**Predicting Student's Level Of Reasoning Through The
TOLT Test**

Research has determined that the ability to reason formally is the strongest predictor of successful achievement in science/physics. Formal reasoners have greater comprehension and generalizing skills. To select appropriate topics, concepts and teaching strategies for their classes, physics teachers need to have an understanding of the levels and modes of reasoning of their students.

While teachers can do nothing to increase a student's mental capacity they can modify their instructional strategies to make concepts easier to comprehend. This may be accomplished through the use of concrete models, illustrations and diagrams and hands on experiences. A student's cognitive developmental growth will increase through exposure to activities requiring them to reason formally. Students, who use integrated science process skills during science activities, increase the level of their cognitive development.

To diagnose the level of intellectual development of students, Piaget developed one-to-one level clinical interviews. Although the preferred mode of assessing the level of formal reasoning, the time required for individual interviews and the lack of objectivity on the part of the interviewer lead to the development of group tests of logical thinking such as the Tobin & Capie Test of Logical Thinking (TOLT), 1980.

The TOLT test evaluates five reasoning abilities which have relevance to the teaching of science/physics. It is a multiple choice test that provides multiple justifications for the selected answer. The TOLT test contains two items from each of the following: proportional reasoning, probabilistic reasoning, controlling variable, correlational reasoning, and combinatorial reasoning. Knowledge of students' proportional reasoning ability is crucial in assessing their ability to work with and understand the quantitative nature of physics. Students who can not reason proportionally have difficulty understanding equations, functional relationships and topics such as velocity, acceleration and density.

The process of identification of variables and variable control is the most important process thinking skill that physics seeks to develop. In order to design experimental investigations students must be able to determine, discriminate and manipulate dependent and independent variables. This skill is necessary in comprehending time and motion relationships. Probabilistic reasoning allows the student to understand the need for repeated trials in investigations as well as the use of averages of collected data from duplicated experiments. To identify and verify the relationships between variables in solving problems, students must have correlational reasoning. To interpret displacement versus time studies students must be able to determine the relationships between variables from collected data.

**Questions and Reasoning**

**Directions**

A series of eight problems is presented. Each problem will lead to a question. Record the answer you have chosen and reason for selecting that answer.

**1. Orange Juice #1**

Four large oranges are squeezed to make six glasses of juice. How much juice can be made from six oranges?

a. 7 glasses

b. 8 glasses

c. 9 glasses

d. 10 glasses

e. other

Reason:1. The number of glasses compared to the number of oranges will always be in the ratio 3 to 2.

2. With more oranges, the difference will be less.

3. The difference in the numbers will always be two.

4. With four oranges the difference was 2. With six oranges the difference would be two more.

5. There is no way of predicting.

**2. Orange Juice #2**

How many oranges are needed to make 13 glasses of juice?

a. 6 1/2 oranges

b. 8 2/3 oranges

c. 9 oranges

d. 11 oranges

e. other

Reason:1. The number of oranges compared to the number of glasses will always be in the ratio of 2 to 3

2. If there are seven more glasses, then five more oranges are needed.

3. The difference in the numbers will always be two.

4. The number of oranges will always be half the number of glasses.

5. There is no way of predicting the number of oranges.

**3. The Pendulum's Length**

Suppose you wanted to do an experiment to find out if changing the length of a pendulum changed the amount of time it takes to swing back and forth. Which pendulums would you use for the experiment?

a. 1 and 4

b. 2 and 4

c. 1 and 3

d. 2 and 5

e. all

Reason1. The longest pendulum should be tested against the shortest pendulum.

2. All pendulums need to be tested against one another.

3. As the length is increased the number of washers should be decreased.

4. The pendulums should be the same length but the number of washers should be different.

5. The pendulums should be different lengths but the numbers of washers should be the same.

**4. The Pendulum's Weight**

Suppose you wanted to do an experiment to find out if changing the weight on the end of the string changed the amount of time the pendulum takes to swing back and forth. Which pendulums would you use for the experiment?

a. 1 and 4

b. 2 and 4

c. 1 and 3

d. 2 and 5

e. all

Reason:1. The heaviest weight should be compared to the lightest weight.

