Qualitative Analysis of New Standards Reference Exam Content

Compared to that of the Core-Plus Curriculum

Greater Philadelphia Secondary Mathematics Project

Spring, 2000

The Core-Plus curriculum focuses on four strands that are repeated across the different grade levels. These four strands are Algebra and Functions, Geometry and Trigonometry, Statistics and Probability, and Discrete (or Finite) Mathematics. Due to the nature of this “spiraling” curriculum, some of the topics for which students have been tested may have been introduced to them, but not to the degree that is required for them to successfully answer the questions. For example, algebra and skills related to it are stressed throughout the curriculum, but conceptual approaches to understanding algebra are focused on before writing equations. Consequently, questions that ask students to write equations are not appropriate for these students at this point. Students take the New Standards Reference Exam towards the end of the sophomore year. Equation writing skills are stressed more in the third and fourth years of the Core-Plus curriculum.

Some questions on the New Standards Reference Exam deal with topics to which students have not yet been exposed. For example, Probability and Logic are two content areas not covered in the Core-Plus curriculum until after students have taken the test. A unit on Probability is scheduled in Core-Plus at the very end of the 10^th grade year, occurring soon after students have taken the New Standards Exam. Logic skills are developed in the Core-Plus curriculum during the third and fourth years. Some topics that were not covered, such as Percentages, Measurement, Proportions, and Rates & Ratios are generally covered as part of a middle school’s curriculum, so it is appropriate that they not be included in Core-Plus.

In terms of the alignment of content between the Core-Plus curriculum and the New Standards Reference Exam, the most striking finding is how many content areas were covered in the Core-Plus curriculum that were not tested. That is, students do not seem grossly unprepared for taking the New Standards Reference exam. However, they are prepared for a variety of topics and content areas for which they are not tested by this exam. The following tables outline the matches between the New Standards Reference Exam and the Core-Plus curriculum, both at the global and item-by-item levels.

Match between Content Areas of Curriculum and Test

Tested Areas NOT Covered	Covered Areas NOT Tested	Covered Areas Which Were Tested
Percentages	Graph Models	Patterns in Data
Measurement	Exponential Models	Patterns of Change
Probability	Simulation Models	Linear Models
Logic	Matrix Models	Patterns in Space
Equation Writing	Patterns of Association	Patterns of Location, Shape, and Size
Proportions	Power Models
Rates & Ratios	Network Optimization

Note: These comparisons are based upon materials explicitly stated in the Core-Plus curriculum. The extent to which these materials were actually covered in classrooms is not known.

Item-by-Item Analyses of New Standards Reference Exam:

Match with Core-Plus Curriculum

Forms C & D—Multiple Choice Section same for both

Question	Type	Content Area	Covered?	If No, when?
1	MC	Percents	No	Middle School
2	MC	Algebra	Yes	Y
3	MC	Algebra	Yes	Y
4	MC	3-d Geometry	Yes	Y
5	MC	Interpretation of graphs	Yes	Y
6	MC	Size transformation	Yes	Y
7	MC	2-d Geometry	Yes	Y
8	MC	2-d Geometry	Yes	Y
9	MC	Measurement	No	Middle School
10	MC	Coordinate graph	Yes	Y
11	MC	Interpretation of graphs	Yes	Y
12	MC	Percents	No	Middle School
13	MC	Probability	No	End of Year 2
14	MC	Probability	No	End of Year 2
15	MC	Permutations	No	End of Year 2
16	MC	Area under a curve	Yes	Y
15	MC	Number line	Yes	Y
18	MC	2-d Geometry	Yes	Y
19	MC	Logic	No	Years 3 & 4
20	MC	Numerical reasoning	Yes	Y

Form C—Short tasks

Question	Type	Content Area	Covered?	If no, When?
1	OE	2-d Geometry	Yes	Y
2	OE	2-d Geometry	Yes	Y
3	OE	Algebra	Yes	Y
4	OE	Algebra	Yes	Y
5	OE	Equation writing	No	Year 3
6	OE	Size transformations	Yes	Y
7	OE	Proportions	No	Middle School
8	OE	2-d Geometry, Spatial	Yes	Y
9	OE	2-d Geometry, Spatial	Yes	Y
10	OE	2-d Geometry, Spatial	Yes	Y

Form C—Long and medium tasks

Question	Type	Content Area	Covered?	If no, When?
1	OE	Probability	No	End of Year 2
2	OE	Probability	No	End of Year 2
3	OE	Algebra	Yes	Y
4	OE	Equation writing	No	Year 3
5	OE	Table reading	Yes	Y
6	OE	Percents	No	Middle School
7	OE	Percents	No	Middle School

Form C—Short and long tasks

Question	Type	Content Area	Covered?	If no, When?
1	OE	Graph estimation	Yes	Y
2	OE	Equation writing	No	Year 3
3	OE	Number line	Yes	Y
4	OE	Number line	Yes	Y
5	OE	3-d Geometry	Yes	Y
6	OE	Algebra	Yes	Y
7	OE	Algebra	Yes	Y
8	OE	Equation writing	No	Year 3
9	OE	Proportions	No	Middle School
10	OE	Proportions	No	Middle School

Form D—Short tasks

Question	Type	Content Area	Covered?	If no, When?
1	OE	2-d Geometry	Yes	Y
2	OE	Algebra	Yes	Y
3	OE	Interpretation of graphs	Yes	Y
4	OE	2-d Geometry	Yes	Y
5	OE	2-d Geometry	Yes	Y
6	OE	Data analysis; scatterplots	Yes	Y
7	OE	Data analysis; best-fit line	Yes	Y
8	OE	Data analysis; outliers	Yes	Y
9	OE	Size transformations	Yes	Y
10	OE	Proportions	No	Middle School

Form D—Short and long tasks

Question	Type	Content Area	Covered?	If no, When?
1	OE	Equation writing	No	Year 3
2	OE	Interpretation of graphs	Yes	Y
3	OE	2-d Geometry	Yes	Y
4	OE	2-d Geometry	Yes	Y
5	OE	Rates & Ratios	No	Middle School
6	OE	Rates & Ratios	No	Middle School
7	OE	Proportions	No	Middle School
8	OE	Proportions	No	Middle School

Form D—Long and short tasks

Question	Type	Content Area	Covered?	If no, When?
1	OE	Data Analysis; central tendency	Yes	Y
2	OE	Data Analysis; central tendency	Yes	Y
3	OE	2-d Geometry	Yes	Y
4	OE	3-d Geometry	Yes	Y
5	OE	3-d Geometry	Yes	Y
6	OE	Rates & Ratios	No	Middle School
7	OE	Rates & Ratios	No	Middle School