Discover Project Follow Through

[ Times Colonist ] Many Canadian provinces adopted discovery-based curriculums about 15 years ago. Newer curricula and textbooks appeared, advocating the use of multiple strategies in the classroom, replacing more conventional methods for teaching arithmetic. The result of this phenomenon has led to a remarkable decline in math skills, and a proliferation of children enrolled in costly learning centres to achieve knowledge of foundational math facts.

These centres and private tutors use more conventional and traditional methods to teach their students, because they have been proven to work. This is something to which our policy-makers must pay attention.

Gee, it didn't work! Project Follow Through came out in the early 1970's--that's fully 40 years ago, which means pretty much every single teacher currently trained and working has been trained after its findings were known...and utterly ignored.

The world has known what works and what doesn't in math education for four decades. Educrats continue to ignore it.

Making kids feel stupid

My new favorite education quote:

“You know what’s the worst kind of instruction? The kind of instruction that makes kids feel stupid. And that’s what a lot of that discovery stuff does; their working memory gets overloaded, they’re confused. That’s bad instruction,” said Anna Stokke, an associate professor in the University of Winnipeg’s department of mathematics and statistics, who wrote the C.D. Howe Institute report. [ Decline of Canadian students’ math skills the fault of ‘discovery learning’: C.D. Howe Institute ]

Going slow

"The Role of Curriculum", by William H. Schmidt:

The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that U.S. eighth- and 12th-graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students, taking an advanced mathematics test, do not fare well against their counterparts in other countries. -

...

By the middle grades, the top achieving countries do not intend that children should continue to study basic computation skills. Rather, they begin the transition to the study of algebra, including linear equations and functions, geometry and, in some cases, basic trigonometry. By the end of eighth grade, children in these countries have mostly completed mathematics equivalent to U.S. high school courses in algebra I and geometry. By contrast, most U.S. students are destined for the most part to continue the study of arithmetic. In fact, we estimate that, at the end of eighth grade, U.S. students are some two or more years behind their counterparts around the world.

By the middle grades, the top achieving countries do not intend that children should continue to study basic computation skills. Rather, they begin the transition to the study of algebra, including linear equations and functions, geometry and, in some cases, basic trigonometry. By the end of eighth grade, children in these countries have mostly completed mathematics equivalent to U.S. high school courses in algebra I and geometry. By contrast, most U.S. students are destined for the most part to continue the study of arithmetic. In fact, we estimate that, at the end of eighth grade, U.S. students are some two or more years behind their counterparts around the world. - See more at: http://www.aft.org/periodical/american-educator/fall-2005/role-curriculum#sthash.lzq4J5TP.dpuf

The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that U.S. eighth- and 12th-graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students, taking an advanced mathematics test, do not fare well against their counterparts in other countries. - See more at: http://www.aft.org/periodical/american-educator/fall-2005/role-curriculum#sthash.lzq4J5TP.dpuf

The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that U.S. eighth- and 12th-graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students, taking an advanced mathematics test, do not fare well against their counterparts in other countries. - See more at: http://www.aft.org/periodical/american-educator/fall-2005/role-curriculum#sthash.lzq4J5TP.dpuf

The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that U.S. eighth- and 12th-graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students, taking an advanced mathematics test, do not fare well against their counterparts in other countries. - See more at: http://www.aft.org/periodical/american-educator/fall-2005/role-curriculum#sthash.lzq4J5TP.dpuf

Of course, that same author went on to sign off on the Common Core as a member of its validation committee. Perhaps he's had second thoughts since, but, apparently, he's been trying to prove after-the-fact that his approval was justified:

Here's Ze'ev Wurman writing on Breitbart:

One does not need to be a content expert, however, to observe the simple fact that, despite the soaring rhetoric of Professor Schmidt in 2005 about how by the end of eighth grade students in high achieving countries “have mostly completed mathematics equivalent to U.S. high school courses in algebra I and geometry,” Common Core firmly placed the first Algebra course in the high school. It also doesn’t take an expert to observe that Common Core’s “college preparation” in mathematics amounts to a poor-man’s Algebra 2 and Geometry courses. The U.S. Department of Education’s own data shows that with only Algebra 2 preparation – even the full course – the chances of a student to end up with a Bachelor’s degree – any Bachelor’s degree – is less than 40%.

The data are clear. Recent results from the Third International Mathematics and Science Study (TIMSS) show that U.S. eighth- and 12th-graders do not do well by international standards—ranking below average in both grades and, in fact, near the bottom of the international rankings on a mathematics literacy test at the end of high school. Even our best students, taking an advanced mathematics test, do not fare well against their counterparts in other countries. - See more at: http://www.aft.org/periodical/american-educator/fall-2005/role-curriculum#sthash.lzq4J5TP.dpuf

Problems with the Core

Much of this article: Can This Country Survive Common Core’s College Readiness Level? R. James Milgram and Sandra Stotsky (PDF) is old hat.

But, I don't think I've ever covered the effects of the Common Core on public colleges and universities, which this article also covers. The Race to the Top program, to which most states signed on, included a rule saying that any student who passed the Common Core final high school assessment--meaning they successfully completed and understood the Common Core's math curriculum--would, no matter what, be admitted to a main-sequence, credit-bearing math class in college and could not ever, for any reason, be placed in remedial math.

Nevertheless, the language in the RttT agreement indicates that states must place new students admitted by their major public colleges and universities into credit-bearing mathematics (and English) courses if these students have passed a Common Core-based “college readiness” test.

One might criticize the generality of the statement above by pointing out that these students don’t have to be admitted or that colleges can admit students who haven’t passed such a test. However, in many states including California the top 30 percent of students graduating from high school are guaranteed admission to an IHE ["institutes of higher education"] or IHE system. Moreover, only the chief administrative officer of an IHE has to sign on to this policy, not the relevant faculty. For the most part, this faculty knows nothing about the changes that Common Core will bring.

