We’ll continue to examine the expectations outlined in the “Action Plan” that was introduced last spring as part of SCASD’s “Complete Elementary Math Program” that includes TERC’s Investigations. The Action Plan was intended to assuage the concerns of Board members and parents that Investigations is unchallenging and does not give enough attention to to computational fluency, knowledge of math facts, or algorithms.
In this post, we’ll look at when standard algorithms for whole number operations (like carrying, borrowing and long division) are expected to be mastered. As with our previous comparison of fact fluency expectations, we’ll present expectations along with what is expected in California and Massachusetts (MA is two documents here and here). California’s and Massachusetts’s are consistently rated as the best sets of math standards in the nation and the Action Plan was supposedly modeled on these standards.
1st Grade
SCASD: “1 digit +/- horizontal and vertical notation; 2 digit +/- (w/out regrouping)”
California: “Solve addition and subtraction problems with one- and two-digit numbers”
2nd Grade
SCASD: “2 digit +/- (regrouping); 3-4 [digit] +/- (w/out regrouping)”
California: “Find the sum or difference of two whole numbers up to three digits long.”
Massachusetts: “Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition (two 3-digit numbers and three 2-digit numbers) and subtraction (two 3-digit numbers).”
3rd Grade
SCASD: “3-4 digit +/- (regrouping); 2 by 1 digit x (with and w/out regrouping)”
California: “Find the sum or difference of two whole numbers between 0 and 10,000; Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 × 3 = __); Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = __).”
Massachusetts: “Add and subtract (up to four-digit numbers) and multiply (up to two-digit numbers by a one-digit number) accurately and efficiently”
4th Grade
SCASD: “2-3-4 digit by 1 digit x (regrouping); 2 digit by 2 digit x (regrouping); 2-3 digit by 1 digit ÷”
California: “Solve problems involving multiplication of multidigit numbers by two-digit numbers; Solve problems involving division of multidigit numbers by one-digit numbers”
Massachusetts: “Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits); Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).”
5th Grade
SCASD: “2-3 digit by 2 digit x (whole numbers); 4-digit ÷ 1-digit Division; 4-digit ÷ 2-digit Division (multiples of 10)”
California: “Demonstrate proficiency with division, including … long division with multidigit divisors.”
Massachusetts: “Accurately and efficiently add and subtract whole numbers. Multiply and divide (using double-digit divisors) whole numbers.”
In summary, it looks like SCASD’s expectations match those in MA in places, but more often is somewhat behind MA and a full year behind CA. Note that, even by 5th grade, students in SCASD are not expected to know how to divide using a 2-digit divisor that is not a multiple of ten (e.g., 4,387 ÷ 37). Note also that SCASD’s expectations seem to depend on whether “regrouping” (carrying and borrowing) is required. SCASD 2nd graders will get practice with carrying only when adding 2-digit numbers, but not with 3- or 4-digit numbers. What is the rationale for this? It would seem that once the concepts behind carrying have been understood that those concepts would generalize readily to problems with more digits, as is done in CA and MA. Finally, why does SCASD limit itself to 4-digit dividends and 3-digit factors, even by 5th grade? If the division algorithm, for example, has been taught and understood, why can’t it be applied to 84,387 ÷ 3 just as easily as it can to 4,387 ÷ 3?
In the final installment in this series, we’ll examine how fractions are covered in SCASD as well as in CA and MA.
All posts about expectations brought me to the next questions:
How SCASD expectations by level compare to national level? It is seems not. Why SCASD needs to come up with different expectations than national? Aren’t our kids going to go to the same universities as kids from all other districts and states? Alternatively, maybe school administration expects teachers in Middle schools and High school to patch up and speed up education there. I would like to hear some answers from Board members and school administration.