Cognitively Challenging Teaching Practices

Three groups of survey items comprise our measure of the degree of emphasis placed by a teacher on providing a cognitively challenging experience for students.  Of course, what is cognitively challenging for one student may be routine and even boring for another.  However, as distinct from emphasizing skill- and knowledge-transmission activities, some teachers emphasized reflective writing, tasks requiring deep thinking (such as asking students probing questions), and problem-solving tasks.  While in some factor analyses, problem-solving items loaded on a different statistical factor from the others, the items classified as reflective writing and those called "deep thinking" differed primarily in terms of the content of the activity.  Together, the reflective writing and deep thinking items are referred to here as "meaningful thinking" teaching practices.

Reflective Writing

Perhaps the most powerful indicator of meaningful intellectual engagement is writing in which students are expected to draw connections between ideas themselves. The three types of writing assignments we asked about were writing in journals, writing of reflective essays, and writing an analysis of the quality of their own work. [6] Teachers who engage their students in these reflective writing activities, regardless of subject, also tend to assign other types of meaningful tasks. What types of reflective writing activities are reported across subjects, and which type of writing is most common?  

Of the three types of reflective writing, the most commonly reported was writing essays in which students "are expected to explain their thinking or reasoning at some length."  One half of all teachers, across all subjects, reported assigning essays of this type on at least a monthly basis, and nearly one-quarter (22%) reported assigning reflective essays on a weekly basis.  Fewer teachers had students do any journal writing at all, but of those who did, more teachers had students do journal-writing on a weekly basis (28% of all teachers).  Written self-assessment was by far the least frequent of these three methods.

Not surprisingly, reflective writing assignments are much more common in English classes than in other subjects. In fact, in the secondary grades, more than a third of all essay and journal writing that was reported took place in English classes. (See Appendix Table A-1.)  Aside from English classes, the secondary subjects where essays are most likely to be assigned are science and social studies. Elementary teachers of self-contained classes also report frequent journal writing by students. [7] For example, 58% of elementary self-contained  and 51% of English teachers have students write in a journal at least once per week, compared to only 14 to 15% of science and social studies teachers. Among applied subjects, vocational teachers appear to be more likely to have students do journal writing than in other subjects; 26% report students keeping a monthly journal compared to only 5% of business teachers.  However, there are only small differences in the other types of writing in these subjects.

In some subjects, there were large differences between middle and high school teachers' use of reflective writing assignments.  Middle school teachers reported substantially more writing activities in science, computer education and mathematics.  For example, 34% of middle school science teachers said students wrote in a journal compared to 9% of high school science teachers.  In applied subjects, the pattern was the same.  Almost half of middle school computer teachers said they had students write essays monthly (47%) compared to 13% of high school computer teachers.  (See Appendix Table A-2.)

Table 8: Prevalence of Reflective Writing
Activities by Subject taught

Tasks and Questions Calling for Deep Thinking

While reflective writing is clearly one way of promoting meaningful thinking around an activity, many other approaches are used, particularly in subjects where writing is less a primary objective of the subject matter than in English.  Additional activities we view as providing an indication of meaningful student engagement include  (a) the types of questions teachers ask, (b) how they introduce new topics (e.g., by having students make conjectures), and (c) how classroom time is spent (e.g., in student-led vs. teacher-led discussions). [8]

Questions without Answers:

One key question we can ask about the intellectual nature of classroom activity is whether or not student work is built around questions or tasks for which the teacher has a clear, pre-ordained "correct" answer in mind.  Where objectively knowable "right answers" prevail, students who are making an effort may be focused on finding out the teacher's answer ("what am I supposed to learn?") and be less inclined towards achieving a personal mastery and deep understanding of the larger content under study ("what do I think or understand about this issue?"). Teachers of different subjects vary quite a bit in terms of the nature of the questions they ask students and the ambiguity of what counts as knowledge, but overall relatively few teachers reported having frequent discussions where the knowledge at issue involved much ambiguity. When asked how often how they give assignments "where there is no indisputably correct answer—where truth is complex and perhaps impossible to know," only 7% of teachers said they did this on a weekly basis and only 23% said they did this at least monthly.  The subject where teachers were least likely to teach in this way was business education (none weekly and only 10% monthly) and mathematics (1% weekly; 11% monthly).  In comparison, about 40% of English and fine arts teachers reported organizing student work around tasks where truth was inherently ambiguous.

A similar indicator that most teachers' pedagogies are structured around presenting truths rather than students constructing their individual understandings comes from a question about how teachers introduce a unit of instruction. We asked teachers whether, at the outset of a unit, they raised questions to which they themselves did not know the answer, an approach that might allow them to model the development of understanding.  Do many teachers present themselves as learners, raising problematic questions with respect to their own knowledge?  Overall, fewer than one-quarter of teachers said that in introducing their current unit, they had brought up questions to which they didn't know the answer. In particular, very few business education teachers did this (5%), far fewer than did teachers in other fields.

