After introducing PBL into the SciMathUS curriculum at Step 7 on Harden’s integration ladder the emphasis remained on the subjects mathematics and science with subject-based
Hybrid PBL approach
CONVENTIONAL PBL CURRICULUM
Step 1 (Harden) Step 7 (Harden) Teacher-centred Learner-centred Content-based Problem-based Subject-based Integrated Mathematics & Science PBL Mathematics Science
Course structure Problem-based Subject-based Integrated PBL Intra-grated PBL Bigger term problems Smaller weekly
problems Problem design Own problem designs Adapted text-book
(Clearinghouse) problems in real-world context
SC PBL & PS PBL problems SC PBL & PS PBL problems
Outcomes Process & product outcomes Process & product Outcomes PBL process 7 jump approach 7 jump approach Education formats Combined classes Separate classes
Small groups Small groups Facilitation & SDL facilitation & SDL Assessment Continuous assessment Continuous assessment
Objectives Self-directed learning Critical thinking Higher order reasoning Improved conceptual understanding in mathematics and science
courses taking up most of the curriculum time. Within this framework, an integrated teaching session (via PBL) was introduced in addition to the subject-based teaching. The three
integrated bigger PBL problems and sessions brought together areas of interest common to
each of the subjects. In this correlation approach a problem-based approach was therefore used in which the problem designed to integrate mathematics and science was given to students prior to addressing the work in class. During class discussions and feedback sessions the contributions of the different subjects were then further used to clarify the problem. This process was followed by a subject-based approach by providing students smaller intra-grated
problems (integrating concepts in mathematics or concepts in science separately for each
problem) on a weekly basis during normal class hours.
Students’ basic science and mathematics frameworks were therefore developed in subject- based teacher-directed study for a portion of the curriculum due to the importance of acquiring a sound knowledge base in these subjects. This was coupled with the integrated problem-based learning thread typified by PBL discussion groups where students worked on larger open-ended problems in a combined classroom, to motivate or introduce topics, to integrate or reinforce concepts, and to enrich the syllabus whilst allowing students to explore cases which commensurate with their developing understanding of these subjects. Support for this type of implementation comes from Barrows’ and Tamblyn’s study (in Albanese & Mitchell, 1993:52) of the added value of a six-hour PBL segment within a classically taught course. The results from their study combined with findings from the present literature review supported the use of PBL to supplement subject-based, teacher-directed instruction. Although staff experienced the process of covering the curriculum as time-consuming initially this was not the case for long. The explanation may be that the Hybrid PBL approach was used where the traditional as well as the innovative curriculum was implemented concurrently in the programme.
3.4.2.4 Problem design
After the curriculum organization and course structure had been determined the team was ready to design the problems. The process began by establishing desired learning objectives which consisted of the following steps:
• Drawing up a meeting schedule for the entire planning period and determining learning objectives for mathematics and science. The process started with defining the purpose
of the curriculum, the prior knowledge, skills and misconceptions of students were also considered. Thereafter staff listed specific desirable outcomes and expectations for their subjects. Both content and process goals were considered.
• Selecting themes for each term relevant to the curriculum.
• Designing a conceptual map or topic tree with keywords indicating the subjects and their overlapping concepts to be covered by the different themes (see Addendum C). Here staff compiled a list of possible topics and why these topics were essential before reaching consensus over the topics.
• Projecting the themes onto a series of problems. Decisions were made on which problems needed to be written.
• Designing problems covering the topics in the themes. Consideration was given to which learning aids would be needed.
• Setting up course schedules and sequencing PBL sessions on the basis of the central theme(s) from a multidisciplinary perspective
To approach the issue of problem design, lecturers asked themselves: “What is it that we want our students to know and know how to do when they leave our programme” (Stinson & Milter, 1996:35)? It was therefore important that the problems would support major course objectives, not just minor or trivial ones and that the problems should integrate subject content, concepts, and skills in order to enhance understanding. Tying content to PBL activities was an important means of determining whether students had grasped key concepts, where they were still experiencing gaps in their knowledge base and whether they could integrate the concepts between the different subjects. The learning objectives (or areas of expected learning) were then written down which served as a guide to the lecturers in order to help them guide students into areas of discussion that lead to productive learning (Barrows, 1996:8).
In addition the following general points in writing good problems were considered:
• Use problems early and often enough to make problem assignments a significant part of the course grade; thus weekly problems were introduced.
• Give the groups something to do that is challenging enough that they will see obvious benefits in collaboration.
• Give students an opportunity to reflect on what may be a new classroom experience and respond to their input.
