High School Test

International Electronic Journal of

Mathematics Education

Volume 3, Number 2, July 2008 www.iejme.com

MATHEMATICS TEACHERS INTERPRETATION OF HIGHER-ORDER THINKING

IN BLOOM S TAXONOMY

Tony Thompson

ABSTRACT. This study investigated mathematics teachers interpretation of higher-order thinking in

Bloom s Taxonomy. Thirty-two high school mathematics teachers from the southeast U.S. were asked to (a)

define lower- and higher-order thinking, (b) identify which thinking skills in Bloom s Taxonomy represented

lower- and higher-order thinking, and (c) create an Algebra I final exam item representative of each thinking

skill. Results indicate that mathematics teachers have difficulty interpreting the thinking skills in Bloom s

Taxonomy and creating test items for higher-order thinking. Alternatives to using Bloom s Taxonomy to help

mathematics teachers assess for higher-order thinking are discussed.

KEYWORDS. Higher-order Thinking, Bloom's Taxonomy, U.S. High School Mathematics Teachers,

Algebra, Assessment.

INTRODUCTION

Mathematics teaching in the U.S. has traditionally relied on factual recall and a focus on

the use of standardized algorithms with little effort to teach or assess for higher-order thinking

(Kulm, 1990; Battista, 1994). As a result, students generally learn mathematics without being

able to use their knowledge to solve problems in diverse or non-familiar situations (de Lange,

1987; Schoenfeld, 1988). Although there has been an effort to reform mathematics education in

the U.S. over the past two decades (NCTM, 1989; 2000), teaching mathematics has changed little

since Schoenfeld (1988) characterized the typical mathematics classroom:

All too often we focus on a narrow collection of well-defined tasks and train students to

execute those tasks in a routine, if not algorithmic fashion. Then we test the students on

tasks that are very close to the ones they have been taught. If they succeed on those

problems, we and they congratulate each other on the fact that they have learned some

powerful mathematical techniques. In fact, they may be able to use such techniques

mechanically while lacking some rudimentary thinking skills. To allow them, and ourselves,

to believe that they "understand" the mathematics is deceptive and fraudulent. (p. 30)

Copyright 2008 by GOKKUSAGI

ISSN: 1306-3030

Thompson 97

This notion of teaching mathematics stands in contrast to teaching for higher-order

thinking skills where students are able to meaningfully apply methods and concepts to situations

previously unfamiliar to them (Donovan & Bransford, 2005; Hiebert, et al, 1997). However,

research indicates that many teachers have a weak conception of higher-order thinking (Harpster,

1999) and that teaching for higher-order thinking is difficult for teachers to sustain as an integral

part of classroom instruction and assessment (Henningsen & Stein, 1997).

Characterizing Lower- and Higher-Order Thinking

Resnick (1987) noted that thinking skills resist precise forms of definition, but lower- and

higher-order thinking can be recognized when each occurs. Lower-order thinking (LOT) is often

characterized by the recall of information or the application of concepts or knowledge to familiar

situations and contexts. Schmalz (1973) noted that LOT tasks requires a student to recall a

fact, perform a simple operation, or solve a familiar type of problem. It does not require the

student to work outside the familiar (p. 619). Senk, Beckman, & Thompson (1997) characterized

LOT as solving tasks where the solution requires applying a well-known algorithm, often with no

justification, explanation, or proof required, and where only a single correct answer is possible. In

general, LOT is generally characterized as solving tasks while working in familiar situations and

contexts; or, applying algorithms already familiar to the student.

In contrast, Resnick (1987) characterized higher-order thinking (HOT) as non-

algorithmic. Similarly, Stein and Lane (1996) describe HOT as the use of complex, non-

algorithmic thinking to solve a task in which there is not a predictable, well-rehearsed approach

or pathway explicitly suggested by the task, task instruction, or a worked out example. (p. 58)

Senk, et al (1997) characterized HOT as solving tasks where no algorithm has been taught, where

justification or explanation are required, and where more than one solution may be possible. In

general, HOT involves solving tasks where an algorithm has not been taught or using known

algorithms while working in unfamiliar contexts or situations.