An additional note about the validity of this survey's data on teaching practices.  As discussed earlier in the report, writers such as Cuban (1993) and Kennedy (1999) have questioned whether teachers' survey responses to general questions about their instruction accurately portrays the frequency that they carry out particular teaching practices.  Cuban, in particular, argues that in-depth observation of teachers in classrooms yields a conclusion that typical practice is much more traditional and fact- and skill-oriented than is suggested by teachers' survey responses.  However, we find that teachers' responses vary a great deal according to specific practices that they are asked about.  The findings of the preceding paragraphs, in particular, suggest that very few teachers report employing approaches that seem fairly central to a constructivist practice—giving students tasks related to problems that lack clear, correct answers and modeling the role of learner and by admitting to ignorance of important issues in an upcoming curricular unit. The distribution of answers to these two survey questions, and others with similarly "traditional" modal responses is evidence that teachers' survey self-reports may be a fairly honest reflection of their teaching practice—and that despite having fairly constructivist beliefs about what constitutes good teaching, most teachers employ only some teaching strategies in pursuit of a constructivist teaching philosophy.

Other Questions Teachers Ask of Students:

Virtually all teachers can be expected to spend some time leading whole-class discussions in which they ask students questions of various sorts.   But the nature of whole-class discussion is open to variation.  Here we examine a few different types of questions teachers ask groups of students and what their goals are in asking students questions.  We asked how often teachers are trying to accomplish the following goals—seeing if students know the correct answer; seeing if they have done homework; eliciting student ideas or opinions; getting students to justify or explain their reasoning; and, having students relate what they are working on to their own experiences.  

All teachers at least occasionally ask students questions to see if they know the correct answer, and half of the respondents in our survey said they did this "very often" or "always."  Fewer teachers reported asking students questions to see if homework had been done; however, a clear majority of foreign language teachers and almost exactly half of business education teachers said they asked questions to check homework "very often."  Although this highlights the traditional approach of these teachers, across all subjects the most frequently reported reasons for asking questions are those that would help provide the teacher with insights into their students' thinking—going beyond just whether the students know the right answer. 

Asking questions that elicit students' own ideas is one of the more common, and probably less difficult, ways of engendering interest and thoughtfulness in a class of students. A large majority of teachers reported that they "very often" asked students questions in order to elicit their ideas.  Similarly, most teachers said they asked questions to get students to justify their reasoning, and a majority of teachers said they asked questions that asked students to relate ideas to their own experiences. (See Table 9.)  More teachers reported asking those kinds of questions than said they asked questions in order to see if students knew the correct answer or to see if they had done their homework. However, compared to other subjects, math and business education teachers were less likely to ask questions in order to elicit student ideas and opinions.  Perhaps teachers in those subjects more often feel that students do not have the requisite knowledge to have formed "useful" opinions, compared to English and social studies, where students have more personal experience in the subject which they can draw upon. 

Table 9:  Reasons Teachers Give for Asking Students Questions,
 by Subject Taught

When we look at middle school versus high school patterns of question-asking by subject, in some cases it is the high school teachers who ask for more probing questions; in some cases, it is the middle school teachers.  High school English teachers generally appear to be more constructivist than middle school teachers in their question-asking practices—much less frequently looking for correct answers (29% of high school vs. 52% of middle school teachers saying they did this "very often") and more often asking students to justify or explain their reasoning. This pattern may be due to the greater focus on skills instruction in middle school English and a greater focus on literature in high school. (See Appendix Table A-3.)  

Similarly, among social studies teachers, high school teachers pursued more probing questions than did their middle school counterparts.  Three-quarters of social studies teachers at the high school level (76%) reported asking students to justify or explain their reasoning very often, compared to only 57% of middle school social studies teachers.  More than three-fifths at the high school level (62%) asked students to relate work to their own experience, compared to 49% of middle school social studies teachers.  Thus, at least in this respect, high school social studies and English teachers appear to be more constructivist than middle school teachers of the same subjects.

In mathematics, the pattern is reversed. Middle school math teachers were more likely to report having their students justify or explain their reasoning than were high school math teachers (93% vs. 80%) and more likely to say they had students relate their work to the students' own experiences "very often" (47% vs. 26%; see Appendix Table A-3.)

The survey asked teachers about one other questioning strategy.  We asked respondents whether, in introducing a new unit to students, they questioned students in order to get them to make conjectures about the topic of the unit.  This is an approach that can activate students' existing related knowledge and opinions and can uncover student interests and preconceptions about the topic.   Overall, half of all teachers in our study indicated that they asked students to make conjectures when they introduced the current unit. About two-thirds of elementary and English teachers reported doing this.  However, teachers of some other academic subjects—specifically mathematics and social studies teachers—were among the least likely to ask students to do this kind of preliminary thinking and hypothesizing.

