Curriculum Focal Points
In 2006, NCTM issued a document called "Curriculum Focal Points" that presented the most critical mathematical topics for each grade in elementary and middle schools. American mathematics instruction tends to be diffuse and is criticized for including too many topics each year. In part, this publication is intended to assist teachers in identifying the most critical content for targeted attention. More such publications are planned.
NCTM stated that "Focal Points" was a step in the implementation of the Standards, not a reversal of its position on teaching students to learn foundational topics with conceptual understanding. Contrary to the expectation of many textbook publishers and educational progressives, the 2006 Curriculum Focal Points strongly emphasized the importance of basic arithmetic skills in lower and middle grades. Because of this, the "Curriculum Focal Points" was perceived by the media as an admission that the PSSM had originally recommended, or at least had been interpreted as recommending, reduced instruction in basic arithmetic facts.
The 2006 Curriculum Focal Points identifies three critical areas at each grade level for pre-kindergarten through Grade 8. Samples of the specific focal points for three grades are below. (Note that the Simple Examples below are not quotes from the Focal Points, but are based on the descriptions of activities found in the Focal Points.)
| Focal points | Related content standard | Simple Example |
|---|---|---|
| Pre-Kindergarten Focal Points (student age: 4 or 5 years old) | ||
| Developing an understanding of whole numbers | Number and Operations | How many blue pencils are on the table? |
| Identifying shapes and describing spatial relationships | Geometry | Can you find something that is round? |
| Identifying measurable attributes and comparing objects by using these attributes | Measurement | Which one is longer? |
| Fourth Grade Focal Points (student age: 9 or 10 years old) | ||
| Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication | Number and Operations, Algebra | An auditorium has 26 rows of 89 seats. How many seats are there? |
| Developing an understanding of decimals, including the connections between fractions and decimals | Number and Operations | Draw a picture of 0.2. What fraction is this? |
| Developing an understanding of area and determining the areas of two-dimensional shapes | Measurement | How could we find the area of this L-shaped room? |
| Eighth Grade Focal Points (student age: 13 or 14 years old) | ||
| Analyzing and representing linear functions and solving linear equations and systems of linear equations | Algebra | The equation y = 4x + 4 shows the cost y of washing x windows. How much more will it cost each time I add 2 more windows to the job? |
| Analyzing two- and three-dimensional space and figures by using distance and angle | Geometry, Measurement | Use the Pythagorean theorem to find the distance between the two points on the opposite corners of this rectangle. |
| Analyzing and summarizing data sets | Data Analysis, Number and Operations, Algebra | What is the median price in this list? Does the median change if I lower the most expensive price? |
The Focal Points define not only the recommended curriculum emphases, but also the ways in which students should learn them, as in the PSSM. An example of a complete description of one focal point is the following for fourth grade:
Number and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication
Students use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts. They apply their understanding of models for multiplication (i.e., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multidigit whole numbers. They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.
Read more about this topic: Principles And Standards For School Mathematics
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