Introduction
This is part of a series of second, fifth, and seventh grade Mathematics Program Reviews. This review includes a summary of the structure of the program, evaluations of a selected set of content areas, and evaluations of program quality. Ratings in these areas were made on a scale from 1 (poor) to 5 (outstanding). The overall evaluation was made using the traditional system of letter grades. For details of the methods used in this evaluation see Methods for Second Grade Program Reviews.
Structure
This National Science Foundation funded program lacks a student text. Instead there are 8 volumes of teacher manuals, each with about 75 to 135 pages of instructions to the teacher as to how to teach. The volumes contain, in addition, a set of black line masters for teachers to reproduce for students to use in the lessons. There is no index or glossary or other supporting materials of that type. The units are entitled
The teachers role in this program is moderately scripted. Even when the exact words that should be used are not given, there are explicit directions as to what to do next. Interestingly, this somewhat restrictive program for teachers is coupled to a complete discovery learning, constructivist philosophy student program. The program is dedicated to setting up ways in which students will be exposed to various situations and will develop their own strategies for doing things such as adding multidigit numbers. Calculators are available at all times and are required for two of the eight units. Mastery of skills or time proven methods is abjured.
The section "About the Investigations Curriculum" describes the nature of the curriculum quite well:
"The following aspects of curriculum ensure that all students are included in significant mathematics learning:
" Students spend time exploring problems in depth.
" They find more than one solution to many of the problems they work on.
" They invent their own strategies and approaches rather than rely on memorized procedures.
" They choose a variety of concrete materials and appropriate technology, including calculators, as a natural part of their everyday mathematical work.
" They work in a variety of groupings - as a whole class, individually, in pairs, and in small groups.
" They move around the classroom as they explore the mathematics in their environment and talk with their peers."
The second half of the last book has as its "Mathematical Emphasis":
" Inventing rhythm patterns using body actions
" Representing rhythm patterns showing sequencing and time
" Communicating with and interpreting written signals and codes."
These two quotes pretty much sum up the entire program: Poor focus, lots of child centered discovery activities and no meaningful mathematical content.
As the program is based on multiple experiential activities, the teacher has a particularly heavy burden in preparing each day for math class, with gathering all the materials, dividing the materials so each group of children has what is needed, copying the black line masters, and so on.
Content Area Evaluations
Addition and Subtraction of Whole Numbers [1.1]
This course guides children through a vast array of games and activities geared to providing them with a "feel" for numbers. In their adamance that facts and algorithms have no place in modern math classes, the authors accept that some children, at the end of second grade, will still add and subtract by drawing pictures and counting, or by counting back and forth on a "100 chart." So much emphasis is placed on personal strategies that an entire activity is devoted to adding 29 + 12 (book 5 page 7). The children do not work with numbers greater than 100, they are never expected to memorize their number facts and never see the standard method to add or subtract multidigit numbers. Place value does not seem to be emphasized. The title page of the book concentrating on addition and subtraction notes, as do all the books, "Grade 2, Also appropriate for Grade 3"(emphasis in original). In other words, so what if kids don't get anything in second grade, they can not get it in third grade as well.
Multiplication of Whole Numbers [1.0]
With the exception of some discussion of counting by 2's, 5's and 10's, multiplication is not obviously introduced. If the word multiplication is used, the reviewers could not find it. The concept of multiplication is hinted at in book 4, Investigation 2, session 3, in which students make rectangular arrays from square counters. The students spend some time "copying" arrays that have been flashed on the overhead for 3 seconds (the purpose of this activity is hard to discern). Later they build rectangles given a fixed number of squares. Since they are asked to describe their rectangles ("I have 2 rows with 7 cubes in each") the idea of 2 x 7 might come out, but this does not appear to be the purpose of the lesson.
Time [1.1]
There is no formal instruction in telling time. Teachers are encouraged to post a daily schedule, using both analog and digital representations. They are asked to identify time in conversations and note that something will happen in 15 minutes, for example, and ask what time it will be then. The teacher is instructed to set a timer for 1 hour intervals making a record of the times the bell rings over the course of a day. This pattern is to be repeated with half hour and quarter hour intervals, etc. Never mind how distracting this will be for all other lessons, or the fact that each time the bell rings and is reset, there will be a period of lost time, such that over the course of a day the 15 minute units will no longer be aligned with the hour. What will students discover then? Instead of doing exercises requiring them to tell time and compute elapsed time, students are asked to go home and collect data on how many clocks, digital and analog, there are in their homes.
Money [1.2]
What little there is to do with money in this book is a series of games based on collecting money to a certain amount (15 cents, 50 cents, a dollar, but no more) based on spinner draws. It is used as a method to "drill" individual addition strategies, not to teach money, change or powerful strategies for adding money.
Measurement of Length, Weight, Volume and Temperature [1.0]
An entire book (number 6) is dedicated to measurement, yet no real world measuring device appears. There are no rulers, no measuring cups, no thermometers, no balances. There are paper strips and non-standard measures such as "person jumps." Much of the time is spent on the computer making and measuring "paths." Area is only, possibly approached in the same lesson that might have involved multiplication but didn't (see multiplication above).
Perimeter [1.0]
Students do use their paper measuring strips to measure across their classroom, but not around, in book 6. Beyond this, there is no obvious evidence that this topic is covered.
Program Quality Evaluations
Mathematical Depth [1.1]
There is little or no mathematics of consequence in this book. Although directed primarily at grade 2, the books all say "Also appropriate for Grade 3" (emphasis in original). They might as well say appropriate for pre-school. If a parent truly cares about his child's math education, as soon as this program begins, the parent should start home schooling or send the child to Kumon.
Quality of Presentation [1.0]
This program is totally dedicated to discovery learning and away from mastery, depth, or any skill or understanding necessary to succeed in any mathematics based profession. The program claims to want to "ensure that all students are included in significant mathematics learning." They succeed part way, all students, living or dead, can participate. The second part, "significant mathematics learning," is missing.
Quality of Student Work [1.1]
Some of the games would be appropriate for a once a week change of pace, but it seems unlikely that a steady diet of such activities will allow any child to acquire the knowledge and skills needed to succeed in real third grade math or beyond. On the other hand, if a child stays in this program, or programs like it, he/she may go a long way before anyone notices how little he/she knows, understands or can do.
Overall Program Evaluation
There is nothing to recommend about this program. The use of this program in our public schools is a strong argument for vouchers.
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