We find these requirements for Common Core states astounding because they apply to all public institutions of higher education, not just to those for which Common Core’s mathematics standards were intended [for community collge], according to the lead mathematics standards writer, Jason Zimba. And even if these requirements are intended only for non-selective postsecondary institutions, they are problematic because non-selective schools have often had to place newly admitted students into intermediate algebra (a course lower than “college algebra”) that was remedial at these institutions. To make matters worse, the first for-credit courses at non-selective institutions are often regarded as remedial at other colleges and universities, yet “articulation agreements” between two- and four-year public colleges seem to require that transfer credit be given. All that the PARCC and SBAC tests can verify is whether freshmen have to start with intermediate algebra if they do not pass, or could start with “pre-calculus trigonometry” or “pre-calculus algebra,” as the first two for-credit courses at a community college are usually described.

Basically, the Race to the Top nonsensically insists that if you make it through high school, you are by definition ready for college math. I'd sincerely love it if that were the case. After all, someone who is trying to get a college degree should be ready for college coursework. However, today, in our college-for-all era, that is far from the case. Across the country large numbers of college starters are currently placed in remedial math. For example, in Ohio, that number is 40%.

College is the new high school; kids who are failed by their high schools have to take high school math in college, only now they are paying for the prospect. Colleges have gone along with this because they make money on the students either way.

But what this new requirement will mean is a dumbing down of college math as well. The schools will not be able to flunk all of the the students who have no business taking college math, so they will simply make the classes easier and pretend that the students are doing college work.

The article also points out that, as far as STEM majors are concerned, almost no one who starts on a remedial track ends up in the science or tech fields.

That's it (II)

This was assigned today (Ths) and is due on Monday. They have 4 days over a weekend to do this:

That's it.

This was the entirety of our 6th grader's math homework last Thursday:

If he couldn't do the entire thing in his head in about a minute and a half, I'd be shocked.

Goldfish

How the Common Core standards are being applied.

At Denman, under the Common Core, eighth-grade students might have to estimate a wildlife population using colored Goldfish crackers, an activity that uses algebraic functions, proportion and estimation, with a built-in snack at the end, Lyon said.

Now, I don't think there is anything inherently wrong with the CC standards--though I don't like the homogenization of standards and eventually curricula across the country; I'd prefer wide variations which allows for experimentation and change. The CC basically locks the whole country down to the same train track; and if the track isn't finished yet, is poorly built, or is heading for a cliff, we'll all face ruin together. The CC standards are also minimalist, and we're running the risk of many schools assuming that they are good or good enough. They're not.

The biggest problem that I see is the way that it throws all the K-12 education balls up in the air at the same time. The education establishment is now scrambling to catch them out of the air or pick them up off the ground and sort them back into a coherent order. That should be a boon to the people who want to drastically change education; but, unfortunately, the ones who are in a position to actually make the changes have been indoctrinated with the sort of world view that makes the quote posted above appealing. If you are the sort that reads that passage and thinks: that's fantastic!!, then, you really shouldn't be allowed anywhere near a K-12 school.

The inmates are running the asylum.

Geometry

This is sad:

The Modern Day High School Geometry Course: A Lesson in Illogic - See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

The Modern Day High School Geometry Course: A Lesson in Illogic - See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

 

The Modern Day High School Geometry Course: A Lesson in Illogic - See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

The Modern Day High School Geometry Course: A Lesson in Illogic - Barry Garelick

Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored.
A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.  Typical courses in geometry are lacking in proof-based problems; instead, they contain many problems in which missing angles or segments are indicated as algebraic expressions.
- See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored.
A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.  Typical courses in geometry are lacking in proof-based problems; instead, they contain many problems in which missing angles or segments are indicated as algebraic expressions.
- See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

 Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored. 

 A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.

Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored.
A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.  Typical courses in geometry are lacking in proof-based problems; instead, they contain many problems in which missing angles or segments are indicated as algebraic expressions.
- See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored.
A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.  Typical courses in geometry are lacking in proof-based problems; instead, they contain many problems in which missing angles or segments are indicated as algebraic expressions.
- See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored.
A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.  Typical courses in geometry are lacking in proof-based problems; instead, they contain many problems in which missing angles or segments are indicated as algebraic expressions.
- See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

Geometry as taught today is for the most part lacking in the most important aspect of the subject: Proofs. Prior to 1980, most if not all high school geometry classes were very much proof-based. While there are those who bemoan the teaching of K-12 math as being mired in “computational” and “procedural” aspects of math while ignoring the larger beauty of what mathematics is about, it is ironic that when it comes to geometry, the true mathematical nature of the subject is largely ignored.
A glance at the geometry textbooks that are typically used in high schools today reveals that the problems students are given in such courses require one or two proofs  that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions.  Most of the problems presented in these textbooks require students to apply various theorems and definitions to find the lengths of line segments and angles.  Typical courses in geometry are lacking in proof-based problems; instead, they contain many problems in which missing angles or segments are indicated as algebraic expressions.
- See more at: http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/#sthash.SCN6i19A.dpuf

Geometry was my favorite high school math course because I loved writing proofs.

Text books

Here's an article on how Common Core adoption is pushing kids out of science careers when they are 13 years old. By only offering limited opportunities to take algebra in 8th grade--which leads to calculus senior year, which leads to possible acceptance into science and engineering schools--the doors to science careers are being closed, with the determination being whether a student manages to grab the few spots available for 8th grade algebra. Miss that cut off, and you are left scrambling with either intensive summer work to catch up, or doubling up math classes in one year.

