Writing Math Items: The Context Dilemma

Writing Math Items

The Context Dilemma

Writing math items is a complicated task that requires much more of the writer than simply understanding the mathematical skill that’s being assessed. It also involves understanding the interests and issues of the students being tested. If math items involved only “naked number” items, those that are purely numeric in nature, this would not necessarily be the case. But math concepts are of little use if they cannot be applied in a problem-solving situation. The phrase “solve real-world and mathematical problems” is used repeatedly throughout the Common Core State Standards (CCSS) for Mathematics. There is, however, a concern that the language load of word problems adds an unnecessary burden on students and leads to an inaccurate assessment of their abilities. The quandary, then, is how to write fair questions that test mathematical ability without letting the context overshadow the skill being measured.

There are a myriad of online resources that offer math help and practice tests for students. Many provide worksheets for teachers to use with their students. The authors of these assessments use interesting topics like sports heroes and world records to make the questions engaging and interesting for students. Websites can be valuable resources for classroom work, but the questions found on these websites are not necessarily the same types of items that are used on a large-scale assessment. Almost the opposite is true. We want to find topics that are so familiar to students that they fall into the background and allow the math to come forward and be seen.

It seems that creating common scenarios would not be such a difficult task, but there are many considerations to be made in the creation of a context. For example, an item that involves the cost of a stamp might seem innocent enough. It is a common topic familiar to most students and not likely to be distracting to them. The problem here is that the price of a stamp might change. If the price changes, the item will no longer be timely and will be of no further use. Topics that involve specific information that might change within the life of the item cannot be used. This is also true of people who students might admire. A pop singer in the news for altruistic behavior today might be in the news for illegal behavior tomorrow.

Item writers also must work outside of the topics that are considered to have bias and sensitivity issues. This list includes obviously inappropriate topics such as drugs, alcohol, death, and violence. It is clear that writing an item about the number of terrorists arrested in a particular time span is not an acceptable context. In some cases, though, the bridge between relative topics and sensitivity issues is less clear. For high school students, a data table giving numbers of lives saved by wearing seat belts might seem to be a positive message. However, this still touches on the negative aspect of car accidents and is not an acceptable topic. Writers must be able to imagine how a topic will impact a student. Contexts that make students particularly vulnerable to distraction because of personal circumstances such as weight, family problems, loss, or abandonment can cause enough stress to affect the results of the assessment.

The students who are reading the test questions come from all walks of life, and finding topics that are common to all of them can be a challenge. Certain topics might be familiar to most students, but if they cause issues for one group, they cannot be used. Birthdays are generally avoided since not all cultures celebrate birthdays. Even dancing might be considered a sensitivity issue. The Smarter Balanced Bias and Sensitivity Guidelines state that most dancing references would be acceptable except couples dancing which is likely to be criticized by some groups. Writers should err on the side of caution when choosing a context; if there is any doubt that a topic will be universally accepted, they should not use it.”

Less overt ideas like regionalism and ageism also fall under the “bias and sensitivity” umbrella. The term used to describe a carbonated beverage might be soda, pop, cola, or tonic, depending on the region of the country. Likewise, rhubarb might be well known in some areas and almost unheard of in others. When writing items about a specific group of people, it is important to avoid stereotypes. Not all older people are ignorant of technology, and not all Asian people are good at math. Sexism is a recurring issue in math items. When an item is written about a girl baking or a boy fixing a car, the argument is that these indicate an unfair treatment of gender roles. Of course, if all of the items were to portray women as firefighters and men as nurses, this would reverse the stereotype, but it would be no less inaccurate. A balance is needed, but when examining individual items it may be difficult to determine which version is better. Often items are written either using gender-neutral names or without reference to a specific person to remove the potential for sexism.

Even after bias and sensitivity issues have been addressed, topics still need to be grade-level appropriate. School elections might be common knowledge for high school students, but they are not well understood at the elementary level. Crayons are ubiquitous at the lower grades so this makes them familiar to almost all students. To upper grade students, however, crayons would not be the most engaging objects to use in a test question, mainly because of the strong connection to younger students. In the age of electronics, it cannot be assumed that all students have knowledge of the latest technology. Items such as DVDs and CDs have been around long enough to be considered familiar to students, but topics such as voice-command software might not be within the sphere of common student knowledge. Contexts need to be so familiar that students need to give very little thought to the situation that the math is wrapped in, so they can concentrate on the math itself.

The importance of familiarity is also true of the language that is used in the items. The vocabulary used should be at or below the grade level being assessed. There are numerous sources that break down words by grade level. The Children’s Writer’s Word Book and EDL Core Vocabularies are two examples. If a word or concept needs to be explained within the item, it is likely not a good word or concept to use. Also, items should be written with short, simple sentences. If there are multiple pieces of information being presented, creating a bulleted list could be helpful. The item should be structured to help students find the information they need, using language that they can easily understand.

High-stakes assessments need to be fair and valid for all students. When measuring mathematic ability, it is necessary to require an understanding of language to assess whether math skills can be applied to a problem-solving situation. Mathematics item writers need to understand the issues involved and create scenarios that support the math involved and not distract from it.

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