is not “drill and kill” math

bellevuemathmom — Sun, 22 Apr 2007 08:01:23 +0000

People always seem to think that Singapore math is about Drill and Kill, and that therefore that is what the people who oppose the reform math must want. I have used Singapore math for three years now. I consider myself an “afterschooler”, a person who homeschools a bit after school to fill gaps in the public school curriculum. Singapore Math is not about kill and drill. I think this review of Singapore math meshes with my experience and is very succinct.

“Singapore Math books are probably more resistant to mis-teaching than many curricula, since they are almost self-teaching books. They are less spiraling than most American texts (which is to say, they expect you to have mastered the previous work and only spend about a week on review at the beginning of each year), and the grade level tends to be off by one from American texts (that is, the Singapore 5th grade corresponds roughly to American 6th grade). There is some natural spiraling for computation, as they gradually make the problems larger.

The Singapore books fall closer to the traditional camp than the reform camp, in that all the students write are numbers and units, but they do emphasize understanding in a way that is missing from both drill-and-kill books (like Saxon) and reform books (like Everyday Math). That is, the Singapore books provide a lot of multi-step story problems that require mathematical reasoning and not just “this is the addition chapter, so we have to add something”. The story problems get gradually more complex through the series, so it might be hard for a student who has never done any mathematical thinking to jump into the Singapore series, even if they have mastered the algorithms of addition and multiplication.”

The beauty of the Singapore system is that it is so adaptable to different kids. Many in the homeschooling community like it because if you have a kid who gets math easily and doesn’t need a lot of repetition you can fly through it, if you have a kid who loves to go deeper there are additional word problems and materials available, and if you have a kid who needs more explanation, those materials are available as well. There is even a companion computer game for fun and practice. I love this curriculum! It is short and sweet.I have been meticulously been going through both the original TIMSS document and the Bellevue-Boeing standards mapping document on the Bellevue web site.

Singapore math has hit every gap between what is going on in my child’s classroom and the TIMMS standards. Also, it only takes us 10-15 minutes per night. I have also given my child the California end of year assessments, and my child has passed (understood everything assessed) with flying colors.

Singapore works! No kill and drill, and Singapore’s concrete-pictorial-abstract framework along with its scope and sequence that is well aligned with world standards makes it absolutely coherent and understandable.

Constructivism favors style over results

bellevuemathmom — Sun, 22 Apr 2007 07:54:58 +0000

Constructivism, the belief that, “each of us makes sense of our world by synthesizing new experiences into what we have previously come to understand,” has become increasingly popular as a model that schools use to structure educational experiences (Brooks & Brooks, 1999, p. 4). Such an approach has a certain meretricious appeal to anyone, especially an experienced learner. Constructivism basically maintains that a learner approaches new information, sorts through it, compares it with what he or she has learned before, and ultimately adjusts this new insight so that it fits in with his or her world view. Without doubt, many constructivist practices, such as an emphasis on using primary resources, encouraging student autonomy, using open-ended questions, and getting elaboration of student answers, are valuable strategies that all teachers should employ (Brooks & Brooks, 1999). Instructional styles that favor constructivist practices have become the preferred method in many districts and some states. At times this preference favors style over results. Some question the necessity, and indeed the value of having learners work through all, or even most, ideas with a good measure of autonomy to achieve understanding(Perkins, 1992). Time is a scarce resource in education; its use must be marshaled efficiently to achieve the optimal outcome.
Perkins suggests that schools must stop worrying about the styles used and instead concentrate on achieving retention, understanding, and active use of knowledge among their students (Perkins, 1992). Retention involves the acquisition of organized knowledge in the mind and the ability to recall that knowledge. Understanding affects the development of intellectual skills and processes, a means of using the knowledge learned or accessed. Active use of knowledge establishes enlarged understanding of ideas and values. Focusing on these goals rather than arguing about learning styles will better assure student progress (Perkins, 1992). From:

Gifted English Language Learners: Developing Talent while Supporting English Language Acquisition

