Of the 42 items rated by teachers on the Materials Review subcommittee, Math Expressions was rated the highest on 26 items and lowest on just 1. Investigations was rated highest on only 13, and lowest on 14. enVisions was rated highest on a mere 2 and lowest on 26.

Broken down by ratings area (e.g., content, instruction, assessment, etc.) and grade level, Math Expressions is rated higher than Investigations 75% of the time:

According to their literature:
“Our new math curriculum Everyday Mathematics teaches a number of ways to do grade-level computations. Some of them are hundreds of years old, but simply aren’t the way we have traditionally taught in U.S. schools. A few of these algorithms are emphasized more than others, and they are called ‘focus algorithms’.”

Everyday Math’s focus algorithms for each operation are:

Mathematical Operation — Name of Algorithm
Addition — Partial-Sums Addition
Subtraction — Trade-First Subtraction
Multiplication — Partial-Products Multiplication
Division — Partial-Quotients Division

Some of the approaches EM endorses you really have to see to believe.

The Math Review Committee members had a chance to look over two grades’ worth of EM materials. What did I learn? In brief: Grade 2 does NOT cover the standard algorithm. Grade 5 encourages calculator use to convert fractions to decimals and percents (p. 325) as well as later addition of fractions. Overall, insufficient, minimal practice is provided and certainly not enough to permit mastery of computations.

That’s odd because the Common Core standards require fluency with the standard algorithm. For grade 2: “Compute sums of two three-digit numbers, and compute sums of three or four two-digit numbers, using the standard algorithm; compute differences of two three-digit numbers using the standard algorithm.” A Grade 4 standard is “Compute products of two-digit numbers using the standard algorithm“. Grade 5 expects students to “Use the standard algorithm for each of the four operations on decimals”.

Clearly, Everyday Math’s ‘Focus algorithms’ aren’t going to cut it in any grade.

It’s safe to get rid of them now, right? After all, SCASD has been piloting enVision and Math Expressions, and I anticipate their results will be shared at the next board meeting on 5/23 and we’ll have a new math program proposed to the Board. Time to clear out some space!

We’re still using the Singapore Math books at home and sometimes for our after-school ‘math club’, so those will stay. And the others? So far, several have been promptly recycled (e.g., Everyday Math, ThinkMath are uselessly constructivist), but others really have good potential to be useful (e.g., Saxon Math) and deserve some longevity.

But what to do with a full set of K-6 Saxon Math textbooks, teacher manuals, and lesson plans? Well, I first offered them to a local elementary school. To my surprise “No, thanks” was their answer. Hmm.

Next stop: the Pattee-Paterno Library at Penn State. Their response: “We would be very happy to have the Saxon materials for the Instructional Materials collection in the Education and Behavioral Sciences Library. Thanks for thinking of us!” yay!

Now, if I can just get my act together to consolidate, load them up, and get them over there Hopefully, by the first of June, these will be available for families that might need or want to work on some math with their kids over the summer. After seven plus years of Investigations, there is definitely work to do….

Grades 1 through 6 are about creating interest and mastering basic skills. Think and speak positively about math and science. Pay attention to math and science teaching in your child’s elementary school. Review your child’s science and math homework. Don’t perpetuate the outdated cultural bias that girls aren’t as good at math. By grade 5 make sure your child has mastered the necessary skills.

In grade 7 – Talk to teachers about whether or not your child is performing at grade level. This is important, because if your child is not performing “at level” in math, science, and English, now’s the time to get some extra help. Likewise, if your child shows interest in math and science, now’s the time to ask about special opportunities for summer or advanced work. Register your child to take Algebra I in the eighth grade. It’s essential preparation for courses to follow.

For grade 8 – If your child has a specific career in mind, make sure he or she is taking the necessary math and science courses make that choice possible. Encourage your child to take Pre-AP or “honors” courses. Stress the importance of taking as much math and science as possible in high school. Your child should take Algebra I in the eighth grade to prepare for math courses to follow. Algebra is the gateway course for math and science literacy for all students, not just the academically gifted.