Several other survey items reflecting practices that prioritize meaningful thinking were included in the survey: for example, holding debates where students argued from viewpoints that may not be their own, having students address the same issue in different ways (multiple representations), and having students themselves plan classroom activities.  Each of these tends to place responsibility for creating knowledge in the hands of students.  Holding debates where students argue a point of view that may not be their own forces students to view different sides of an issue and to use evidence in support of taking a position.  Only 12% of teachers overall reported using this practice even on a monthly basis; the most frequent affirmative responses were given by social studies teachers (24%).  Use of multiple representations was reported by about one-half of teachers in each of the academic subjects, but only between one-quarter and one-third of "applied" teachers.  Students "helped to plan learning activities" in about one-quarter of all their classes, most often in English (38%) and least often in science (17%), math (12%) and business (10%) classes.

Index of Meaningful Thinking

In every school subject there is a high correlation among reflective writing tasks, teachers asking probing questions, and other tasks requiring relatively deep thinking. That is, within a subject the teachers who do more reflective writing also report more of the other thinking tasks as well, and vice versa. Taking each subject separately, the correlation between the reflective writing index (comprised of three items) and an index comprised of 10 other deep thinking tasks (see below) is greater than 0.45 for elementary, social studies, English, and science teachers. (The correlation coefficients are presented in Appendix Table A-4.)  Because of this pattern, we created a combined measure of "meaningful thinking" that is based on teachers' scores on reflective writing and on the other tasks and questions calling for deep thinking that we asked about.  Combining these items for use as a criterion measure was strongly supported by empirical analysis—e.g., the items consistently loaded together in factor analysis. The alpha reliability of the scale, for example, was 0.81.  Corrected item-total correlations were all in the range of 0.30 to 0.60. More importantly, we think that, conceptually, an index of these items makes sense, and, as suggested earlier, we regard an emphasis on meaningful thinking as the central aspect of constructivist-compatible teaching practice.

Table 10: Frequency of meaningful thinking by subject and level taught
(index mean z-score)

Overall, English teachers appear more likely to assign work that would generate meaningful thinking than any other group of secondary teachers.  Only elementary teachers approach English teachers in this respect.  However, elementary teachers' scores are difficult to compare with secondary teachers' because most of the items are "frequency-based" (i.e., estimates of how often different practices occur) and most elementary teachers teach the same students for a full day, far longer than secondary teachers who generally teach classes for only 50-minute periods. 

Three of the four groups of teachers who report the least frequent use of these reflective writing, probing questions, and deep thinking tasks teach subjects that are applied in nature rather than strictly academic—computer teachers, business education teachers, and fine arts teachers. However, high school math teachers also fall in this group, and even when we use a broader definition of higher-order thinking that incorporates problem-solving (see below), the typical high school math teacher still appears to put less of an emphasis on cognitive engagement than other teachers do.

Problem-Solving Activities

Problem-solving involves a more-or-less cognitively challenging activity that can also be more or less meaningful. In other words, the construct of problem-solving could include students solving routine algorithmic problems in a workbook.  However, the particular aspects of problem-solving which are included in the TLC questionnaires—students working on problems with no obvious solution, deciding on their own problems to solve, and deciding on their own procedures to try—clearly are cognitively challenging.  We expected that teachers who reported more of these types of problem-solving activities also would report more of the other forms of meaningful student engagement.

Not many teachers report that they have students do this kind of challenging problem-solving very often. Only a minority of teachers—fewer than two out of five—report that they have students work on problems with no obvious solution even on a monthly basis.  About the same proportion say they have students develop their own procedures for solving a problem and then discuss what they did with their peers.  Fewer teachers, only one-fifth, have students design their own problems to solve,  as often as once per month. These statistics suggest that most student work in classrooms is closely prescribed, focused on factual knowledge or specific skills, and is teacher-designed.

Generally, we would expect math teachers to be among those who report the most involvement in problem-solving activities. However, this is true only in one respect: math teachers are more likely than other teachers to report having students decide on their own procedures for solving a problem and then discuss results with their classmates.  On the other types of problem-solving (working on problems with no obvious method of solution; and solving problems by their own procedures), math teachers were not distinctly different from science, English, and social studies teachers.  The one exception is that social studies teachers much less often reported having students design their own problems to solve (only 8%, combining middle and high school teachers).

For subjects where there are a sufficient number of teachers at both middle and high school levels, Table 11 presents information about subject-specific use of problem-solving strategies by level. Middle school math teachers are more likely than high school teachers to have students work on problems with no obvious method of solution (42% vs. 31%), and are also more likely to have students decide on their own procedures and discuss results among themselves (57% vs. 40%).  For vocational teachers, the pattern was reversed, with high school teachers reporting more problem-solving activities.

Table 11: Frequency of problem-solving activities
 by subject and level taught

Table 11 also has a summary column showing the average score of teachers in each level-subject combination on an overall Problem-Solving Index. [9]  Overall, middle school mathematics, secondary vocational, and elementary teachers report the highest average scores while middle school social studies, secondary foreign language, and business education teachers have the lowest average scores on Problem-Solving.

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