• Provide recommended resource lists or provide students access to learning resources based on student needs and levels.
• Have assessment aligned with problem activities (Adapted from Engelbrecht, 2001:42-43).
In the specific writing of the problems the staff made an outline describing the relation between the problems, topics and the subjects. During the problem design stage, it was important for the problems to be presented in a relevant real-life context so that the contents of the problem adapted well to the prior knowledge of the students. It was further important to add a scenario and include several cues in the problem statement that would stimulate discussion, help students generate learning issues and encourage literature searches, sustain discussion and facilitate the exploration of alternatives. It was challenging, in the case of subjects such as Mathematics and Physical Science, to design the problems in such a way that they were not too structured or obvious as learning outcomes but also not too complex to solve. This was especially important since SciMathUS has a broad band of access and a very diverse student population which therefore included stronger and weaker students. This motivated the decision to replace the SC PBL model (student-centred PBL model) where students were totally responsible for generating their learning issues (during the pilot phase of the study) with a combination of the SC PBL model and the PS PBL model (Problem stimulated PBL model, during the case study phase of the study) where lecturers or the problem statement itself provided more learning objectives to students. It was found that students from disadvantaged backgrounds had many gaps in their existing knowledge and needed more direct mediation. This decision supported the view of Kirschner, Sweller and Clark (2006:75, 83) that certain aspects of the PBL model should be tailored to the developmental level of the learners where the advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. The lecturers felt this to be especially important for subjects such a Mathematics and Physical Science and especially for students with low prior education levels.
During the pilot and case study phase of the study the students were provided with the opportunity to assess the quality of the problems after its completion. Some of the questions in the assessment were: What did you like most about the problem? What didn’t you like
about the problem? Did it challenge you to think and do research? Was the problem appropriate for the proposed course? Do you have any suggestions for improvement? These results were then reported during evaluation sessions and the problems were adjusted accordingly. One significant change that was made after the first evaluation session on 15 June 2006 resulted in the replacement of bigger, once off problems with a combination of bigger and smaller regular problems (in other words the PBL project approach during 2006 was replaced with a problem-based combination approach during 2007 consisting of a
combination of three bigger subject integrated problems and smaller subject intra-grated
weekly PBL problems). The rationale behind this decision was that the PBL project approach was experienced as an add-on by the students and the lecturers whereas the combination approach, or subject inter- and intra-gration approach formed a more integral part of the academic programme and provided lecturers with a way of analyzing misconceptions before starting with new work. During October 2006 the Mathematics and Physical Science lecturers thus planned their curricula together and searched for overlapping themes that lend themselves for integration. The science lecturer also wrote four smaller PBL problems for the first term in 2007 which the Mathematics lecturers reviewed. Duplications between subjects and connections and content that covered the same general ideas were explored.
Since the lecturers did not feel equipped to design bigger integrated problems without support they were registered at Clearinghouse in order to view existing PBL problems available on the network and adjust them for their context. Although many science problems were available, no problems were available for mathematics. The book “Problem-based learning problems for Mathematics and Science” was therefore ordered to address this need. In designing the smaller weekly intra-grated problems, the lecturers doing Physical Science and Mathematics adapted their textbook or classroom problems by placing them in real-world contexts. The bigger integrated problems that were designed were titled Pedestrian fatalities, Crossed- circuits, Palmiet power plant, The amazing race and The two oceans marathon.
Scheduling of problems
During the initial part of the pilot phase of the study, students experienced PBL as an add-on. They simply viewed the PBL exercises as doing Mathematics in the Physical Science class or Physical Science in the Mathematics class rather than making the links between the different subjects. It was therefore important to pay special attention to the scheduling of problems. The following scheduling options were presented to the lecturers during the staff planning
meeting in October 2006, namely shorter in-class problems during the first and second terms and a bigger integrated problem during the third term, no bigger problems (only shorter PBL problems during class times for all three terms) or a combination of bigger integrated and smaller inter- and intra-grated problems throughout the three terms. The third option was chosen by the lecturers since, like Drake (1998:95) and Dochy et al. (2000:63-64), they felt that PBL exposure must occur with enough regularity for students to gain the necessary skills and to be able to make the connections among subject areas without getting mixed signals. Another question that arose was whether it was wise to provide students with a new problem just after completion of the examinations. The fear was that this could impede student motivation and lead to PBL not being experienced as forming an integral part of the curriculum. The scheduling options for the bigger integrated PBL problems (usually at the beginning or ends of terms) were therefore reconsidered to offer more flexibility for staff and to make the implementation of these problems most effective for all those involved.