In grade 9 – Students should take Geometry, part of the essential foundation to move forward in today’s technologically competitive world. Your child also should take Pre-AP Biology to put them on a path to take both Chemistry and Physics before graduation.

For grade 10 – This is the time to take Algebra II, another keystone for success in today’s world. Your child should also take Pre-AP Chemistry, which is the prerequisite to all of the AP science courses.

In grade 11 – This is the time to take Algebra II, Pre-Calculus, or AP Statistics, to acquire an even stronger math and science foundation. Usually students take Pre-AP or honor physics at this point. Students can also take a second science course such as AP biology or AP chemistry. This is the year most students start taking AP classes like AP English language or AP science.

From Investigations:

From Singapore Math:

So, in which assignment is something about math actually being taught and learned?

If this weren’t so stupid, it would almost be funny. Almost.

I. The third problem set in “Unit 4: What’s that Potion?” in the 5th grade (TERC) Investigations Math Student Activity Book, Session 1.1:

Everyday Uses of Fractions, Decimals, and Percents

List in the spaces below the everyday uses you find for fractions, decimals, and percents. Cut out your examples from used magazines and newspapers, and attach them to this sheet.

Everyday Uses of Fractions

[space to attach]

Everyday Uses of Decimals

[space to attach]

Everyday Uses of Percents

[space to attach]

II. The third problem set in “Unit 3: Fractions” in the 5th grade Singapore Math Primary Mathematics Workbook 5A, pp. 53-54:

Add. Give each answer in its simplest form.

1.

(a) 7/8 + 3/4 = 7/8 + ?/8 =

(b) 2/3 + 4/9 = ?/9 + 4/9 =

(c) 4/5 + 3/10 =

(d) 3/4 + 7/12 =

(e) 5/6 + 2/3 =

(f) 1/2 + 9/ 10 =

2.

(a) 1/6 + 3/4 = ?/12 + ?/12 =

(b) 5/9 + 1/2 = ?/18 + ?/18 =

(c) 1/2 + 3/5 =

(d) 2/5 + 3/4 =

(e) 9/10 + 1/6 =

(f) 3/10 + 5/6 =

Keiser (2010) helpfully reports on outcomes for middle school students who were instructed using Investigations in Number, Data and Space during their elementary school math classes. Her study reports on sixth- to eighth-grade students assessed with the following problem:

“Problem 2: Consider the problem 26 X 45. First estimate what you think the product would be. Then solve for the exact answer using two different methods” (p. 221).

Her findings are disturbing:
2 digit multiplication for pqme

Sadly, only 62.2% of the approaches applied by middle school students trained with Investigations correctly calculated the correct answer to this basic multiplication problem. No errors were made using the partial product method, but it was used in only 7.3% of the students’ attempts. The standard algorithm was attempted by only 12.6% of cases and 57.8% of those answers were incorrect. Similarly, incorrect answers were obtained in 31.0% and 38.5% of students’ application of the array and cluster methods, respectively.

Overall, only 54.7% of the middle school students correctly answered the question. That is absolutely pathetic. What this tells me is that the highly touted flexibility and multiple approaches to problem solving that Investigations stresses have failed to produce students who can solve simple math problems.

Moreover, if only 1 in 10 even attempted to use the standard algorithm, it is would seem nearly impossible that grade 5 students instructed via Investigations will be able to meet the simple standard above: Fluently multiply multi-digit whole numbers using the standard algorithm.

9+1=10 1+9=10 8+2=10
5+5=10 7+3=10 3+7=10
2+8=10 4+6=10

OK, so a couple numbers were written backwards and 0+10=10 and 6+4=10 were missed. What’s odd to me is that this approach isn’t considered as ‘advanced’ because no pictures were drawn or words written. The funny thing is that complete and accurate number sentences/equations were used — which is certainly more advanced than drawing circles around pictures.

A similar proficiency issue is mirrored in a recent article in NCTM’s electronic newsletter (“Shifting our computational focus”, v 16 no 4, August 2010). Math educator Jane Keiser details middle school teachers’ concerns with students skills after years of TERC Investigations instruction (but strangely she misses the real concerns evident).