But here's what I see as the worst line in the story:

According to Martin, textbooks are “a 20th-century concept.” Teachers are now “finding their own resources and putting them on the website for students to access,” he said. “In almost every curriculum area, the investment districts used to make in textbooks is beginning to change.”

Textbooks, at least the best of them, are a carefully designed sequence which thoroughly and thoughtfully walks students through the material and allows them to access the concepts and practice needed for mastery. When stumped, students can look back or can look at example problems to figure out which way to go.

I have absolutely ZERO confidence that teachers grabbing things ad-hoc from wherever can do half as good a job as even mediocre text books. It will leave students with no resources beyond the teacher's word.

I've had courses taught to me by the teacher, using a text book they themselves had written--or worse, a photocopy of transparencies the teacher displayed in class. I always hated it! Having two independent resources at hand is vastly preferable to having one. With a single source, there is no other opinion as to what is most-important, what should be stressed, what should be skipped or deëmphasized, there is no alternative explanation you can turn to when the first isn't working.

I find the idea that teachers are superior textbook authors, better than textbook authors themselves, to be arrogant and misguided.

The Banality of Deeper Learning

Quotes from:  The Banality of Deeper Learning | Brookings Institution

Teachers have been taught not to teach actual information, but to try to get kids to learn how to learn--like that isn't innate. A simplistic version of teachers' thinking is that with all the information in the world at their fingertips, all kids really need to know is how to Google.

However, most parents aren't fooled; some can afford remediation, some can't (from "Banality"):

The premise is simple.  If public schools don’t teach algebra or chemistry or history or great literature or how to write well—the old-fashioned learning that has been around for centuries and remains high status knowledge in most cultures—rich kids will get it somewhere else.  Poor kids won’t.

From the same "Banality" article:

The first graders were being taught addition of two-digit and one-digit numbers using word problems. [...] Three acceptable strategies were shown for solving the problem.  All involved “chunking” the numbers into groups (in the case of fifteen, three groups of five or one group of ten and another group of five), with each group presented in a circle or box.  The groups are then added together.  The addition must be shown graphically.

One unacceptable strategy was also shown:[...] Please do not have your child stack numbers [traditional algorithm]. 

[One kid's parents] were alarmed that the standard algorithm for addition was being discouraged, let alone not being taught as the simplest, most efficient method for solving addition problems. [...]

A compromise was struck [with the school].  Solutions using standard algorithms would not be marked wrong, the parents were told, but their son would be required to “illustrate his understanding” through graphical representations of math problems.  In his blog, [the parent] includes a worksheet that shows the laborious process his son went through, drawing with the uncertain strokes and still developing fine motor skills of a first grader, to prove that three tens make a total of thirty and three fifteens make a total of forty-five. 

This is another reason why boys tend to lag girls right from the start. In general, girls' fine motor skills develop before those of boys. Boys have more trouble sitting for laborious tasks, have poorer pencil control, and report more hand pain than girls (see Ralph Fletcher's "Boy Writers"). 

 In the case of the particular child discussed above:

The [parents] observed several classrooms using CGI for math instruction at the school.   They eventually withdrew their children and sent them to private school.

Which goes back to the first point: parents with options, who are generally wealthier than those without options, will exercise them, leaving poorer kids stuck and left behind.

New law dumbs down Calif. math performance | CalWatchDog

This is horrible. What it boils down to is this: not only has the adoption of the Common Core slowed down California's math curriculum by a year (algebra in 9th instead of 8th,)  it destroys the possibility of a calculus-track for top math students.

New law dumbs down Calif. math performance | CalWatchDog

Furthermore, SB1200 is so poorly drafted that it doesn’t just roll back the expectation of Algebra 1 in grade eight. It does more than that by requiring “one set” of standards “at each grade level,” and precluding typical mathematics course options for students in high school.

California high schools have always offered different math classes to students in the same grade who have different levels of preparation. Accordingly, California historically has adopted course-level math standards for high school — preserving local control at the district and school level to decide when it would be best to offer rigorous courses to each student based on the student’s ability. But SB 1200 would outlaw that practice by mandating only one set of mathematics curriculum- content standards, textbooks and training and teacher materials for all students in each K-12 grade.

Officials of Brown’s administration have offered rhetoric about how they will not have to implement the plain language of the law. But they do not have the statutory authority or capacity to violate the law’s provisions. Efforts to get around the wording of the law will lead to confusion about policy on curriculum, textbooks and testing — and hence invite lawsuits and re-ignite the math wars.

Trespassers in Wonderland

Yep:

Barry Garelick: Trespassers in Wonderland | Education News

Math follies

And you thought it couldn't get any worse!

The weak, Everyday-Math based, math program at our kids' school has been a major complaint for a decade or more. Our soon-to-be 7th grader spent 8 years under this program, and only got into a good junior high/high school because we had taught her a lot at home. Any change would be an improvement...or so we thought...

Near the end of the school year a letter came from the school (aka: Dot School), saying that they were changing the math program. There really was much rejoicing. They are moving from the pure-constructivist EM, to the practice-to-mastery-based Singapore Math. This is a massive improvement. Singapore is really a strong program, and their "Singapore Bar Method" is an amazingly powerful system. It allows kids in 5th and 6th to do complex algebra and ratio problems which would otherwise have to wait until later.

Then the details of the school's switch started to become apparent. First of all, next year, the only change will be at the lowest grades: the kindergarten and 1st grade classrooms. For 2nd-5th the transition will happen the following year. For the middle school, it will only begin to change as next year's 4th graders move through 6-8th grade. The full roll-out, therefore, won't be complete until the 2016-2017 school year. It also means, that the incoming 5th graders will never see the improved program.

Guess which grade our kid will be in next year?

