In Investigations and in other standards-based programs, students are used to explaining their strategies and may not be used to working under tight time constraints. And compared to traditional programs, students focus more on understanding concepts and less on notation and vocabulary. This may pose a problem when teachers face the difficult task of preparing their students for many of the standardized tests. What to do in this situation? Here are some tips and stories gathered from teachers who have been there.
1) Explain the rules
Explain to your students that the rules for standardized tests are different than in most of their math work. Nancy Buell, a grade 4 teacher in Brookline, Massachusetts, advises teachers to go over the following rules with their students:
- work alone
- paper and pencil only, no calculator or manipulatives (if applicable)
- mark only one answer to each question
- do not explain your answer (if applicable)
- skip problems that seem unfamiliar and return to them later if there's time
- time is limited
She also emphasizes with her students that the goal of the test is to get as many correct answers as you can in the time allotted. Students who are used to having ample time to explore, solve, and explain a problem need practice switching gears and working quickly, skipping problems that slow them down.
2) Familiarize students with the unfamiliar throughout the year
Many teachers spend a few class sessions before the standardized test familiarizing their students with notation and vocabulary they may not have seen much of in Investigations -- for example, < and > symbols, in-out machines, and the term perimeter. This may help to some extent, but the goal should be for teachers to be familiar with the test early in the year so that they can incorporate terms, vocabulary, or notation where appropriate in the context of the curriculum. The students will learn more this way than doing it all at once, out of context, in one period right before the test. For instance, if you teach the grade 3 unit "Turtle Paths" then your students know the concept of perimeter well; they can easily incorporate the word perimeter into their vocabulary if you use it regularly during this unit. (The word perimeter is used in different places in Investigations, but not stressed as much as in a traditional program.)
Be sure to use the vertical format for addition, subtraction, and multiplication "naked number" problems throughout the year. Teachers should talk with students about how the format for these problems does not dictate how they are to solve the problem. (Many students see the vertical format and think it means to solve the problem with the traditional algorithm.)
On the other hand, a few sessions to familiarize students with the format and materials of the test, as well as to discuss rules and test-taking strategies as described elsewhere, are best done just before the test is given. Give students practice problems with the same format as the test, e.g., with ovals to bubble in or with boxes on the right hand side to put answers in. If students are allowed any materials other than pencil and paper on the test, such as paper rulers, give them time to get familiar with these as well.
You might also want to give students some practice problems in prep sesions before the test. Ask your students to put each practice problem in their own words. Sometimes Investigations students need to think of a simple word problem for a "naked number" problem in order to make sense of it. All problems require students to make sense of them, whether they use in-out machines or the > sign or whether they ask for factors or for area or for interpreting a graph. Many of us trained with traditional algorithms didn't bother thinking what the problem meant; we just asked ourselves which procedure to use. But Investigations students have the wonderful habit of making sense of problems and their answers and they need to practice doing this with standardized test problems. They should not take the time during the test to write down what each question means; they should just try to think about the questions in familiar terms and try to think what strategies they might use that they have used before.
Try to resist teaching unfamiliar content through prep session practice problems. For some standardized tests, content areas like measurement or probability may need more attention than Investigations gives at certain grade levels. The students may have also missed some content because of the number of units teachers were able to cover so far that year or in previous years. But even more than notation and vocabulary, learning concepts takes time. If you need to teach some additional content outside of Investigations to prepare for a standardized test, again, make it part of a year-long plan and don't cram it into test prep sessions. You'll get more improvement in the scores if you focus the prep sessions on format, rules, and test-taking strategies.
3) Discuss test-taking strategies
It is important to explicitly discuss test-taking strategies with your students in your prep sessions. Nancy Buell suggests having your students generate their own test-taking strategies.
"Give students practice problems from commercial test prep materials or ones you have made up yourself. Then ask students: What did you do to try to get the most right answers you could in the time you had? This discussion should bring out most of the test-taking strategies you would hope for. Write them down. On another day review the strategies and give another practice test to see if students can use the strategies to improve their score. This can lead to more discussion of test-taking strategies and perhaps one more practice session."