Teaching for HOT

According to the National Center for Education Statistics (1996), teaching for HOT along

with professional development in HOT were found to be two of the top five variables positively

associated with improved student achievement. Students of teachers who teach for both LOT and

HOT outperform students whose teachers only teach for LOT (Wenglinsky, 2002). However,

98 International Electronic Journal of Mathematics Education / Vol.3 No.2, July 2008

national and international assessments in mathematics indicate that U.S. students are not doing

well on items requiring the use of HOT (Mullis, et al, 2004). U.S. students performing poorly on

national and international exams is reflected in the research which indicates that most U.S.

teachers do not teach and assess for HOT (Kulm, 1990; Senk, et al, 1997).

U.S. teachers not assessing for HOT is well-documented and is not limited to

mathematics. Reynolds and Menard (1980) found that teachers' classroom tests were heavily

reliant on LOT tasks (interpreted as knowledge, comprehension and application in BT). Similarly,

Fleming and Chambers (1983) used BT to analyze over 8000 test items from K-12 teacher-

developed tests and found that consistently across all grade levels over 90% of test items

measured LOT. In a study of high school grading practices in mathematics, Senk, et al (1997)

found that the percentage of LOT items on mathematics teachers' tests ranged from 53% to 90%

with a mean of 68%. These studies analyzed existing tests created by teachers; in contrast,

Harpster (1999) found that when mathematics teachers were specifically asked to write a single

task representative of HOT, sixty-percent of teachers created a task that assessed LOT.

In general, teacher assessments tend to focus on LOT even when teachers say they want

to teach and assess for HOT; however, teachers are often unaware of this inconsistency (Black &

Wiliam, 1998). Any endeavor to improve assessing for HOT depends on whether or not teachers

can identify and create items that assess for HOT (Costa, 2001; Kulm, 1990; Resnick & Resnick,

1992). Numerous efforts to improve assessing for HOT include Bloom s Taxonomy which is often

used to evaluate the level thinking required on tasks. How is HOT characterized in Bloom s

Taxonomy?

Bloom s Taxonomy and higher-order thinking

For over 50 years, Bloom s Taxonomy (BT) (Bloom, 1956) has heavily influenced

teaching and assessment throughout the world (Anderson & Sosniak, 1994) and is still commonly

used in mathematics education. For example, Kastberg (2003) and Vidakovic, Bevis, &

Alexander (2003) provide examples of how high school and collegiate mathematics teachers can

use BT to develop test items. Numerous studies have used BT as the standard for judging whether

test items are LOT or HOT. The thinking skills in BT considered LOT include knowledge and

comprehension, while the thinking skills of analysis, synthesis and evaluation are considered

HOT. Application often falls into both categories.

Thompson 99

In BT, for a test item to be at the level of application or higher, a new situation (to the

student) is required. Bloom emphasized in his original work in 1956 and subsequent discussions

on this issue (Bloom et al, 1971, 1981) that application and higher levels in the taxonomy do not

refer to test items where only minor changes are made, but otherwise, the procedure was the same

to that practiced in class. As Bloom, et al (1981) stated:

By new problems and situations we mean problems and situations which are likely to be

new to the student. These are similar to those which were included in the instruction but

have some element of newness or unfamiliarity for the student. Students should not be able

to solve the new problems and situations merely by remembering the solution to or the

precise method of solving a similar problem in class. It is not a new problem or situation if

it is exactly like others solved in class except that new quantities or symbols are used (as in

mathematics or physics). (p. 233)

Despite the widespread use of BT, it is not well understood how mathematics teachers

interpret BT or whether BT facilitates the development of HOT test items in mathematics.

RESEARCH QUESTIONS

As discussed above, teachers test items have been investigated regarding whether they

assess for LOT or HOT; however, researchers used BT or variations of BT (Cooney, 1992;

Wilson, 1971), or other frameworks (e.g., Quellmalz, 1987) to determine whether test items were

HOT or LOT. In these studies, teachers were not using BT as a guide in the development of their

own HOT test items (e.g., Stiggins, Griswold, & Wikelund, 1989; Fleming & Chambers, 1983;

Harpster, 1999). Therefore, this study was designed to investigate the following questions:

1. How do high school mathematics teachers define lower- and higher-order thinking?

2. Which thinking skills in Bloom s Taxonomy do high school mathematics teachers

associate with higher-order thinking?

3. What type of Algebra I final exam items do high school mathematics teachers perceive

are representative of thinking skills in Bloom s Taxonomy?

According to Bloom (1956), BT was designed to classify types of thinking likely required

on a test item after students have been taught the specific objectives being tested. Therefore, for

research question 3, a final exam context was chosen to ensure teachers developed test items

based on the type of thinking likely used by a student after s/he had been taught the material. An

Algebra I context was chosen to provide uniformity in the types of test items being analyzed.

