#exploringthecore

Consider a math test covering seven state standards taught so far and defined by targeted assessment questions that measure individual student ability for each standard, no longer measuring a student's ability to simply "do math".

Without standards-based grading, students that answers 4 out of every 7 questions correctly would receive 57% on the test as a whole - generally failing the math class at this point.

With standards-based grading, students that show proficiency in 4 of the 7 standards (each standard being weighted equally among the test questions) would receive a breakdown of which standards they have mastered and which they have not mastered. The student would still be failing the math class at this point, but the teacher and parent would be better informed as to which math skills are weak and should (or should not) be addressed.

Consider that the following third-grade math standards were assessed:

NBT.1 - rounding to the nearest 10 or 100 NBT.2 - add and subtract up to 1,000 OA.3 - use multiplication/division in word problems OA.4 - find unknown in multiplication/division OA.5 - apply properties of operations OA.7 - fluently multiply/divide up to 100 OA.8 - solve two-step word problems

If a student is proficient in FOUR of these seven standards, how would that knowledge benefit teachers and parents? Taking it one step further, if one of the standards NOT mastered is NBT.1, rounding to the nearest 10 or 100, how critical is this standard in regards to a student being prepared for the following grade level?

This image shows that rounding is introduced for the first time in grade three. The two years that follow apply this same basic skill but with larger numbers. The skill itself does not become more complex. As a teacher, I would not use this standard at this grade level to determine a child's ability to "do math". As a parent, it is important to know how a skill develops *across* grade levels to know when a skill is at a critical development point. With three other standards in need of improvement, I would prioritize which skills are targeted for students.

On the other hand, some skills in that same grade level are also introduced for the first time but clearly develop into more complex ideas with each passing grade level. Consider adding and subtracting fractions.

This image shows how adding and subtracting with fractions begins at this grade level and quickly develops conceptually with each passing year. A student that does not show mastery of this particular skill at each grade level will likely have a more difficult time as the skill does evolve into more complex concepts.

Bottom Line

Standards-Based Grading is a critical process for tracking individual student progress. It takes teachers time and effort to fully prepare and implement. It also takes a knowledge of what the standards say and how skills develop.

Both teachers and parents benefit from knowing how the standards develop in - and across - grade levels. Communication about strategies most appropriate for individual students improves when Standards-Based Grading is applied.

“Common Core is crazy!” - anyone that hasn’t read the standards.

Download the app “Exploring The Core” and swipe to see how core skills develop across grade levels according to the state standards.

Today, I asked a fifth grader to multiply 43 times 15. He got out a paper and pencil, lined up the 43 over the 15 and multiplied the 5 times 3, carried the 1, the 5 times 4, then the 1 times 3, the 1 times 4, put a zero as a placeholder, then added everything up and got an answer. Well, he had made an error in one of these steps so his answer was wrong and he was left frustrated because he had to go step by step to figure out what step of that process was wrong. 

Here’s why this matters...

This student refuses to acknowledge that any other way to multiply exists because he has never been required to use anything but this shortcut. He never bothers to consider the numbers being multiplied, only that "it works” and is repeatedly frustrated when it doesn’t work and can’t understand why.

In this problem 43x15, when multiplying the 1 times 3 and the 1 times the 4, it's easy to forget you are multiplying 10 times 43, which is 430. As for the 5 times 43, that’s 5x40 (200) and 5x3 (15) and adding 200+15 shouldn’t require a multi-step paper-and-pencil procedure - at most a post-it to jot down what you need to add... 

10x43=430. 5x40=200. 5x3=15. So... 430+215 = 645. 

Or if you prefer...

      43

   x 15

   215

+ 430 

   645

It's easy to rally behind passion, but this complaint is misguided.

The "common core" math problem presented is not in the Common Core State Standards. This particular problem comes from a textbook that chose to use a strategy for solving a problem that involves multiplication/division. Now whether that strategy is the best fit for that problem, or for a particular child, should be the target of this lady’s complaint. Strategies are NOT in the Common Core State Standards.

The sample problem in question reads: "18 students count around by a number and end with 90, what number did they count by?" The council was quick to answer because they are all adults and can guesstimate that 18 probably goes into 90 five times. If the next question was "how do you know?", I imagine the room would get very quiet, or responses would be similar to the speaker’s response: “because it makes sense.” This type of response is a double-standard for academic expectations especially in the K-5 grades. Rigor does not mean “learn the shortcut and move on because it works”. Rigor is providing deeper understanding of “why” and “how” shortcuts work the way they do. 

Again, whether this strategy is the best fit for a particular child solving this particular problem should be the target of complaint and conversation.

Not all strategies meet the learning styles for all students. Yet, only teaching one shortcut, or "memorizing" a procedure, in order to solve a problem has created generations of adults that think they are simply no good at math, except for the percentage that "got it".