Test-taking strategies for a multiple choice test might include, for example, eliminating wrong answers, being aware of "trick" questions (where one choice results from a common error), and checking every few problems that you aren't off by one in filling in the answer sheet.
4) Focus on efficient algorithms year-round
TERC advocates moving students to efficient algorithms regardless of whether your students face a traditional standardized test. (See the Spotlight: "The Algorithm Issue".) But this is a struggle for many teachers, who are trying to balance the goal of algorithm efficiency with a constructivist approach.
Marilyn Wolfson, a Grade 3 and 4 gifted teacher from Madison School District in Arizona, noticed several children in her class who had a 20-point spread between problem-solving and procedures on the Stanford Nine test. She decided to increase her efforts to focus on the most efficient ways to attack a problem, so that students can finish timed tests before the time runs out.
"If I have, say, five strategies up on the board, then we talk about the more efficient ones -- which would take us the less time, can we see how combining those numbers will save us the time and still come out with the correct answer -- which is what we all want. For example, we had a problem, 139 divided by 9, and this little girl did multiples of nine and she put them all down. Then we went through the idea of: do you know nine times ten would already get you to 90, and see the value of that, and then we can use our knowledge that nine times five is 45. In two steps she had the problem as compared to doing all the multiples. And yet it still uses her basic approach of multiples of nine and it still is clear without missing a beat on understanding."
Marilyn will find out later this year if her efforts have paid off with better results in the area of procedures on this year's Stanford Nine test.
It is both an art and a skill to run such a discussion and to ask the right questions so that the student has understanding and ownership of the more efficient algorithm you are hoping to "move" her to. Some believe this to be the biggest challenge of all in teaching Investigations. Practice helps, as does observing other teachers who do this well. And the need to prepare for a timed standardized test can also help: it is a good motivator for not letting students linger with inefficient strategies.
5) Have faith
Finally, have faith in Investigations. Using this program helps students become flexible thinkers who are not easily intimidated by unfamiliar-looking problems. It also helps them develop good number sense and mental math skills that make it easier to eliminate multiple choice answers that are much too big or small. And the strategies students use for computation often take less time than you think. Solving a problem mentally often takes very little time; it is explaining what you did and why it works so that someone else can understand it that can make the strategy feel more time consuming or less efficient. In general, most teachers find that their students know the content of the standardized test; they just need some practice with the format.
Believing any program is good preparation for standardized tests is hardest the first year you teach it. Lynn Alloway, who also teaches in the Madison School District in Arizona, learned a valuable lesson her first year using Investigations in a 2nd grade classroom:
"At first I went ahead and did what I was supposed to do, knowing that these standardized tests were out there, and the students were great with what they were doing with their adding and subtracting on their own. But then I got a little nervous that first year about two weeks before the test and I went ahead and taught them the algorithm or taught them how to do that regrouping piece. Then they absolutely stopped doing all those neat things they were doing. They tried to do what I had showed them to do and they fell flat on their face, because they were trying to do what the teacher wanted them to do, and they didn't understand it.
That right there was the kicker for me. The students had been breaking apart the tens and ones and adding the tens, doing all that stuff they're supposed to do and that they do so naturally without us interfering. They were doing great, and I blew it! I think that's when I actually became such a firm believer in Investigations because I saw how I messed it up. It took me many weeks to get the students beyond that, many weeks of telling them 'it's okay, you don't have to do that part, do it the way you know how to do it.' They finally came back to it by the end of the year. But I understand what the teachers are feeling when they get to that test. You have to tie your hands, put on the tape and try not to go back to that other stuff."
Thanks to Nancy, Marilyn, and Lynn for sharing their stories and tips on this issue. And thanks to all the Investigations teachers I have worked with through CESAME who have helped to inform this article.
Wendy Gulley, CESAME, Northeastern University
April, 2000
This information was reprinted with permission of CESAME, Northeastern Univ., and the Educational Alliance, Brown University.