Stephen T. Schroth

Educational Studies Department Knox College Galesburg, Illinois

Gifted Education Press Quarterly Spring 2007 Vol. 21, No. 2

Use Singapore math as “math insurance”

bellevuemathmom — Sun, 22 Apr 2007 07:53:18 +0000

I keep going on about
Singapore math. I love it. It’s cheap and easy from my perspective. The books are something like $10 each. My child has worked his way through the three years of the Singapore curriculum. I love the way it is so cohesive (concepts build on each other in logical order), it hits the TIMMS standards, and the California standards, concentrates on mental math more than you’d think –gives strategies for the mental math, uses a concrete-pictoral-abstract approach (which is not just mindless drill), and is multi-cultural in the children it depicts.I think of it as math insurance while my school still uses TERC Investigations.

You will hear the criticism that it would take a lot of professional development for a teacher to use. It least in the 1 -5 grades, I’m not buying that argument, having worked with the curriculum intensively (page by page). I think it’s easy enough for any parent with a reasonable elementary math education to use. You can get it from www.Singaporemath.com or from Math ‘n Stuff in
Seattle.

You want the U.S. Edition. The only difference between that and the third addition used in Singapore is that the
U.S. edition uses American money and fruit. Once we bought the third edition (not
U.S.) by accident and had fun adding duriens to rambutans instead of apples to oranges. I thought that was fun, but it is good to learn American money in the U.S Edition. My child did 4 -5 pages a day all summer long. It took 10 – 20 minutes. When school is on and there is other homework, we do a page a day in the workbook (5 minutes).

Is this really middle class math?

bellevuemathmom — Sun, 22 Apr 2007 07:44:37 +0000

I believe in my heart of hearts that having a program that is so geared to the middle class (TERC investigations) that requires playing games with parents and finding newspapers and things around the house, and does not provide a workbook to take home, really shortchanges our low income students. Parents in this state have spent millions on tutoring to fill in the gaps in this program, and the low income students can’t afford that. I can tutor my own child, so this is not about me; it’s about the kids who can’t afford it.

Bellevue math in the Wall Street Journal

bellevuemathmom — Sun, 22 Apr 2007 07:03:48 +0000

Here are some Bellevue specific experts from an article that appeared in the Wall Street Journal. For the full text, you can go to: http://nychold.com/art-wsj-060912.html .

If you’d like to see how your child would do on the Californian (world class) standards, the tests mentioned in the article can be found here: http://www.csun.edu/~vcmth00m/practice.html .

I haven’t noticed vigorous drilling on the basics in the Bellevue curriculum, at least it is not in all classrooms, more on that in other posts.

Critics of ‘Fuzzy’ Methods
Cheer Educators’ Findings;
Drills Without CalculatorsTaking Cues From
Singapore By JOHN HECHINGER
September 12, 2006; Page A1

Polle Zellweger and her husband, Jock Mackinlay, both computer scientists, moved to Bellevue, Wash., from
Palo Alto, Calif., two years ago so their two children could attend its highly regarded public schools. She and her husband grew suspicious of the school’s Investigations program. This summer, they had both children take a
California grade-level achievement test, and both answered only about 70% of the questions correctly. Ms. Zellweger and her husband started tutoring their children an hour a day to catch up.

It was a really weird feeling,” says their daughter, Molly Mackinlay, 15. “I do really well in school. I am getting A-pluses in math classes. Then, I take a math test from a different state, and I’m not able to finish half the questions.“

Eric McDowell, who oversees Bellevue’s math curriculum, says parents misunderstand Investigations. Mr. McDowell says schools supplement the program with more traditional drilling in the basics, and students end up flourishing in the system’s rigorous high-school courses. “It’s not an either/or situation,” he says.

Thirty percent of Bellevue 10th graders don’t have basic math skills

bellevuemathmom — Sun, 22 Apr 2007 05:05:18 +0000

This information comes directly from the OSPI website. It is the state’s own analysis of what the approximately 30% of tenth graders in Bellevue who did not pass the WASL math section need to know.

