Adapting Literacy Strategies to Improve Student Performance on Constructed-Response Items
"Show your work or provide an explanation to support your answer."
Most Ohio high school students have had the opportunity to respond to constructed-response questions on state tests prior to taking the OGT. Short-answer and extended-response items have been included in Ohio's statewide tests for over 10 years, appearing first on the fourth and sixth grade Proficiency Tests and now on the Ohio Achievement Tests for all grades 3 through 8. But even though the number of students responding to short-answer and extended-response questions on the OGT has increased from 2004 to 2007, state data for the Ohio Graduation Test indicate little improvement in student performance on these constructed-response questions.
Constructed-response questions require a different level of thinking than do multiple-choice questions, which ask students to select from among a small number of options. And while we hope selecting the correct choice represents a certain level of understanding and skill, we cannot know for sure. In comparison, responses to constructed-response questions provide a better glimpse into student thinking. We need to ask ourselves, then, how can we help our students improve their performance on constructed-response questions? Part of the answer is to help students better respond to the frequently given direction: "Show your work or provide an explanation to support your answer."
Constructed-response questions require students to be able to draw upon both their mathematical understandings and a variety of "tools" to carry out and communicate a solution process. Among those tools are problem solving, reasoning, representation, connections, and communication—the skills addressed in the Mathematical Processes Standard. So now the question becomes, how can we help our students effectively communicate the important mathematics and their thinking when responding to constructed-response questions on the OGT?
Since the communication skills in the Mathematical Processes Standard are related to the skills that our colleagues in English language arts address, it is useful to look at some of the reading and writing strategies that they use and to adapt them for the mathematics classroom. While there is no silver bullet for improving student performance on constructed-response questions, students will gain much from talking and writing about mathematics.
"Students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically."
—National Council of Teachers of Mathematics, Principles and Standards for School Mathematics
Many students have difficulty making sense of the situations presented in constructed-response questions. In this case, you might adapt a reading comprehension strategy called K-W-L (What do I know? What do I want to learn about? What did I learn?). After reading a word problem, students write their ideas and answers to these three questions on a graphic organizer, a sheet of paper divided into three sections labeled with the three letters and questions.
It is a useful strategy, as is the variation known as K-W-C (What do I know for sure? What do I want to find out? Are there any special conditions that I have to watch out for?), described by Arthur Hyde (2007) in Educational Leadership. In case you are not familiar with this type of graphic organizer, here is an example of K-W-C using Question 10 from the March 2006 OGT.
Mrs. Foyle told Yolanda that her test had 38 problems worth a total of 100 points. Each test is worth either 5 points or 2 points. Yolanda wanted to determine how many 2-point and how many 5-point questions are on the test.
In your Answer Document, determine how many questions of each point-value are on the test. Show your work or provide an explanation to support your answer.
What do I know for sure?
What do I want to find out?
Are there any special
conditions I have to watch
o There are 38 questions.
o Some are worth 2 points.
o Others are worth 5 points.
o The sum of the points for all items is 100.
The number of 2-point questions on the test.
The number of 5-point questions on the test.
The number of 2-point questions and the number of 5-point questions must add up to 38 exactly.
Similar adaptations can be created to strengthen students' skills. For example, some students just need a jump-start when faced with a constructed-response question when they do not immediately identify a procedure or solution process for answering the question. The questions can be modified to What do I know for about the situation? What do I want to find out? and What is one first step I can take or new piece of information can I find? This third question helps students engage in the solution process even when the path to the answer is not known.
Showing Work or Providing an Explanation
"If our students learn to do mathematics silently, they may find that they don't have words readily available to describe mathematical ideas."
—Rebecca Corwin, Talking Mathematics: Supporting Children's Voices
Many students choose to show their work without realizing that it requires more than just jotting down a few and what sometimes appears to be random calculations. When we solve a problem for ourselves, we only need to write the things we cannot "keep in our heads." When we need to show our work to others, we need to not only write down what we can do mentally, but also think about how to organize our work in a manner that is easily followed and understood by someone else.
Graphic organizers can be used to help students identify and organize the steps needed when solving multi-step problems. For example, a student can create a "storyboard," flowchart, or two-column chart to show and describe the steps used for finding the answer to problems in the classroom. While there may not be time or space to use graphic organizers on the OGT, classroom experiences using them will result in students' being more diligent in recording their thinking and in recording their work in a complete and organized manner when responding to constructed-response questions.
