Last year was the third year of Prince William County Schools’ TERC Investigations mandate. The program was followed in every PWC elementary classroom from kindergarten to 4th grade, with fifth grade beginning use of the program this past Fall.
Each year the school district receives various reports from our testing contractor indicating how many students correctly answered each question. The district spent millions to create a data warehouse to store this information so that it could be easily extracted and enable school administrators to identify areas where our children face challenges.
One of our contributors asked the district to provide her with the overall percentage correct on the Math SOL for Grades 3, 4, and 5 from 2005 to 2009 by SOL subject area (content strand in SOL speak). This individual was told that it would cost the district over $200 simply to determine whether the data existed, and that the cost to obtain that data would likely be much higher. We found that to be quite telling, as it indicated to us that no one in the district has even bothered to look at our students performance by SOL area to see if there are areas where our children need a little more work.
We were able to obtain a copy of a report entitled “Student Performance by Question” for the 2009 math SOL. This report was given to the district for each school and lists the percentage of students who correctly answered each question on the SOL by subject area for the school and district as a whole.
We only have one year, so our analysis is limited, but even one year’s report indicated that there are areas where our children struggle. We chose a cut core of 85% correct and listed any question with 85% or fewer correct responses as presenting a challenge to our students. The areas our children appear to struggle with include: rounding, subtraction, division, fractions, probability or likelihood of outcome, and using and interpreting mathematics vocabulary.
Our children appear to have difficult rounding accurately. Our students were below the cut score on every rounding question in Grades 3, 4, and 5. Our students were above the cut score for questions involving identifying the place value of specified digits, so this area of concern appears to relate to the actual process of rounding as opposed to a difficulty grasping the concept of place value. Rounding digits within a number, as opposed to rounding the leading digit, appears to be particularly challenging for our students.
The VA DOE Curriculum framework suggests the 5 or above round up strategy for students. PWC, in its Curriculum Map, removed that language and suggested that students develop their own “meaningful” strategies for rounding (see here). Perhaps the county ought to consider brining back that old strategy.
Subtraction appears to present a challenge to our students in Grades 1, 2, 3, and 4 – both identifying situations where subtraction is necessary and subtraction operations. Subtraction did not appear to pose challenges in Grade 5. Addition did not appear to pose any challenges to our students in any grades.
In Grades 1 and 2 subtraction was our area of greatest weakness based on the data from the SDMT (see here). There were 4 questions on the SOL for Grade 3 and 4 relating to subtraction. Three of the four questions in each grade involving subtraction were below the cut score. For instance, in Grade 4 students were able to correctly estimate sums but not differences. Students struggled to subtract whole numbers, fractions, and decimals.
Many parents have observed that their children struggle with subtraction. These test results back up that observation.
Our students appear to struggle with division involving dividends larger than 1-digit. Our students were able to accurately model division, identify situations where division was warranted, and solve problems with 1-digit dividends even in problems with remainders. But division with dividends larger than 1-digit were challenging for our students.
You may recall that Investigations, the program our students follow, and the PWC curriculum framework suggest that a calculator is best used to solve “tedious” problems like division with dividends larger than 1-digit (see here). Perhaps it’s time to toss the calculator in elementary schools.
Parents of 3rd and 4th grade students will not be surprised to learn that fractions posed a challenge for their children.
Our students appear to be able to accurately identify and combine fractions of various magnitudes when given a graphical representation of those fractions. They struggle to order and compare different magnitudes of fractions and to subtract fractions of different magnitudes, especially when a model is not given.
Every question in Grades 3, 4, and 5 relating to ordering fractions, comparing the magnitudes of fractions, and identifying the lowest fraction was below the cut score. Three of the four questions relating to subtracting fractions were below the cut score.
Fractions is one of those areas where models only get you so far. The test data indicate that our students do well when given models, but falter when those models are taken away. Models, especially with fractions, are useful in helping students understand fractions, but models can not be the only tool available to students to solve problems involving fractions. Our children need to understand what common denominators are and how to find them quickly and accurately without folded bits of paper and clock faces.
Probability or Likelihood of Outcome
Our children struggled to predict the probability of an event and struggled to identify the most likely and least likely outcome. These difficulties were evidenced in each grade – from Grade 3 to 5. Four of the five questions relating to predicting outcomes were below the cut score.
Several questions which relate to understanding and using the language of mathematics crop up in Grades 3 and 5. For instance, our children struggled to identify the characteristics of various shapes and to select the appropriate quantitative symbol given a scenario in words.