We protested loudly. We wrote a detailed almost-four page letter detailing our dislike of EM and preference for jumping on the SM bandwagon immediately. That letter is here (names have been changed to protect the guilty):

In your prior e-mails you have said that K1 will transition to Singapore Math next year and the rest of the school the following year and the junior high program will change as the kids who have transitioned to Singapore Math reach 6^th grade.  This means that next year's 5^th grade class would stick with Everyday Math and the current junior high math program through 8^th grade.  You have done a thorough review of these programs, so I am sure that you know more about it than we do, but here are the reasons why we prefer the Singapore program.

 

Spiral vs practice to achievement.

While some math skills have no prerequisites, for the most part, math builds on earlier knowledge.  Everyday Math’s spiraling curriculum means that topics are repeatedly gone over lightly, and there is no attempt at making sure one concept has sunk in before progression to the next skill.  Without fully building the foundation, subsequent topics don’t make as much sense and are harder to grasp.  With Singapore Math, you do not progress until you have spent sufficient time to master a skill.  That is a key difference: repeated, light coverage vs. practice to mastery.

In addition, the Everyday Math books were designed to work with a public-school calendar of roughly 180 school days. Dot School’s calendar is six weeks shorter, and Dot School kids miss many other days of math class for special events.  Because the experiential learning activities in Everyday Math take so much class time, it is difficult to compress the curriculum into the shorter school year, and about one-third of the material in any given year is never covered.  This is deadly in light of the spiraling nature of the curriculum—it means many skills are not presented enough times and in enough detail to really sink in.   At least with Singapore, if a previous year’s teacher doesn’t get to the end of the book, it is very clear where the class left off, and what skills they need to work on to make up the gap.

Standard algorithms

Everyday Math presents multiple algorithms for solving arithmetic problems.  For multiplication, four different methods are presented.   The program does not emphasize standard algorithms, so these are not mastered.   Singapore instead focuses on one or two algorithms, and then takes the time to ensure the student achieves mastery.  Using too many methods leads to a great deal of confusion.   Many of the algorithms taught (lattice multiplication being a prime example) are not robust enough and do not scale to more difficult problems.  Try doing a lattice multiplication problem with four or five digit numbers, or with decimals; it quickly devolves into a mess.  Using the classic algorithm for such problems—or even harder ones—is straight forward, and you don’t have to waste time drawing the lattice.  The Everyday Math Teacher’s Reference Manual actually states that the lattice method was originally added for its “recreational value and historical interest,” not it's mathematics value, and that, “It is not easy to understand exactly why lattice multiplication works.” (K-3 Edition, 2001, pg 107.) In other words, it’s something to play with, but is hard to understand and not worth spending the kind of time that Dot School spends on it—time which could be spent actually working to master a robust algorithm. Obviously, Singapore doesn’t teach this at all.  I won't even talk about long division, the problems with Everyday Math are well known.

Level 5 Everyday Math still does not emphasize the standard multiplication algorithm.

Instead, it rehashes partial-products (which does have a great deal of value when just beginning multiplication…in third grade,) but it doesn’t scale well to large problems—they become unwieldy.  A simple 3X3-digit multiplication problem leads to 9 lines which have to be added together—and for kids, this means keeping their columns very straight, which many have a hard time doing; while the standard algorithm gets it done in 3 lines.  In addition, the partial products method gets much more confusing when you start throwing in decimal points, and are multiplying hundredths by hundreds.

Level 5 Everyday Math also continues to emphasize the lattice method, which is mathematically confusing and of little mathematical value.  If the idea of favoring partial products, as Everyday Math does, is so that kids are always remembering that the digits stand for hundreds and thousands, etc, then the lattice method throws all that out in favor of a party trick.

Fractions

Much of Fifth Grade is taken up by fractions, including multiplying and dividing them.  Instead of teaching that division is the opposite of multiplication and introducing the idea of a reciprocal, Everyday Math skips teaching fraction division entirely, believing that the subject is too confusing, and teaches kids to reach for a calculator instead.  It is hard to understand why Everyday Math skips over this, as fraction multiplication and division is so much easier than fraction addition and subtraction.

Algebra requires students to be able to work fluidly with fractions, including fraction division.   It is difficult to find the square of a polynomial which includes fractions, if the only way you know how to do fractions is to reach for a calculator.  Math skills build on one another, and skipping this simple, yet crucial, bit of fraction arithmetic handicaps Everyday Math-taught kids as they advance.  Singapore Math does cover fraction division and doesn’t (ever) emphasize reaching for a calculator.

Exponents

On page 14 of the Singapore Math Primary Mathematics 5A workbook, there are already problems with exponents.  Our girl wasn't taught anything with exponents until 6^th grade.  Again, this is a very easy thing to learn—especially squares and most cubes—yet it is missing from Everyday Math.  Just as multiplication is introduced as repeated addition, so too can exponents be introduced as repeated multiplication.

Geometry

Everyday Math, at least as our kids have both experienced it at Dot School, doesn't get around to the properties of circles until very late.  When our boy talked with his table mates about "pi", he was derided and asked if there was also a number called "cookie."  This was near the end of fourth grade, and most of his class had never heard of pi.  Our girl's class this year covered volume and surface area of cubes, rectangular boxes and pyramids, which is covered earlier in Singapore math.  Being able to calculate the volume of a rectangular prism—not to mention cylinders and spheres—is actually a useful life skill, yet this, again, seems to be missing from Dot School's current math program.

Mental Math

The mental math aspects of Singapore are great, adopting ways of thinking about problems that speed calculation, increase accuracy, and emphasize the meaning of numbers.  These are the sorts of skills that a student will use for life.