It is interesting to note that according to the Bellevue School district website, of districts with at least 5,000 students, our 10th graders ranked #1 in Math. We are number one in the state with a 30% fail rate on the material listed below. The state as a whole had 50% of the 10th graders fail. This says something about the state of math in Washington.

Notice the items I put in bold on the document below. These are basic math skills. It is also interesting to note that statistics concepts are giving students so much trouble. These are supposed to be one of the major strengths of the constructivist math curricula.

http://www.k12.wa.us/assessment/WASL/Mathematics/Modules/BigIdeasTaughtDuringSummerSchool.doc

BIG IDEAS TAUGHT DURING SUMMER SCHOOL

(for 10^th graders who did not pass the WASL)

1. Using a fitted line

2. Stem and Leaf Plot

3. Using information from a table

4. Using information from 2 sources—such as a table and graph

5. Measures of central tendency 6. Box and Whisker Plot7. Using a circle graph8. Order of operations

9. Experimental probability

10. Theoretical probability

11. Geometric probability

12. Working with percentages

13. Working with fractions

14. Perimeter vs. Area

15. Coordinate points

16. Transformations

17. Reading/interpreting graphs

18. Using formulas

19. Using right triangle properties

20. Scientific notation

21. Decoding contextual-based problems

22. Equivalent measurements

23. Estimation in context

24. Venn diagram

25. Permutations and combinations

26. Circles—area, circumference, diameter, radius

27. Surface area

28. Volume and conversion

29. Volume vs. Perimeter—connection between the measurements

30. Patterns

31. Drawing conclusions and supporting with evidence

32. Basic computation skills for non-calculator day

33. Decimals to hundredth place

34. Labeling when appropriate—measurement

What would a mathematically enriched household look like?

bellevuemathmom — Sun, 22 Apr 2007 04:03:46 +0000

Here is something to consider when thinking about discovery math and economically disadvantaged children. The original TERC/UW grants in this state talked about creating a community of mathematical learners in the classroom. I think some of these folks had the best of intentions in giving the kids something that they were missing at home. I think many educators are trying to drill down on what it is that makes kids from some homes better at math than others.

So why do some kids from advantaged homes in Bellevue wind up doing fairly well in math no matter what curriculum you throw at them? It’s not just the tutoring their parents can afford.

I empathize with the educator’s efforts, but I think they are misguided. The schools can not possibly hope to replicate these advantages with the limited time and money that they have. I think that’s why instruction by example and direct teaching has worked best with disadvantaged populations. For evidence of this in California you can refer to the paper by Bishop and Hook http://www.nychold.com/report-wbwh-040619.pdf.

Instruction by example (teaching the kids how to do the math) bypasses the time consuming living math experience (but you should do as much as you can as enrichment), and cuts to the chase. However, for some insight into exactly what a math enriched home looks like (and just how big a hurdle it may be for kids who don’t have this), consider the following ideas from a very discovery-oriented website. Personally, I have done all of these things without even trying. I’ll bet many Bellevue parents do many of the things listed below without even considering them as math enrichment activities. It’s just fun, as long as you have the time and money.

Spread A Discovery Learning Buffet, quotes excerpted from www.livingmath.net

In our living area I have baskets and shelves that are open and contain pattern blocks, Lego’s, dominoes, Jenga and other blocks, snap blocks, Zome Tools, those magnetic balls and stick toys, K’nex, playing cards, dice, and base 10 blocks.

Then we have all your classic games, chess, checkers, Battleship, Connect Four, Chinese checkers, Pente, Othello, etc.

Because my girls enjoy activity books, I have baskets where these are stacked in the area they draw, color and do any table work in. Many times my youngest daughter will just pull one out and work it through without me even knowing it, I’ll be cleaning up and see the entire book worked. On those desks (which are in between the kitchen and the living room so they are in plain view and constantly accessible) are pencils, colored pencils, crayons, markers, rulers, pencil sharpener, compass, protractor, calculator, etc.