100 International Electronic Journal of Mathematics Education / Vol.3 No.2, July 2008

METHOD

Participants

Thirty-two high school mathematics teachers from four school districts in a state in the

southeast U.S. participated in this study. Teachers were asked to volunteer for this study while

attending workshops at their school during professional development days. Participants were

from rural and semi-urban communities, predominately female and Caucasian with ages ranging

from early twenties to late fifties. No additional demographic information was collected (e.g.,

gender, race, years teaching, highest degree earned, etc.).

Data Collection

The high school mathematics teachers were first asked to write a definition of lower- and

higher-order thinking. Second, after writing their definitions, teachers were given a handout

summarizing the thinking skills in BT (see Appendix). The thinking skills were listed in

alphabetical order to avoid biasing teachers perceptions of whether a thinking skill might be

LOT or HOT depending on its order in the handout. Third, teachers were asked to identify

whether they were very familiar, somewhat familiar, or not familiar with BT, and to briefly

describe where, if at all, they had learned about BT. Fourth, teachers were asked to classify each

thinking skill in BT as either LOT or HOT. And lastly, teachers were asked to write an Algebra I

final exam item for each thinking skill.

Using the characterizations from the literature described earlier, test items in this study

were classified as LOT and HOT as follows:

a) LOT Algorithmic Thinking : Solving tasks that require the recall of information or the

application of well-known algorithms in situations and contexts likely familiar to the student.

b) HOT Non-algorithmic Thinking : Solving tasks where no specific algorithm has been

taught to the student; or, using known algorithms in contexts or situations likely unfamiliar to

the student.

As noted earlier, Bloom (1956) stated that when testing for higher levels of

thinking, the problem situation must be new, unfamiliar, or in some way different from those

used in the instruction (p. 238). In this study, the differences between LOT and HOT are

consistent with the differences in BT between comprehension and application. Comprehension is

characterized in BT as using known algorithms. In contrast, application involves using knowledge

in new situations and solving problems without being told which algorithm or method to use. For

Thompson 101

Bloom, the emphasis in writing application items is on getting situations new to the student (p.

130) and if a problem or one just like it had been solved in classwork, [it] would be a

comprehension rather than an application item (p. 133).

Data Analysis

Teachers categorization of thinking skills as LOT or HOT were analyzed using

descriptive statistics (frequencies and percentages). The test items created by teachers were

classified as HOT or LOT using the definitions above. A graduate research assistant also

classified each test item as LOT or HOT independent of the researcher; the agreement in

classifying items was 92%. Disagreements over a test item being LOT or HOT were resolved in

favor of the teacher s classification. The research focused on teachers interpretation of HOT

while using BT; test items were not independently analyzed as to whether they fit with a

thinking skill in BT only whether an item matched the LOT or HOT classification of the

teacher.

RESULTS

Seventy-five percent of teachers indicated that they were either very familiar or

somewhat familiar with BT. Teachers familiar with BT indicated they used the taxonomy while in

their undergraduate or graduate teacher education programs to develop test items as part of an

educational psychology, methods, or evaluation course.

Research Question 1: How do high school mathematics teachers define lower- and higher-order

thinking?

Many teachers definitions of LOT and HOT included characteristics of LOT and HOT

often discussed in the literature. A summary of teacher descriptions are included in Table 1.

Table 1: Teachers descriptions of LOT and HOT

LOT HOT

Following rules Discovering patterns

Performing computations Solving word problems

Definitions / vocabulary Interpreting information

Simple applications Complex applications

Procedural knowledge Conceptual understanding

Copies teacher / rote learning Critical thinking / analyzing

However, not all teachers viewed HOT in these terms; approximately one third of

teachers included as part of their definitions of LOT or HOT (a) level of difficulty, (b) number of

steps required to solve a task, or (c) solving tasks involving higher math . One teacher wrote,

102 International Electronic Journal of Mathematics Education / Vol.3 No.2, July 2008

A math problem is higher order thinking if it takes 3 or more steps to solve. She later provided

as an example of HOT, Simplify (3x3 6x + 9x2) 3x while writing in the margin of her paper

three steps. Several teachers wrote that LOT problems are easier than HOT problems (e.g.,

Higher order thinking involves solving difficult or challenging math problems. ) However,

there are many mathematics tasks that are computational / algorithmic in nature that are quite

difficult or challenging; therefore, although HOT items tend to be more difficult, level of

difficulty is not a characterization in the literature on HOT and LOT (de Lange, 1987).