Singapore Bar Method

The Singapore Bar method is a powerful tool.  Using it, kids in early grades learn complex algebraic concepts and study ratio problems that they would otherwise have to wait years to get to.  It is really an impressive system, and of great value.  Obviously, Everyday Math doesn’t use this at all.

Junior High and Beyond

The standard college prep math track leading to Calculus in 12^th grade would start with pre-Algebra in 7^th grade and Algebra in 8^th grade.  The Chicago Math program uses a slightly different sequence.  In order to allow students more time to learn Algebra, first year Algebra is split into two years and sandwiched around Geometry which is taken in 8^th grade instead of the traditional 9^th grade.  To get to Calculus in 12^th grade, pre-Algebra has to be taken in 6^th grade.  The sequence looks like this;

                6^th grade:  Transitions (pre-Algebra)

                7^th grade:  Algebra

                8^th grade:  Geometry

                9^th grade:  Algebra

               10^th grade:  Advanced Algebra/Trig

               11^th grade:  pre-Calculus

               12^th grade:  Calculus

Dot School uses the pre-Transitions book in 6^th grade.  This book is mostly a review of 4^th and 5^th grade math.   A full two trimesters are spent reviewing addition, subtraction, multiplication, division and fractions.  The new material covered, mostly ratios, statistics and geometry, are covered in earlier years in Singapore Math.  Dot School kids have to transition to another school in 9^th grade and will not have received an Algebra curriculum comparable to kids moving from other schools, because they will have made it through only the first year of the three year Algebra sequence in Chicago Math.  Presumably, if basic math skills are mastered in grade school and ratios, statistics and basic Geometry are learned earlier, as covered in Singapore math, students will be prepared for Transitions in 6^th grade or the school will switch to the Singapore junior high curriculum. 

Dot School is not an island, isolated from the schools and students in the surrounding communities.  When Dot School's students leave, whether in 8^th or 6^th, they will face competition with students from around the city.  Many of Dot School’s peer-schools begin tracking students as early as fourth grade and Dot School's current curriculum leaves many students struggling in their next school.   As math is a foundation for the physical sciences, students will struggle in subjects like physics and chemistry as well.  Dot School kids have to choose between struggling to catch up and retaking Algebra in 9^th grade.  Because high school AP Calculus is now all but a requirement to study STEM and related fields at competitive colleges, the latter option makes it unlikely that students will choose these career options.

Schools that have adopted Singapore Math often see tremendous gains in achievement in the first year, and the fifth graders next year would benefit tremendously from it.  You already know the weaknesses of Everyday Math and the strengths of Singapore Math better than I can point out.  I know you are aware of the lengths parents are going to supplementing math outside of school and what students go through preparing for the ISEE.  You know the perennial and vocal protests from parents about Dot School’s math program—you were on the receiving end of some of that anger at the math meeting a few months ago.  You have already determined that Singapore Math is the better program, but you are telling next year's 5^th grade parents that our kids can't have it.   Please reconsider.

Yesterday, my sister met with the head of the  elementary school to discuss trying to get the boy placed in 6th grade math. He, Mr. H, said it would not be "developmentally appropriate" for him to advance beyond his classmates, and that it would be damaging to allow him to actually learn something new in math next year. And, since 6th grade math is pretty much a review of 3rd-5th grade math, they have no intention of teaching him anything new until he gets to pre-algebra in 7th. By that time, hopefully, he will be departing the school and mooning them on the way out.

Instead of learning something new, the boy will be presented--by virtue of being advanced from many of his peers in math--with "leadership opportunities" in the classroom. We have been down this road before. That is exactly what they told us when he was 5 years old and we wanted him in kindergarten; they wanted him in pre-school. It would be good for him to be in a class with kids who are barely verbal, they said, because he could develop leadership skills! Instead, he spent a lonely year, with no one to talk to, and almost no one on his level to play with; all the while, watching his former classmates actually learning something in kindergarten. What he learned that year wasn't leadership. The school taught him that he was too stupid to go up to K with his friends, and he learned to hide behind potted plants in the hallway when the K classes walked by.

But, I forgot to mention, they are going to change the 5th grade math curriculum next year! Yay!

They are going to make it worse!

Instead of learning something from their institutional embrace of Singapore Math, and asking themselves what makes that program better (direct instruction and practice, practice, practice,) and applying that to the handicapped EM curriculum that they insist on using, they are doing the exact opposite.

They are taking the constructivist EM curriculum to new, never-before seen heights. They are going to ditch most classroom instruction completely in favor of a student-discovery, centers-based classroom! This is the same centers-based system that was used at the school in kindergarten, so the kids will be familiar. That means that there will be about four stations every day for the kids to cycle through. The goal of this is to keep them unfocused and increase the frenzy and distraction in the classroom. The more movement and noise, the better kids will learn math! The student-discovery aspects will mean that kids won't have a clue how to do some of the work; which is great, because they don't really want to do it, and the teacher doesn't really want to teach them anyway! Win-Win!

Yesterday, I tried to find any evidence that the fad of "project based learning,"  which is what they are calling this at the school, is a good way to actually teach, impart knowledge, and to get kids to achieve. Guess what? There is no significant evidence for this method. There are a handful of month-long demonstration projects that showed some improvement, but there has never been a quantitative, random assignment, long-term, longitudinal study of this method. In other words, a couple classrooms have used it temporarily, and they liked it! However, it should be noted that studies have also shown that any change in a curriculum--whether it is eventually proven beneficial or harmful--improves things in the short-run. Enthusiasm over the newness goes a long way. Real studies require long-term quantitative results, not quick "we liked it! we really liked it!" studies. There is no such research approving "project-based learning."

So, we're tearing our hair out...and spending the summer teaching him real math.

My sister has written another letter. Beautifully snarky. I'll see about posting it after the school has seen it.