I allow my kids full access to things like tape measures (this has provided hours of fun for all my kids, especially the metal kind that can be balanced up to the ceiling so you can see how high the vaulted ceilings are, LOL – yes, we cover safety and none have gotten hurt). When I’m sewing they help me measure and cut. When dh is in garage doing projects he involves them in how he does things. Then they imitate and I provide them any tools they need to imitate.

We have a “great room” style living / family / kitchen area so even a child sitting down at the piano can talk to me while I’m cooking . . . I can stop, go over and show them how the time signature and notes form fractional relationships . . . Up until this week my kids would just play around on the piano, only my oldest 2 were taking music lessons for violin and cello, but my girls have bugged me for piano lessons. I never noticed until a couple years ago how much math there is in the earliest music lessons in learning how to read note rhythms. In this book my daughter got this week, they exposed her to 4/4 time, 2/4 time and 3/4 time, so she learned to relate quarter notes to half notes, whole notes and dotted halfs – all strictly fractional concepts.I hung an analog clock in our kitchen near their work area so they could see time in fractional ways.

Other essential resources are tapes and videos. We have the schoolhouse series, skip count tapes, Cyberchase. I have baskets and shelves for these, they pick them out.

Major Gaps in Bellevue’s Second Grade Math Curriculum

bellevuemathmom — Sat, 21 Apr 2007 22:18:07 +0000

Note: This was current as of summer 2006. The district has made changes since then, but these are still things to look for in your child’s second grade homework. The following items are part of the International TIMMS math standards for second grade but not covered adequately in Bellevue.

Numbers and place value up to 1000

TERC Investigations only goes to 100 for number notation and 200 for place value.
Current Bellevue Second Grade curriculum uses TERC Investigations Coins, Coupons, and Combinations unit, also taught in First Grade

Adding and Subtracting Numbers up to Three Digits

Three digit adding and subtracting (TERC Investigations only goes up to 100, uses 100 chart as addition and subtraction strategy)
Formal algorithm instruction for regrouping in addition and subtraction.
Adding and subtracting mentally involving: 3-digit numbers and ones; 3-digit numbers and tens; 3-digit numbers and hundreds.

Multiplication and Division

Know the facts in the 5 x 5 multiplication tables and recall fluently.
Multiply by 10 and 100
Introduce division as another way of expressing multiplication through fact families, e.g.: 2 X 3 = 6 can be rewritten as 6 ÷ 2 = 3 or 6 ÷ 3 = 2.
Emphasis on the relationship between multiplication and division.

Fractions

Place ½, 1 ½, 2 ½ , etc. on the number line.
Work with unit fractions from 1/12 to 1/2. TERC Investigations does not cover 1/7, 1/9, or 1/11.
Identify unit fractions between 1/12 and 1/2 as larger or smaller than other unit fractions in the same range.

Measurement

Estimate and measure length in meters, centimeters, inches, feet, and yards. (relies on third grade science to teach this)
Draw and measure the perimeters of rectangles and triangles. (again third grade science)
Third grade science will not cover perimeter and circumference which remain as gaps.
There are no rulers, no measuring cups, no thermometers, no balances. There are paper strips and non-standard measures such as “person jumps.”

Time

Tell and write time from the clock face and from digital clocks. (they suggest using lessons from www.time-for-time.com)

Graphs

Vertical picture graphs.

Money

· Read and write money using standard decimal notation.
· Add and subtract money in mixed units (combinations of dollars and cents)

Geometry — Identifying Shapes and Attributes

· Circumference and three dimensional elements of spheres, cones, and cylinders.

The above information is based on differences between the world class TIMMS standards given to the district by Dr. Schmidt of the TIMMS study, and the current Bellevue first grade curriculum. These gaps exist even after the district realigned the curriculum last summer and attempted to plug some of the holes. This information is current as of June 2, 2006.