#### FROM: *INDEPENDENT STUDY OF WASHINGTON STATE: **K-8 CURRICULUM REVIEW FINAL REPORT*, NOVEMBER 5, 2008

Summary, by blaineparents.org, Full text quote follows this summary

- Development of multiplication strategies for single-digit multiplication leading to fluency.
- Good representation of fractions and their addition and subtraction through clock and rectangular depictions.
- Students have the opportunity to maintain and practice learned skills and numerical fluency.
- Learn through exploration: discovery learning.
- Foundational concepts for area are well-developed in the main program. Supplemental activities provide practice with formulas for the areas of rectangles.
- Addition and subtraction of fractions has a good start with strong models.
- Students develop strong visual models for challenging concepts such as fractions, multi-digit multiplication, and area.

“Investigations

“**The strength of Investigations in the multiplication thread is the **

**development of strategies for single-digit multiplication leading to fluency.**The primary weakness is that the program does not lead to fluency with the standard algorithm. Although a supplementary activity does a nice introduction to the standard algorithm, relating it to the partial products algorithm and the place value area representation for multiplication, it is a standalone activity that is not mathematically incorporated into the program. The main program continues to develop multiple strategies, unaware that the standard algorithm has been developed, without providing the concentration necessary to provide fluency. With the help of a one-page supplement, the formulas for the areas of rectangles, parallelograms, and triangles are developed. The work with triangles is weak: the height of a triangle is not defined. There are an inadequate number of good problems.

**“The representation of fractions and their addition and subtraction, through representations, is nicely done in Investigations with their clock model and their rectangular grid model.** However, this follows weak and confusing work in grades three and four that fails to give students a solid start. Work in Investigations is limited to fractions with sums of less than 2 and there is very limited work with mixed numbers, leaving students unprepared to deal with fractions as simple as 11/3. Most importantly, common denominators are not well-developed, leaving students to struggle with arbitrary fractions. A typical student, using this program alone, is unlikely to meet the standards at the top of each of these mathematical threads.”

Page 24, emphasis added

“Investigations (K-5)

**“A typical day begins with “10 Minute Math” which gives students the opportunity to maintain and practice learned skills and numerical fluency**. Most of the remainder of the day is spent with students working in groups to investigate a mathematical situation or problem, which is different than applying mathematics they know to solve word problems or a problem based on a realistic context. *Investigations*, as the name suggests** favors an approach to learning that is exploratory in nature**. There is an emphasis on students discussing their strategies and solutions and skilled, knowledgeable teachers are critical to guide discussions and consolidate student understanding. Explanations of the mathematics and worked sample problems are rarely included in the student materials.

“Fluency with the standard algorithm is not developed, although **all of the necessary components of whole number multiplication are there and well presented. **The standard algorithm is taught, but followup practice problems and word problems are missing. **Foundational concepts for area are well-developed in the main program. Supplemental activities provide practice with formulas for the areas of rectangles,** but fail to properly develop the formula for the area of triangles. In particular, the height of the triangle is not defined. **Addition and subtraction of fractions has a good start with strong models,** but this foundation is not brought to closure with good development of common denominators. A typical student would not be well prepared for the next level of Washington mathematics using only this program.

**“The strength of the program is in the suggestions for conceptual development of key concepts. It is hard to stress how well this is done in Investigations. Students develop strong visual models for challenging concepts such as fractions, multi-digit multiplication, and area.** However, the transition to abstract fluency or generalization is not always developed or evident. For example, students develop good number sense, but may not develop efficiency in operations. Two other issues should be mentioned. Pacing may prove challenging. While each lesson is appropriately designed for a class period, the teacher is frequently asked to identify additional problems and to provide enough time for struggling students to understand the concept. At the same time, there are insufficient extensions or enrichments to engage adept students who may have already learned the concepts. Also, at some grade levels Investigations includes a great deal of content that does not align to Washington’s standards. For example, as much as half of the content in grade four Investigations matches to standards at other, usually lower, grade levels, suggesting Investigations teaches content later in a student’s career than the state’s standards require.”