The focus of school mathematics is shifting from a dualistic mission—minimal mathematics for the majority, advanced mathematics for a few—to a singular focus on a significant common core of mathematics for all students.—Everybody Counts(NRC 1989)

- students who have been denied access to educational opportunities, as well as those who have not;
- African-American, Hispanic, American Indian, and other minority students, as well as those considered to be part of the majority;
- females as well as males; and
- students who have not been successful, as well as those who have succeeded in school and in mathematics (NCTM 1990).

## What Is Core-Plus Mathematics?

## A Look at the Curriculum

- What information might the manager want to know about the kinds of shoes the customers prefer? Make a list.
- It's not enough to just have information. The manager needs to be able to organize and manage the information in order to make good decisions. What are some ways the manager might organize the information?

*Phase 2.*Once the context is set, the students, working in groups of four or sometimes pairs, explore the mathematical features of the situation through a series of more focused activities. The following activity, taken from the athletic shoe store lesson, illustrates the types of work students engage in. Previously, the students had collected class data on different brands of athletic shoes worn by class members.

#### Athletic Shoe Brands

A Common Core of Math for All - Table

Men | Women | |
---|---|---|

Converse | ||

Nike | ||

Reebok |

- The matrix above has three rows and two columns. How many rows were needed to display the class data? How many columns?
- Could you organize the class data using a matrix with two rows? If so, how many columns would it have? Which display would you prefer?

#### Monthly Sales

A Common Core of Math for All - table 2

J | F | M | A | MJ | J | J | A | S | O | N | D | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

L.A. Gear | ||||||||||||

Nike | ||||||||||||

Reebok |

- For each shoe brand, which month has the highest sales? What could be a reason for the high sales?
- How many pairs of all three brands together were sold in February?
- Which brand has more variability in its monthly sales? Explain how you determined variability. What is another way that you could determine variability?

- The Bass Shoe Outlet sells women's shoes sizes 5 to 11 and men's shoes sizes 6 to 13. The manager would like to have an organized display of the number of pairs of shoes sold in 1994 for each shoe size. Explain how a matrix can be used to organize this data. How many rows does this matrix have? How many columns?
- What are some advantages of using matrices to organize and display data? Disadvantages?
- Can the same information be displayed in a matrix in different ways? Explain.

*Phase 4.*Following this sharing and summarizing activity, students apply their mathematics to problem situations in different contexts, connect their newly developed mathematics to other mathematical ideas in the same or a different strand, reflect on the development of their mathematical thinking, and extend or formalize their mathematics. Each unit's final lesson gives students an opportunity to look back over the unit and consolidate their learning through a set of new modeling tasks.

## Benefits for Students

Teachers' perspectives.Students come to mathematics classes with different gifts and talents. By integrating the four strands in the curriculum each year, CPMP emphasizes the connected nature of mathematics and provides variety in content to accommodate and capitalize on individual interest, background, skill, and understanding. The following comments from three teachers who field-tested the first year of the curriculum support the attainment of this goal: The students who are more visual tend to enjoy the geometry and discrete math units, the tessellations, transformations, digraphs. Some students become "techies"; they enjoy program-writing. And then some students think more abstractly and are able to write symbolic representations for patterns. Because all of these diverse personalities are in the classroom together, the students work together and share ideas.I see the program as an equalizer for girls in math. It takes away the advantage the boys tend to have in symbolic manipulation skills.... It allows girls to see that there are other avenues for mathematics.My first-hour class had 10 students with special ed notations by their names.... These 10 students interacted appropriately with their classmates, contributed wonderful insight, and, during exams, showed very creative (and correct!) answers.

*Achievement data.*We field-tested Course 1 nationally during the 1994-95 school year with a broad, diverse cross section of approximately 5,650 students in 36 high schools in urban, rural, and suburban areas. Achievement measures were administered in a pre/post-evaluation design to all project classes and, for purposes of comparison, to 9th grade students enrolled in traditional courses, primarily algebra, in 10 of the schools.