While showing work and providing explanations require different types of responses, giving students regular opportunities to write about their mathematical thinking and solutions will help students become better writers and thinkers. A language-rich learning environment—one in which students hear and engage in "math talk" with others on a daily basis—is needed to build skills in writing about mathematics. Teachers need to model and encourage student talk by asking good questions and facilitating interactive whole-class and small-group discussions. A key strategy for supporting student writing is for teachers to talk and write about their own thinking—turning a think-aloud into a write-aloud. Students benefit from seeing and hearing how someone else thinks through and writes a response to a variety of problem situations.
A three-part scaffolding process for supporting students in writing about mathematics is described by O'Connell and Croskey (2008):
- The "write-aloud" stage allows students to hear and see the teacher's thinking. The teacher models how he or she writes the solution to a question or task on chart paper, overhead, or chalkboard. And the teacher talks while writing—describing decisions made along the way, such as what work to show or how to organize and explanation. You might consider making the process interactive by asking students to brainstorm ideas and recording them.
- The "write-along" stage engages students in writing with support. The teacher asks guiding questions, makes suggestions, and engages students as they write. Students may work with partners or in small groups to produce a written response. Collaborative writing helps students share and work together to think through and communicate their ideas and strategies as well as develop vocabulary and writing skills.
- The "write-alone" stage engages students in writing without teacher or peer support.
This three-part process supports students as they develop their writing skills while allowing for greater independence. Do students engage in all three stages in one lesson or every time they write? Probably not. However, the stages represent ways in which a teacher can build and support student writing by carefully planning for and incorporating writing activities into classroom instruction based on the level of student confidence and writing skills.
"The process of learning to write mathematically is similar to that of learning to write in any genre. Practice, with guidance, is important."
—National Council of Teachers of Mathematics, Principles and Standards for School Mathematics
The two strategies that follow are aimed at helping students improve the quality of their responses to a prompt or question. Both are designed to build a "habit" of focusing attention on the characteristics of a clear and complete solution. Both communicate to students that it is important to reflect upon their work—that the time it takes to read through and revise their work is time well spent.
The first—a peer review strategy—helps strengthen student responses by providing opportunities to view and discuss others' writing and solution strategies. However, this process is only effective when guidance—and a risk-free environment—is provided. Specific questions, appropriate for the writing task, will lead to helpful feedback and higher-quality responses. Some examples of guiding questions include:
- Does the solution respond fully to the question(s) posed?
- Is sufficient work shown? Does the explanation contain enough detail to support the writer's answer?
- Is the solution process or explanation presented in a logical order? Is it easy to read and follow?
- Does the writer use appropriate mathematics vocabulary and symbols?
- Is there anything that confuses you? What additional information might be helpful?
The second strategy—a guided rewrite process—can be used to improve writing and foster a mind-set of reviewing responses in the classroom as well as on a test like the OGT. O'Connell and Croskey (2008, pp. 90-91) provide an example of a guided rewrite process that includes the following steps:
- Students independently write their responses to a question.
- Once students complete their responses, the teacher facilitates a discussion about reasonable responses to stimulate ideas for improving their responses. The teacher might ask:
Students are then asked to revise their responses using ideas that were discussed. The goal is for them to select one or two that they feel will improve their response rather than to attempt to include all the ideas discussed.
Students talk about, share, or write about how they improved their work.
- What key vocabulary terms might you hear when someone is explaining his or her answer to this question?
- Would an example help someone understand your solution process?
- Would a diagram make it clearer?
- What would you do first? Next?
- Would someone not in our class understand how to solve this problem after reading your explanation?
These few examples provide a starting point for professional discussion, collaboration, and implementation of strategies to improve student performance on the OGT constructed-response items. For more strategies and ideas for supporting literacy, see the mini-collection "Constructed Response Items." A second mini-collection, "Constructed Response Items from NAEP," contains released items from the National Assessment of Educational Progress which can used in a variety of ways.
Corwin, R. B. (1996). Talking mathematics: Supporting children's voices. Portsmouth, NH: Heinemann.
Hyde, A. (2007). Mathematics and cognition. Educational Leadership, 65(3), 44-47.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
O'Connell, S., and Croskey, S. G. (2008). Introduction to communication, Grades 6-8. Portsmouth, NH: Heinemann.