While neither teacher asked for feedback from learners to review, refine and improve their lessons, they ensured that they always provided learners feedback whether it was through learners correcting their own work and/or making use of their peer corrections.
Teacher 1: “When they are doing corrections.”
Teacher 2: “I focus more on their peers marking, their work and then they check where they have gone wrong.”
Both teachers elaborated the typical layout and schedule that they are obliged to use as math teachers. They both started with introducing the objective of the day for 15 minutes, while Teacher 1 was actively teaching, and Teacher 2 taught the content passively. This was then followed by guided practice where the whole class guides the teacher to solve a word problem for another 15 minutes. The last section of the lesson took 30 minutes with learners practicing their problem-solving skills of various word problems related to the objective taught.
Although both teachers followed the school’s lesson setup, they used very different methods and techniques to ensure that learners were engaged, and that critical thinking was promoted within the lesson. These are summarized in Chapter 5.
4.3 TEACHERS LESSON OBSERVATIONS
Following teacher interviews, educators’ lesson presentations were observed, making use of the 5-Step Model classroom observation rubric (Appendix C), for a week to identify the various ways in which they promoted critical thinking and enabled learners to solve mathematical problems.
This included how lesson objectives were determined, whether teaching occurred through questioning, whether the objectives were practiced with learners before the teacher assessed whether learners grasped the objectives, if the educator reviewed; refined; and improved learners’
understandings, and lastly whether the educator provided feedback and checked for understanding by assessment of learning at the end of the lesson. Teachers were assessed using a scale from 1 to 4, with the score guidelines mentioned in Appendix C.
Table 4.3.1, (please refer to Appendix D), indicates that Teacher 1 scored 31 out of 52 while Teacher 2 scored 33. Although both teachers ensured that the objectives were communicated to learners and written on the board, these objectives were not emphasised throughout the lesson.
Both educators focused more on how to solve the sum rather than what sums they were solving;
nor did they emphasise on stretching learners to give answers that showed the ability to link prior knowledge from several areas and create new and/or original work.
The table further shows that both teachers rarely focused much on asking questions that required learners to apply, construct, solve, discover, and show their work, but focused on analysis that needed a response from learners that showed that they could identify patterns and categorize data, ideas, and models into sections as well as asking questions that required learners to scrutinize, organize, categorize, separate, and analyse word problems.
Both teachers placed significant emphasis on teaching through questioning, including Teacher 2 who claimed to be more passive when introducing an objective to learners in the first 15 minutes of the lesson. Teacher 1’s questions were very brief, and answers were also expected to be brief.
Table 4.3.2, in Appendix D, further highlights that Teacher 1 focused more on convergent questions while Teacher 2 focused on divergent questions, and guided learners to the answer by redirecting the questions/responses until learners got to the correct answer on their own.
Both teachers showed strength in allowing learners to practice solving the word problems for most of their lessons with both observing and reflecting, as well as facilitating activities that encourage critical thinking through information and ideas, reflection, and hands-on experience.
Teacher 1 rarely focused on what it was that learners were learning and what the value of the objective was, as shown in Table 4.3.3.None of the learners from either class could answer
questions about what they were learning, the value of what they were learning, how they were learning or what more they needed to learn.
Both teachers put considerable emphasis and time on reviewing and improving answers as Table 4.3.4 indicates, but they lacked in monitoring and tracking learner participation. Random nomination was used in both classes which did not ensure that every learner participated, while Teacher 1 showed minimal to no monitoring and tracking of student participation during the session. Feedback was always one way, downwards. Both teachers focused more on giving learners feedback on how they did when solving word problems, and rarely focused on whether their lessons were productive or not. As shown in Table 4.3.5, neither teacher spent significant time helping learners to grasp the standards and criteria of what was being taught.
4.4 LEARNER ASSESSMENTS
According to Lai (2011), “background knowledge is necessary...for enabling critical thoughts within a given subject”. This goes with Mandernach’s (2006) finding that teachers who can teach more content in depth and analyse their subject contents critically, mostly struggle to implement critical thinking in young learners due to the learners’ limited critical thinking skills and the minimal and/or lack of prior content knowledge needed to participate in a task.
The purpose of the assessment was to identify whether learners were on the same SEAL and LFIN levels, with similar mathematical background knowledge before identifying if Teachers 1 and 2 effectively employed strategies which promote critical thinking skills.
Learners were presented with one problem a day to solve over a period of five days (Appendix A), as a method to identify whether teachers’ strategies had been effective. These problems were differentiated based on three mathematical ability groups in the classes. A brief class discussion took place with the purpose to reiterate the aim of the assessment, but for the most part, learners solved the problems on their own. The researcher walked around the class as learners solved each problem to observe and ensure that learners were working. To preserve anonymity, learners were named as stipulated in Table 3.2.