As I make another pass at “The Report” I have decided to include my thoughts here. I have moved the report into Google Docs where I am trying to have some of my colleagues collaborate on the report to generate ideas for how this will fit into whatever new math series we choose. I have lifted some pieces of the report and included my comments and questions. Feel free to add to them.
The first section they summarized was:
- To encourage the development of students in Grades PreK–8 at an effective pace, the Panel recommends a set of Benchmarks for the Critical Foundations (Table 2, page 20-See below). They should be used to guide classroom curricula, mathematics instruction, textbook development, and state assessments.
Fluency With Whole Numbers
By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers.
By the end of Grade 5, students should be proficient with multiplication and division of whole numbers.
Fluency With Fractions
By the end of Grade 4, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals.
By the end of Grade 5, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.
By the end of Grade 6, students should be proficient with multiplication and division of fractions and decimals.
By the end of Grade 6, students should be proficient with all operations involving positive and negative integers.
By the end of Grade 7, students should be proficient with all operations involving positive and negative fractions.
By the end of Grade 7, students should be able to solve problems involving percent, ratio, and rate and extend this work to proportionality.
Geometry and Measurement
By the end of Grade 5, students should be able to solve problems involving perimeter and area of triangles and all quadrilaterals having at least one pair of parallel sides (i.e., trapezoids).
By the end of Grade 6, students should be able to analyze the properties of two-dimensional shapes and solve problems involving perimeter and area, and analyze the properties of three-dimensional shapes and solve problems involving surface area and volume.
By the end of Grade 7, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.
So are the NYS standards going to change/be modified to align more closely to this report? Do we need to move towards the Curriculum Focal Points? Do we need less topics and more depth? As they mention in their first things first section (xiii) PreK-8 should be streamlined and should emphasize a well-defined set of the most critical topics in the early grades. I interpret that one way, meaning making sense of number, developing an understanding as well as having fluency of addition and subtraction combinations., etc. For some reason, I am conjuring up an image of students sitting in rows and teachers with rulers in their hands.
To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, each facilitating learning of the others. Teachers should emphasize these interrelations; taken together, conceptual understanding of mathematical operations, fluent execution of procedures, and fast access to number combinations jointly support effective and efficient problem solving.
What we need to be discussing is best practice. How do we discuss best practice? We have tried through curriculum writing. We have tried through mandatory staff development. We have tried with coaches. I have found what has work well are the informal discussions when people are not threatened with being embarrassed about not knowing. A better idea would be to start some Professional Learning Communities. They are sorely needed, will be better then any top-down imposed 18-hour Staff Development, and can lead others to seeing the value in Personal Learning Networks. I like this quote from the comments in the blog, Ruminate (from the post I linked to above):
Comment by D’Arcy Norman
Last for today:
Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall of addition and related subtraction facts, and of multiplication and related division facts. It also requires fluency with the standard algorithms for addition, subtraction, multiplication, and division. Additionally it requires a solid understanding of core concepts, such as the commutative, distributive, and associative properties. Although the learning of concepts and algorithms reinforce one another, each is also dependent on different types of experiences, including practice.
Does being fluent with the standard algorithm mean including all the work it takes to understand such algorithm? I still think we need to use the distributive property in 4th and 5th grade and then move to algorithm if needed. But since the traditional algorithm of multiplication is actual the reverse of how we multiply binomials, why do we even bother (FOIL vs. LOIF)? If Algebra is the push, why are we pushing illogical practice? Is it because that is the way it used to be taught? Is it politics?
To be continued…