Thursday, June 4, 2015

Math problems of the week: 6th grade Smarter Balanced "number sense" problems, cont:

More from the Smarter Balanced Consortium and its Common Core-aligned tests: the final items on a 6th grade number sense assessment.

Stimulus: The student is presented with a real-world or mathematical context and a graph of ordered pairs.

Example Stem 1: This grid shows the location of three points.

Enter the distance, in units, between point A and point C.

Rubric: (1 point) Student enters the correct numeric value for the distance (e.g., 7). Units of measure should be assumed from the stem.

Example Stem 2: This grid represents the layout of Tom’s neighborhood. Each unit on the grid represents 1 square mile.
• Tom’s house is located at (4, 2)
• A store is located at (–3, 2)
• Tom’s neighbors are located at (4, 4).

Enter the distance, in miles, from Tom’s house to the store.

Rubric: (1 point) Student enters the correct numeric value for the distance (e.g., 7). Units of measure should be assumed from the stem.

OILF Extra Credit:

1. Follow up to extra credit on last week’s POW: discuss the correlation between conceptual “depth” and mathematical challenge.

2. Discuss the lost opportunity in the above problems vis-a-vis a real-world application of the Pythagorean Theorem.

Auntie Ann said...

When I first glanced at the three dots on the grid, I was thinking this was a problem like: these three dots represent the corners of a parallelogram, give 3 possible locations for the fourth corner. But, nope.

Barry Garelick said...

Pythagorean Theorem, which used to be taught in 7th grade and sometimes 6th grade, has been moved to 8th grade in the Common Core standards.

SteveH said...

The fundamental flaw of yearly standardized testing of understanding and critical thinking is that it can't be done well and it doesn't provide good NCLB-sort of feedback of what to fix. It would be better to have these tests check for things like the times table, basic fraction manipulation and simple word problems. Rather, schools get rubric scores back that talk about problem solving and number sense. As in a meeting I attended at my son's school, poor problem solving grades led to the solution to work harder on problem solving.

Besides, teachers are the ones best placed to make judgments on a students' critical thinking and understandings. They see them day after day. Why would they need a yearly test to give them any sort of feedback. It won't work. It's too vague and most schools only care about results below the low proficiency level where basic skills are more important. Yearly tests can only be used as a way to catch really bad schools. It has nothing to do with any critical thinking and learning above a minimum. It's not part of a higher level teaching feedback loop. Talk of critical thinking and understanding is only cover for low expectations.

Really bad raw percent correct scores on these tests are turned into better looking percentages of how many kids reached a pathetically low proficiency cutoff. Then our school looks at their ranking in the state. Suddenly, really bad raw percent scores on simple tests become "Fourth in the State!" in the paper. Nobody sees the basic assumption that all students in K-6 are not taught on a math path that leads to STEM prep classes in high school. By definition. Nobody asks what the parents of the best student did at home. It would be a simple task. The assumption is that I did some really advanced work with my son in math. No. I ensured the basics.

S Goya said...

On the other hand, as an elementary math teacher in an English-language school for Chinese students, I find these kinds of problems useful for familiarizing the students with the English they need for the topic. Maybe ELL teachers in America have experienced the same benefit. But then of course to move on to real math. At that point, I either have to translate Chinese math problems, or find problems in American curriculum at least three grades above the grade I am teaching.