2. All pendulums need to be tested against one another.

3. As the number of washers is increased the pendulum should be shortened.

4. The number of washers should be different but the pendulums should be the same length.

5. The number of washers should be the same but the pendulums should be different lengths.

**5. The Vegetable Seeds**

A gardener bought a package containing 3 squash seeds and 3 bean seeds. If just one seed is selected from the package, what are the chances that it is a bean seed?

a. 1 out of 2

b. 1 out of 3

c. 1 out of 4

d. 1 out of 6

e. 4 out of 6

Reason:1. Four selections are needed because the three squash seeds could have been chosen in a row.

2. There are six seeds from which one bean seed must be chosen.

3. One bean seed needs to be selected from a total of three.

4. One half of the seeds are bean seeds.

5. In addition to a bean seed, three squash seeds could be selected from a total of six.

**6. The Flower Seeds**

A gardener bought a package of 21 mixed seeds. The package contents listed:

3 short red flowers

4 short yellow flowers

5 short orange flowers

4 tall red flowers

2 tall yellow flowers

3 tall orange flowers

If just one seed is planted, what are the chances that the plant that grows will have red flowers?

a. 1 out of 2

b. 1 out of 3

c. 1 out of 7

d. 1 out of 21

e. other

Reason:1. One seed has to be chosen from among those that grow red, yellow or orange flowers.

2. 1/4 of the short and 4/9 of the talls are red.

3. It does not matter whether a tall or a short is picked. One red seed needs to be picked from a total of seven red seeds.

4. One red seed must be selected from a total of 21 seeds.

5. Seven of the twenty one seeds will produce red flowers.

**7. The Mice**

The mice shown represent a sample of mice captured from a part of a field. Are fat mice more likely to have black tails and thin mice more likely to have white tails?

a. Yes

b. No

Reason:1. 8/11 of the fat mice have black tails and 3/4 of the thin mice have white tails.

2. Some of the fat mice have white tails and some of the thin mice have white tails.

3. 18 mice out of thirty have black tails and 12 have white tails.

4. Not all of the fat mice have black tails and not all of the thin mice have white tails.

5. 6/12 of the white tailed mice are fat.

**8. The Fish**

Are fat fish more likely to have broad stripes than thin fish?

a. Yes

b. No

Reason:1. Some fat fish have broad stripes and some have narrow stripes.

2. 3/7 of the fat fish have broad stripes.

3. 12/28 are broad striped and 16/28 are narrow striped.

4. 3/7 of the fat fish have broad stripes and 9/21 of the thin fish have broad stripes.

5. Some fish with broad stripes are thin and some are fat.

**9. The Student Council**

Three students from grades 10, 11, 12 were elected to the student council. A three member committee is to be formed with one person from each grade. All possible combinations must be considered before a decision can be made. Two possible combinations are Tom, Jerry and Dan (TJD) and Sally, Anne and Martha (SAM). List all other possible combinations in the spaces provided.

More spaces are provided on the answer sheet than you will need.

STUDENT COUNCILGrade 10. . . . Grade 11. . . . . Grade 12

Tom (T). . . . Jerry (J). . . . . Dan (D)

Sally (S). . . . Anne (A). . . . Martha (M)

Bill (B). . . . Connie (C). . . . Gwen (G)

**10. The Shopping Center**

In a new shopping center, 4 store locations are going to be opened on the ground level.

A BARBER SHOP (B), a DISCOUNT STORE (D), a GROCERY STORE (G), and a COFFEE SHOP (C) want to move in there. Each one of the stores can choose any one of four locations.

One way that the stores could occupy the 4 locations is BDGC. List all other possible ways that the stores can occupy the 4 locations.

More spaces are provided on the answer sheet than you will need.

**ANSWER SHEET**

Name ___________________________ . Birthdate ___________________________

. . . . . . . . . . . Month . Day . Year

Grade __________ . . . . . Date _______________________________

Problem Best Answer Reason

1.............. _____________ . ____________

2.............. _____________ . ____________

3.............. _____________ . ____________

4.............. _____________ . ____________

5.............. _____________ . ____________

6.............. _____________ . ____________

7.............. _____________ . ____________

8.............. _____________ . ____________

Put your answers to questions 9 and 10 below:

9. . . TJD . SAM . . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ , _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

10. .....BDGC . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______

_______ . _______ . _______ . _______