Reform math fails

An interesting article.

It tracks kids from a reform math high school program into college to see how they did. As the program was implemented, you could see their math achievement drop precipitously. The students placed into lower-level college courses and received lower grades than their peers from schools not using the specific curriculum. There was an exception for the top math students, whose grades outpaced their peers--which might be attributable to AP Calc classes taken by the top students.

You must be joking!

Large excerpt from interview with on Education Next Stephen Wilson is: "a professor of mathematics at Johns Hopkins University, served on the National Governors Association-Council of Chief State School Officers “feedback group” for the Common Core standards, and was mathematics author of Stars by which to Navigate? Scanning National and International Education Standards in 2009: An Interim Report on Common Core, NAEP, TIMSS, and PISA."

My comment notes follow.

[Education Next]: Will the Common Core put an end to what has sometimes been termed the “math wars”? In your view, do the math standards resemble those recommended by the National Council of Teachers of Mathematics (NCTM), and what do you make of that similarity (or lack thereof)?

[W. Stephen Wilson]: The end of the math wars! You must be joking.

There will always be people who think that calculators work just fine and there is no need to teach much arithmetic, thus making career decisions for 4th graders [1] that the students should make for themselves in college. Downplaying the development of pencil and paper number sense might work for future shoppers, but doesn’t work for students headed for Science, Technology, Engineering, and Mathematics (STEM) fields.

There will always be the anti-memorization crowd who think that learning the multiplication facts to the point of instant recall is bad for a student, perhaps believing that it means students can no longer understand them. Of course this permanently slows students down, plus it requires students to think about 3rd-grade mathematics when they are trying to solve a college-level problem.

There will always be the standard algorithm deniers, the first line of defense for those who are anti-standard algorithms being just deny they exist. Some seem to believe it is easier to teach “high-level critical thinking” than it is to teach the standard algorithms with understanding. The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared.[2] Avoiding hard mathematics with young students does not prepare them for hard mathematics when they are older.

There will always be people who believe that you do not understand mathematics if you cannot write a coherent essay [3] about how you solved a problem, thus driving future STEM students away from mathematics at an early age. A fairness doctrine would require English language arts (ELA) students to write essays about the standard algorithms, thus also driving students away from ELA at an early age. The ability to communicate is NOT essential to understanding mathematics.

There will always be people who think that you must be able to solve problems in multiple ways. This is probably similar to thinking that it is important to teach creativity in mathematics in elementary school, as if such a thing were possible. Forget creativity; the truly rare student is the one who can solve straightforward problems in a straightforward way.

There will always be people who think that statistics and probability are more important than arithmetic and algebra, despite the fact that you can’t do statistics and probability without arithmetic and algebra and that you will never see a question about statistics or probability on a college placement exam [4], thus making statistics and probability irrelevant for college preparation.

There will always be people who think that teaching kids to “think like a mathematician,” whether they have met a mathematician or not, can be done independently of content. At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics. They are wrong. You learn Mathematical Practices just like the name implies; you practice mathematics[5] with content.

There will always be people who think that teaching kids about geometric slides, flips, and turns is just as important as teaching them arithmetic. It isn’t. Ask any college math teacher.

The end of the math wars! You must be joking.

[1] " making career decisions for 4th graders "

This is one of the big problems I have with the kids' school. Their curriculum makes it almost impossible to follow a path towards a STEM career. Our school uses the weak "Everyday Mathematics" curriculum, but even does that poorly--every year, they only get through about 2/3rds of the material. Year after year, those 1/3rds left behind add up. The entire 6th grade math curriculum is a review of 1st-5th grades, because the kids are so poorly prepared for pre-algebra. And even there, they are already 60% of the way through their school year (even counting the week-long trip that is coming up in March) and are only through chapter 5 of a 13 chapter text. Chapter 6 is the always-exciting "Using Multiplication"!! This is supposed to be 6th grade, third trimester work, and these kids have no idea how to work with fractions, calculate the area of a circle, or the volume of anything! This is simply not a track that will allow kids to take calculus senior year of high school, which is what many STEM majors in college need.

[2] "The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared."

Try the lattice method with large numbers or decimals! At open house for 4th grade this year, the parents were doing a good job of eating the teacher alive. Sure enough the lattice method came up, and someone asked about doing it with bigger numbers. My sister piped up and asked about doing it with decimals--The teacher didn't know how to do it! Another parent, with an older kid, started to explain, and my sister said--"Yes, we know how to do it; the point is she (the teacher) doesn't know how to do it!" Yet, they still spent several weeks doing it this year, and if you used the standard algorithm on your homework, you were graded down.

I remember when the 3rd grade teacher wanted to show his students how well and quickly the lattice method worked. He had someone come up and do the standard algorithm on the board while he did the lattice method. Lo and behold, the teacher won! Our kid came home defending the lattice as "quick!" I had to point out to him that the teacher had cheated; he had drawn the lattice in advance—the most time-consuming part was thus ignored. I showed our kid how long it actually takes to do the two methods. But it's a strange thing, kids can get very defensive about their teachers, even when the teachers are full of … The kid got mad at me for showing him the teacher was wrong.

[3] " you do not understand mathematics if you cannot write a coherent essay "

This is actually a bigger problem than it seems. There has been a push for many years to drive reading and writing into every class, including math. No similar push has been made to get math into reading and writing classes—leaving less math time for actual math. But that's not even the big problem.

Some kids excel at language, some kids excel at math. Not all the kids who are good at one are also good at the other—though many are. In particular, many boys hate the language parts of school (especially when they are forced to write or read self-reflective pieces about emotions, hopes and dreams—sometimes it's better when they are allowed to blow things up with words and read snot jokes.) For many of the boys who struggle with language (and it can be something as simple as have slower-to-develop fine motor skills which makes writing a (literally) painful chore) math is their salvation. They can be good at math without having to put any of it into words.