Regarding using basic versus advanced mathematics as a key characteristic of LOT

and HOT, one teacher wrote that Lower order thinking involves solving basic math problems

e.g., adding, multiplying integers / fractions, etc., while higher order problems are beyond basic

math; e.g., algebra and calculus. When writing their definitions of HOT, none of the teachers

included the concept of familiarity with an algorithm or a problem situation. However, this is a

fundamental concept in distinguishing LOT and HOT in the literature and in BT.

Research Question 2: Which thinking skills in Bloom s Taxonomy do high school mathematics

teachers associate with higher-order thinking?

Using the descriptions in the handout or their prior experiences with BT, teachers were

asked to identify each thinking skill in BT as either LOT or HOT. The results are presented in

Table 2.

Table 2: Teachers classification of thinking skills

Bloom s Taxonomy LOT HOT

LOT # Knowledge 29 (91%) 3 (9%)

Comprehension 13 (40%) 19 (60%)

LOT or HOT

Application 9 (28%) 23 (72%)

HOT

Analysis 3 (9%) 29 (91%)

Synthesis 6 (19%) 26 (81%)

Evaluation 18 (57%) 14 (43%)

Teachers classification of thinking skills in BT indicates that a description of a thinking

skill by itself (or least the summary provided for teachers in this study) is not sufficient to help

teachers differentiate LOT and HOT. Over 90% of teachers correctly identified knowledge as

LOT and analysis as HOT. However, comprehension (LOT) was interpreted as HOT by 60% of

mathematics teachers. Evaluation and synthesis are considered HOT in BT; however, over half of

the mathematics teachers interpreted evaluation as LOT and approximately one-fifth of teachers

indicated synthesis was LOT.

Thompson 103

Many teachers correctly identified the levels of thinking in BT as either HOT or LOT;

however, teachers who defined HOT by (a) number of steps, (b) level of difficulty, or (c) algebra

as a higher-order subject tended to list all thinking skills (except occasionally knowledge) as

HOT. Given teachers interpretation of HOT in BT, do mathematics teachers write HOT test

items for thinking skills in BT they classify as HOT?

Research Question 3: What type of Algebra I final exam items do high school mathematics

teachers perceive are representative of the thinking skills in Bloom s Taxonomy?

Teachers were asked to create Algebra I final exam items for each thinking skill in BT.

Test items fell into one of three categories: Items classified as LOT by both the teacher and

researcher (LOT LOT) [Table 3]; items classified as HOT by both the teacher and researcher

(HOT HOT) [Table 4]; and items classified as HOT by the teacher, but LOT by the researcher

(HOT LOT) [Table 5]. No items classified as LOT by teachers were classified as HOT in this

study. For the LOT items in table 3, it is likely that students have been taught an algorithm or

general procedure to answer each question. Items in Table 4 are HOT under the assumption that

students were previously not taught procedures or algorithms to solve these or similar problems.

Table 3: Sample LOT-LOT items

State the quadratic formula (K)

Solve x + 2 = 6 (K)

Simplify: 3x 7y + 5 x + 8y (C)

Change 3x + 4y = 12 to the form y = mx + b (C)

Simplify: (3b2c)(8b3c6) (Ap)

Multiply: (2x 5)(x + 8) (Ap)

What is the greatest common factor of 3x2 - 9x4 + 6x3? (An)

Simplify 3x + 7xy 2x + 3(x y) xy (S)

Solve 4(x 7) + 5 = - x 3; check you answer (E)

If x = -2 and y = 10, what is 2x + 3y = 26? (E)

Note: Teachers categorization in BT: K = Knowledge; C = Comprehension; Ap = Application;

An = Analysis; S = Synthesis; E = Evaluation

Table 4: Sample HOT HOT items

Write a problem where the expression 2x 1 can be used to solve the problem (C)

4, 7, 10, 13, __ Find the next term in the sequence. 50th term? Nth term? (Ap)

For 2x2 bx + 3, what integral values of b will the equation factor? Explain your reasoning (Ap)

John stated that (x + 5)2 = x2 + 25. Explain why John is or not correct. (An)

Explain the differences between x, - x, and (-x) (An)

How many lines with slope m = 2 go through point (1, 3)? Explain (S)