“We heard teachers complain that they have noticed a change in their current students’ abilities. For example, one teacher mentioned that students in the sixth grade did not seem to know what the term long division meant. When she would probe her students’ thinking, she realized that students could perform division but that they used other strategies to accomplish the task. Teachers noticed unfamiliar computational strategies for other operations as well,
and it often took students longer to perform a computation. ” (p. 2)

Given these and other concerns, the middle school teachers did mini-assessments with their sixth through eighth graders.

“Our first surprise was the amount of time it took our students to perform one simple computation. Some teachers reported that the following problem took the entire forty-two-minute class period for students to complete and share.”

Problem 1: Consider the problem 13 × 7. Create a real-life situation when you would use multiplication to solve this problem. Solve the problem, and be sure to show your work.

A whole period? This should take no more than 10 minutes to do and share. Of one teacher’s 90 students, here’s what they did to solve the problem:

Investigations clearly teaches and encourages use of arrays and clusters rather than the traditional algorithm. Sadly, approximately 1 in 5 was still using repeated addition in middle school. That’s a bit frightening, and if a whole period is required to answer a simple multiplication problem, proficient and efficient problem solving is not a high priority.

In a pattern similar to PSSA results in 2008 and 2009, socioeconomically disadvantaged kids are consistently doing better in surrounding districts at every single grade level in comparison to SCASD. While improvement in grade 4 in SCASD is visible and 85.7% are advanced or proficient (perhaps parts of the Action Plan were beneficial, e.g., giving kids more practice and fluency with math facts?), we still have only 58.1% and 63.3% of the disadvantaged 5th and 6th graders performing at that level, whereas 72.7-87.5% of similar Penns Valley and Bald Eagle students in those grades are proficient or better. One might posit that this ‘cumulative deficit’ directly reflects the impact of Investigations in K-5 on kids’ math skills.

Notably, the average instructional expenditure per pupil per year for the other four local districts is $6,255 (range: $6,096-$6,395), whereas SCASD spends $7,782 per pupil (per IES Common Core Data, 2010). Put another way, for each classroom of 20 students in SCASD, we spend $30,540 more than the surrounding districts. I certainly believe this is a worthwhile investment; however, it is also clear to me that a change in core curriculum/program and a smarter expenditure of instructional funds in mathematics cannot come quickly enough for our kids, especially for those who are economically disadvantaged.

Following the states’ widespread adoption of the Common Core Standards this summer, major publishers such as Pearson, McGraw-Hill Education, Houghton Mifflin Harcourt and others have been evaluating the extent to which their existing programs meet the new standards.

Gewertz’s recent article in Education Week (8/20/2010) indicated, “As teacher guides, course outlines, lesson plans, and other supports for the common standards begin to flow into the marketplace, many in education policy circles are raising questions about how to interpret the makers’ claims that their products are “aligned” to the common standards.” Notably, this article highlighted that “Some skills in math, for instance, are introduced at different grade levels in the common standards than in some publishers’ programs.”

The SCASD has invited the publishers of the math programs still being considered to present their materials to the district and Math Program Review Committee in early October. Parents, teachers, and community members are encouraged to attend and learn more about the available program options.

Wednesday, October 6th – Mount Nittany Middle School Cafeteria
6:00pm  -  Everyday Mathematics, McGraw-Hill, https://www.everydaymathonline.com/
7:15pm  -  Math Expressions, Houghton Mifflin Harcourt, http://hmheducation.com/mathexpressions/
update: these Wed times have been changed to 7:30 and 8:45 pm
Thursday, October 7th – Mount Nittany Middle School Cafeteria
6:00pm  -  Think Math!, School Specialty, http://www.harcourtschool.com/thinkmath/
7:15pm  -  Investigations in Number, Data & Space, Pearson, http://investigations.terc.edu/
8:30pm  -  enVisionMATH, Pearson, http://www.envisionmath.com/

Reviews of some of these programs are available through links on the right (e.g., NYCHOLD, etc).