At least, they used to be able to. Now half the problems are word problems, and half their answers have to be too. This is one of the reasons boys are having so much trouble in school. For the more math-oriented boy, they no longer can escape their weak language skills.

Also, ask yourself this: which do you think is easier for kids to master, a set of 26 symbols with 42 different sounds, joined together in increasingly complex and confusing ways. Or a set of 10 well defined symbols that always mean the same thing and follow simple and easy to experience rules. "Wind" can be something that blows, or "wind" can be something that rolls up. 10 is always 10, 15 is always 15. There is some evidence that pushing arithmetic at an earlier age and backing off on the language skills could be beneficial for a non-negligible segment of kids. In essence, kids can develop a natural and strong understanding of numbers before they develop a similar understanding of phonics, vocabulary, language and the motor skills needed for reading and writing.

[4] " you will never see a question about statistics or probability on a college placement exam "

I'm not so quick to dismiss statistics. I think it is the most-important worst-taught subject in school. If it is not part of the regular math sequence, I think it should be a separate semester-long class at the high school level. Every single day we are bombarded with statistics, and without learning how they can be manipulated, exaggerated, and misused, we are all apt to fly off the handle when we hear our (completely insignificant) RISK HAS DOUBLED! Or 50% of people polled think you're an IDIOT (when they only asked your best friend and your twerp of a brother.) People need a far better understanding of statistics than they currently have. My high school required a one-semester economics course; they should also have required one semester of statistics.

[5] " You learn Mathematical Practices just like the name implies; you practice mathematics"

Amen. I keep telling the kids this one. You can only get good at math and science by doing as many problems as you can get your hands on. If the teacher assigns the even problems, and the book has the answers for the odd in the back, do the odd too! The more, the better.

This is also the biggest problem with the ALEKS online math program. They give a kid three problems, and if they get them right, that's it. Eventually, the kid will be given a test on whether they've really learned it or not, and often will have to repeat the section, again and again—with a feeling of failure instead of mastery. It would have been better to be given many more examples before letting the student cross that topic of their list. It takes a lot of practice to really learn long division or how to find a least common denominator. Practice makes perfect.

Paying the price

The 9-year-old boy is bored.

This is becoming quite a problem, and he's complaining about it more and more.

First of all he's bored in science class. This particular problem started when I decided to be sneaky. I noticed that "The Magic School Bus" was airing on TV, commercial free in the mornings, so I set our DVR to record it. If you don't know about this show, it is a science-based cartoon where a magical teacher takes her third grade students on science adventures. They might shrink to the size of cells and enter a body to see how the immune system works, or they might go back in time to see the dinosaurs. The episodes are well done and actually informative. If you watch all of them, you really would have a good elementary-school level knowledge of science. When I began recording the show, I didn't tell him to watch it, or even tell him that I was recording it. I thought he might find it on his own on the DVR's menu. He did. It became one of his favorite shows, and he's watched each episode several times.

The problem is, now everything he is supposed to be learning in science class he has already learned from "The Magic School Bus," so he's bored in class. I still think there are valuable things for him to learn in class, and the teacher is one of the best in the school, but most of what he's being taught he already knows. The one good thing on the horizon is the school science fair. In third grade they present an animal (he did Great Horned Owls) and in fourth grade they present either a recent development in science or a major historical invention (his sister did the Mars rovers Spirit and Opportunity). That project should start up in the second semester, and should help alleviate his science boredom.

The second problem is in math class. Because he's been working on Aleks, and has done a sizable chunk of the 4th grade standard curriculum (in 2 months), everything in his math class is going to be review. The other day they started to work with variables in his class; he said he'd done this already, and the teacher asked him to help her present it. That was nice for him, but he's still bored and frustrated that he isn't learning anything new in math class. As far as I can tell, this problem is permanent. I'm going to keep him moving in math at home regardless of what happens in school. (I spent some time this morning creating and finding some supplementary material on multiples, primes, and factoring.) He needs to spend some time outside of Aleks solidifying some skills that only come through practice: standard arithmetic algorithms for addition, subtraction, and multiplication. Lots of practice with long division (which his school's text book literally doesn't believe should be taught at all.) And lots of work with fractions. But I see him getting to the 5th grade curriculum within a month or two.

That's fine by me. The school's curriculum moves too slowly and they allow no opportunity for kids to work ahead. But moving ahead will make all math at school from this point on review and, thus, boring.

I guess the kid will just have to be bored.

Aleks update

It's been about a month since the boy bumped up to the Level 4 course on Aleks. When he started, he knew about 63% of the fourth-grade curriculum, according to the California state standards.

One month later, he has spent about 9 hours working on the program. He is finding fractions very confusing; in part because he is always trying to figure them out pictorially, and he doesn't know how to go about it. Today however, I got him to some level of understanding of the "bowtie" method of adding and subtracting fractions with different denominators.

Bowtie method:

1) Get a common denominator by multiplying the two denominators together.
2) Multiply the left numerator by the right denominator
3) Put in the correct sign
4) Multiply the right numerator by the left denominator.

I also think I drew enough pictures so that he sort-of gets it. He needs more work on fractions in general, though. Especially converting mixed and improper fractions, and reducing fractions.

I have been assigning him some extra work in multiplication, which the program allows me to do. They call it a quiz, but I think of it more as a review worksheet. Sometimes you just have to work dozens of problems before it really sinks in, and Aleks doesn't do that unless you tell it to.

So, after a month, the boy has learned about 20% more of the curriculum, and currently stands at 84% of the CA standards for 4th.