Given a graph of a real-world linear relationship, find the slope of the line and explain what the

slope means in this particular situation (S)

Use you calculator to find a decimal approximation of 3. (a) Describe a situation where this

approximation would be more useful. (b) Describe a situation where the exact value (i.e., 3)

would be more useful. Explain your reasoning. (E)

Note: Teachers categorization in BT: K = Knowledge; C = Comprehension; Ap = Application;

An = Analysis; S = Synthesis; E = Evaluation

104 International Electronic Journal of Mathematics Education / Vol.3 No.2, July 2008

Test items in table 5 were labeled as HOT by teachers, but they were not classified as

HOT in this study since they likely involve the use algorithms or procedures for which most

students have been taught and therefore should be familiar on a final exam. Of the 114 items

developed by teachers for the thinking skills they labeled as HOT in BT, only 51 items (or 45%)

were classified as HOT in this study.

Table 5: Sample HOT LOT items

Write out a set of steps to show how to solve the equation 2x 7 = 5 (K)

Solve for a: ax + by = az (C)

Given a table of values, write an equation and graph (C)

Find the distance between points (5, 7) and (9, 10) (Ap)

John can mow a yard in 2 hours; Sam can mow the same yard in 3 hours. How long would it

take them to mow the yard working together? (Ap)

Which of the following is the graph of 2x 5y =10? (several choices given) (An)

A line has a slope of 4 and a y-intercept of - 3. Which of the following is the equation of the

line? (several choices given) (An)

Given the equation x2 + x 6, make a table of values and graph the equation (S)

The perimeter of a rectangle is 120 feet. If x is the width of the rectangle, write a function that

represents the area of the rectangle (S)

Evaluate 2x + 3y if x = -1/2 and y = 2/3 ; show your work (E)

Note: Teachers categorization in BT: K = Knowledge; C = Comprehension; Ap = Application;

An = Analysis; S = Synthesis; E = Evaluation

In the analysis of test items, several patterns were apparent. First, it was common among

teachers to classify as HOT those items that asked students to explain their answers regardless

of students familiarity with the task. Second, several teachers included multiple choice items as

representative of HOT but rarely for LOT. In discussing the results with teachers at a later date,

several commented that these items might have been labeled HOT by teachers since students first

have to analyze or evaluate the choices before they can answer a question. Third, test items

that teachers would likely identify as difficult or take several steps to solve were often classified

as HOT regardless of students familiarity with the algorithm or solution methods. And finally,

the term evaluation was defined or interpreted by many teachers as finding the value of

instead of how it is defined in BT. Thus, despite being given the definitions of the thinking skills

in BT, many teachers continued to use their own interpretations of these terms or defined these

terms as they are used in teaching mathematics.

Thompson 105

DISCUSSION

The findings in this study are consistent with research that indicates teachers tend to over-

estimate the level of thinking required on test items. For example, Senk, et al (1997) found that

the percentage of LOT items on mathematics teachers' tests averaged 68%. Harpster (1999) found

that when mathematics teachers were specifically asked to write a single task representative of

HOT, 60% developed a task that assessed LOT. However, in the studies cited above, teachers

were not using BT as a guide to write HOT test items. This study indicated that although

mathematics teachers were often able to identify various characteristics of LOT and HOT, many

teachers often did not write HOT items. Approximately 55% of test items labeled as HOT by

teachers were categorized as LOT in this study. Although none of the teachers listed familiarity

in their definitions of HOT, teachers who defined HOT as problem solving, discovering patterns,

interpreting information, and conceptual understanding were much more likely to write HOT

items than teachers who did not use these terms. In contrast, teachers who defined HOT based on

characteristics such as (a) number of steps required to solve a task, (b) level of difficulty, or (c)

algebra as a higher order subject created LOT items almost 100% of the time.

It is worth noting that teachers who were more familiar with BT were no more likely to

write HOT items than teachers who were not familiar with BT. One teacher, in particular, who

was unfamiliar with BT wrote and correctly identified HOT items consistently (e.g., table 4, #8).

Overall, familiarity with BT did not appear to affect teachers interpretation of BT or their ability

to write HOT test items. Overall, this research indicates that a key concept in the literature on

HOT and in Bloom s (1956, 1971, 1981) discussion on this issue missing from mathematics

teachers interpretations of HOT was the level of familiarity students have with the algorithms,

methods of solving a problem, or the context / situation of the task needed in a test item. As a

result, teachers often misinterpreted BT and over-estimated the amount of HOT in test items they

created. In this study, BT did not appear to affect teachers perception of HOT or their efforts to

write HOT test items for their students.