He is doing about 7 topics per hour, and he has about 32 topics left. So another 5 hours or so should get him through. I would love for him to complete level4 before he does standardized testing in mid-November. That should be doable.

Aleks says...

A few days ago, the boy (9) was working on Aleks. He had 3 of 5 pie pieces done, and another one was nearly done. Then, he got a bee in his bonnet and spent over an hour two days straight on the program. It's a really nice problem to have when you think your kid is working too hard and should back off! I didn't want him to burn out.

Still, yesterday, with the promise of getting his very-own real-world pumpkin pie if he finished his virtual math pie, he got through the rest of Level 3. This means in less than a month, he has done 45% of the California state standards for 3rd grade. How well he knows it, I'm not sure. Each topic only needs about 5-6 problems done correctly to pass it. It might be too much of a once-over-lightly approach, but, since math is cumulative, I'm hoping it will stay in his head.

Here are his pies:

Tomorrow, I'll switch his account to Level 4, and he'll take the Level 4 assessment for the first time, and get a brand new pie to work on.

Today, he was very proud of himself, and was shouting: "I won the pie!"

To which I answered; "I two the pie."

"I three the pie," he answered.

"I four the pie."

"I five the pie."

"I six the pie."

"I seven the pie."

"I eight the pie," I said, triumphantly.

"YOU ATE MY PIE!!!" he said as he attacked me.

We laughed and had a good day.

Spending time with Aleks

The 9-year-old boy has now used the Aleks program about 4 times. Some of that time was working with their "Quick Tables," which is a math-fact learning tool.

Quick Tables was a bit frustrating at first, because before they throw one math fact at you, they want you to have the keyboarding skills to be able to type in the answer quickly. After several sessions of simply typing in numbers, I punted. Though he was getting faster, he still wasn't getting to the point of the exercise: math facts. So, I took over the keyboard and now do the typing for him. We've used it twice, going over all 4 types of facts, but focusing more on multiplication. The program works cleverly. You begin with very simple facts like x1 or x2, then move up from there. It knows what you know and works on improving. I like it. I also like that it isn't flashy or time-wasting. Many online math games are more game than math. The kid ends up spending their time shooting asteroids instead of doing math.

The second part of the program is the Pie. The boy has a pie chart with each segment partially shaded. The shaded area shows how much of the pie he has mastered. He gets to choose which pie piece to work on, and which topics to learn. For each topic the program offers a few problems with an explanation there if you need it--you don't have to see it if you don't need it. After you've done a few problems--I think you have to get 3 or 4 in a row correct, the program allows you to move on. I'm happy that the boy realizes that three or four problems are not enough to really get a math concept, and he will often choose the "More Problems" option without any prompting from me. After a couple more problems, the program moves him on and back to his pie to choose another topic. He has already mastered 14 topics of the total 127 in the 3rd grade curriculum. That means he has moved from a 55% to 66%, To put it another way, he's learned 11% of the 3rd grade curriculum in just 4 sessions.

Instead of logging into the program and walking away, I sit with him. I can catch when he is going wrong, prompt him to use the explanations, and explain further if he needs it. The one time I walked away, he found it frustrating. I don't think he wanted to look at the explanations, or he didn't understand them if he did.

I also wonder if the initial assessment wasn't off because we did it near the end of a lazy summer vacation. I think that probably caused him to get a lower score on the basic arithmetic, but while sitting with him, I realized he has some big gaps. He's been doing geometry and was confused about the terms perimeter, parallel, and perpendicular. The perimeter problem surprised me a great deal. He was presented with a grid with a shape shaded in the middle. He easily counted the shaded squares to get the area (or multiplied if he could), but he wanted to count the number of unshaded squares around the outside and call that the perimeter. I think he got straightened out now, but he needs to review that a couple of times to lock it in. He also had no clue about equivalent fractions (x/5 = 12/20, what's x?,) but caught on very quickly. I don't think he's done much in the way of fractions at school other than counting what fraction of a figure is shaded.

I'm going to continue working with him every-other or every day if we can manage it. I don't want to do long sessions and burn him out, but he seems to enjoy it, and would often go on longer. Right now, I have my sites set on his standardized testing for this year. He'll do it in November, and at this rate, he should be done with the 3rd grade content and on into 4th grade math by then.

Update: We finally got past the assessment for multiplication, and I saw a great difference in his interaction with it almost immediately. He was shown the grid of multiplication, shown which he's already mastered and which need work. The program then offered several for him to focus on. We must have had some typing problems because there were several x2's that he certainly knew. With the chart in front of him, he quickly became interested in mastering the unmastered. In addition, he now has access to a couple math games. He also worked on a few new math topics in the main section of Aleks. He's almost up to knowing 70% of the 3rd grade curriculum! Wheee.

Aleks says

In an effort to make sure that the 9 year old boy isn't playing catch-up as much as his sister, I've signed him up for Aleks.com's math program. It is an online math tutoring program that I found mentioned on several home schooling and parent websites. It starts with a 30-question evaluation of what the student knows.

I gave the boy, who is going into 4th grade, the 3rd grade evaluation. I wasn't entirely surprised, but I was entirely disappointed, that he only scored 55% on the test. That means he knows 55% of what he should--and that is comparing his knowledge to the California standards (we live in Los Angeles.) He was okay with the basics, but weak in geometry and fractions. His math program is philosophically opposed to teaching long division, so he will need some work with that, and his sister hasn't really been taught unlike fractions either, or division of fractions. Aleks, I hope, will fill in the blanks.

I gave his sister the 6th grade test (she's going into 6th and has been getting a great deal of tutoring in the last 6 months) and she scored a 71% on it--not bad. She already knows 71% of this year's curriculum and school doesn't start for a few days yet.

So, I will be using Aleks for him and not for her.