Although BT can be used effectively by mathematics teachers (Kastberg, 2003;

Vidakovic, Bevis, & Alexander, 2003), the study lends support that BT might not be an effective

method of helping mathematics teachers assess for HOT. One alternative is to use a modified

version of BT specifically developed for mathematics (e.g., Wilson, 1971; Cooney, 1992 cited in

Harpster, 1999). It is unknown if these modified taxonomies are more effective in teaching and

assessing for HOT, but Bloom, et al (1971) noted that BT would likely need to be adapted to meet

the needs of individual disciplines. Another alternative would be for mathematics teachers to

106 International Electronic Journal of Mathematics Education / Vol.3 No.2, July 2008

supplement BT (or the modified versions of BT) with the definition of HOT used in this study.

This will help teachers consider students familiarity of a procedure or situation when selecting or

identifying test items as either LOT or HOT.

And lastly, mathematics teachers can use thinking skill frameworks apart from BT

specifically designed to assess for HOT in mathematics. For example, the thinking skills

framework developed by Smith and Stein (1998) uses four categories of cognitive demands to

classify mathematics tasks based on the type of thinking required of the students. Mathematics

teachers can also use the 2005 National Assessment of Education Progress mathematics

framework. This framework classifies tasks as low, moderate or high complexity (U.S.

Department of Education, 2001). Both frameworks are mathematics specific with descriptors

consistent with the characterization of HOT as used in this research and as found in the literature

on HOT. Although more professional development on teaching for HOT in mathematics is

needed, teaching and assessing for HOT is very difficult even with extensive professional

development (Henningsen & Stein, 1997; Harpster, 1999). Therefore, more research is needed on

creating models of professional development that support teachers effort to assess for HOT.

LIMITATIONS

There are several limitations in this study. First, although most teachers were familiar

with BT, given greater training in its use or given illustrative mathematics examples for each

thinking skill, mathematics teachers might interpret HOT within BT differently. Second, teachers

were restricted to developing items only for Algebra I; in the U.S., Algebra I is often taught

procedurally and thus emphasizes LOT. Asking teachers to write test items for other subject

areas (e.g., Geometry) might have yielded different results. And lastly, teachers were not

randomly selected and were restricted to a small geographic area of one state in the southeast U.S.

Results may differ for a larger, more diverse sample of teachers. Despite these limitations, this

study provides insights into mathematics teachers interpretations of BT and the complexity of

assessing for HOT in mathematics.

Thompson 107

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Thompson 109

APPENDIX

Teacher Handout: Thinking skills in Bloom s Taxonomy*

In Alphabetical Order

ANALYSIS Ability to breakdown concepts into their component parts so that the hierarchy of ideas is clear; clarify

existing information by examining parts and relationships; identify relationships and patterns; identify errors and

logical fallacies and where possible, correcting them.

APPLICATION Ability to use prior knowledge within a new situation. This involves bringing together the

appropriate information, procedures, generalizations, or principles that are required to solve a problem without being

told to do so or without any specific or immediate cues.

COMPREHENSION Ability to understand what is being communicated and make use of the material or idea being

communicated without necessarily relating it to other material or seeing its fullest implications. This may be shown by

(a) translating concepts from one form to another, (b) interpreting and summarizing facts, and (c) contrasting,

comparing, or predicting consequences.

EVALUATION Ability to judge or assess the value of material and methods for given purposes as well as to

compare and discriminate between ideas; assessing the reasonableness and quality of ideas including establishing

criteria (setting standards for making judgments) or verifying (confirming the accuracy of claims).

KNOWLEDGE Ability to recognize or recall facts, methods, processes, patterns, structures, basic concepts,

conventions, principles, and theories.

SYNTHESIS Ability to work with pieces, parts, elements, etc., and arranging and combining them in such a way as

to form a whole or constitute a pattern or structure not clearly there before. This may also include generalization from

given facts, relating knowledge from several areas, predicting, and drawing conclusions.

* Summarized from Bloom, B. (Ed.) (1956). Taxonomy of educational objectives: Book I, cognitive domain.

New York: Longman Green

Author : Tony Thompson

E-mail : **********@***.***

Address : Department of Mathematics and Science Education

Flanagan Bldg 327, East Carolina University

Greenville, NC 27858

Phone : 1-252-***-****

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