Challenges and Opportunities for Ob Essay Example

content to be learned. In this perspective, knowledge is built by individuals through their interactions with the environment. Unlike traditional learning where the teacher takes a leading role and learners passively receive information, constructivists believe that learning should be learner-centered.

Simon (1995) states that our perception and experience, as well as our prior knowledge, play a role in shaping our understanding of the world (p. 115). When teachers see students as empty vessels who require information from an authoritative figure, the learning environment becomes teacher-controlled. This control is referred to as the 'banking concept' of education by Freire (1970), where teachers exercise their authority over students.

The traditional banking concept of education sees the teacher as the only source of information, but it is important for teachers to involve students in the learning process so they can actively construct knowledge. The Educational Broadcasting Corporation (2004) agrees with this approach and suggests that a constructivist teaching method includes activities like experiments and real-world problem-solving to engage students.

Kennedy (1997) states that the method of instruction greatly impacts students' learning. Math, as a subject requiring active engagement, necessitates learners to construct their own knowledge. This study examines the extent to which learners were given the opportunity to do so in math lessons. The problem statement highlights the need for a different teaching approach for math in Botswana. Research indicates that most teachers in Botswana tend to present math knowledge for students to memorize and reproduce instead of helping them develop independent skills to construct their own understanding of math (The Report on the process of learning in Botswana: An in-depth study of the quality of mathematics

teaching in sixth grade classrooms and its effect on learner achievement, 2011). Additionally, it has been discovered that teachers in Botswana lack adequate skills to effectively teach math (The Report on the process of learning in Botswana, 2011).

Teachers must change their instructional techniques to engage learners actively in their own learning, rather than being passive recipients. It is essential for learners to develop mathematical communication and critical thinking skills. To ensure future educational growth, Botswana requires learners who are creative, analytical, and adept problem solvers. The constructivist approach can be employed at school level to enhance these skills. Various research studies in mathematics education have extensively explored the constructivist theory of teaching and learning (Katic, Hmelo-Silver ; Weber, 2009; Steele, 1995).

The theory states that students are not passive recipients of information. Instead, they actively generate new knowledge using their prior knowledge and new experiences. Unlike traditional methods where students simply repeat what teachers say, constructivism promotes a more radical approach to teaching and learning. This approach values and encourages learners' original ideas, which are then developed through various engaging teaching techniques.

Multiple studies have confirmed that the constructivist approach to teaching and learning is more effective compared to the conventional drilling and reciting method (Hmelo-Silver, Duncan, & Chinn, 2007; Steele, 1995). In Steele's (1995) study titled "A construct visit Approach to mathematics teaching and learning…," it was found that using constructivist learning strategies provides various advantages. One of these benefits is creating an interactive learning environment where students can acquire mathematical skills and improve their self-confidence.

Research shows that students who develop their own understanding are more likely to

comprehend mathematical concepts and think mathematically. Additionally, a study conducted by Katic, Hmelo-Silver ; Weber (2009) on Material Mediation indicates that materials can stimulate and aid collaborative problem-solving discussions among participants. In their particular investigation, Katic et al.'s teachers utilized diverse resources to address a math problem and elucidate the learning process. They also posed questions pertaining to the problem in order to clarify their solutions.

The method of encouraging learners to stay on task is often endorsed in social theories such as constructivism. While constructivist learning theory does not provide instruction on how to teach mathematics, teachers with a constructivist background can support learners in constructing knowledge by utilizing various constructivist teaching approaches that are consistent with this learning theory. This form of mathematics teaching serves as the foundation for this study.

In Botswana, several studies have found that teacher centered approaches are predominant in classrooms. These studies include research conducted by Prophet and Rowell (1993), the Republic of Botswana (1993), and Tabulawa (1997, 1998). Tabulawa's (1997) study on Pedagogical Classroom Practice reveals that students in these classrooms are passive recipients of knowledge and are not given the opportunity to construct their own knowledge.

The commission on Education (1977) has identified the issue of teacher dominance in Botswana's education system as a significant concern. According to the commission's policy, the information transmitted to students is frequently abstract and relies heavily on memorization, resulting in a call for a radical shift in classroom practices. The aim is to promote student growth through learner-driven teaching and learning.

According to Tabulawa (1998), the impact of teachers' perceptions on their classroom practices is a

cause for concern. He also highlighted that certain factors, including teachers' beliefs about knowledge and student perspectives, contribute to the prevalence of teacher-centered approaches rather than learner-centered practices.

The aim of this study is to assess the extent to which teachers incorporate constructivist teaching and learning in math instruction. It is well-known that this theory significantly improves students' capacity for independent learning. To accomplish this goal, the researcher utilized data from the 2009/10 Human Research Science Council (HRSC) - Stanford - University of Botswana Regional Education Study, which examined teacher quality and student performance in Botswana and South Africa.

Data on instrumentation was collected from a total of 58 schools and 64 classrooms in Botswana. Of the sampled schools, six had two math classrooms taught by the same teacher. The study specifically focused on low-income schools within a 50-kilometer radius of the South African border in five districts: Gaborone (18 schools and 617 students), Kgatleng (16 schools and 495 students), Lobatse (6 schools and 152 students), South East (10 schools and 305 students), and Southern (8 schools and 205 students).

Data was collected by videotaping 83 standard six mathematics teachers teaching at least one mathematics lesson. Over one-third of the teachers were recorded twice. Trained personnel from the University of Botswana's Thenjiwe Emily Major et al. 142 Botswana team conducted the filming at the middle and end of the year. The teachers whose classes were videotaped were informed in advance about the research team visits and were assured that the videos would only be used for the study. Data Analysis

Trained personnel from the University of Botswana and the U.S.A. conducted

a video analysis. They chose cognitive demand levels that were pertinent to the paper's emphasis on the learner's thought process. The categorization of higher and lower cognitive demand by Stein et al.'s (2000) rubric was used to establish these levels, which encompass Lower Level Demand 1.

Memorization is the act of recalling previously learned facts, formulae, or definitions and committing them to memory. This task requires the exact reproduction of previously seen material, without the use of procedures. It is typically needed when procedures do not exist or when the time frame is too short to use a procedure. The focus is on reproducing what is clearly and directly stated, without any connection to the underlying concept or meaning.

Processes without Connections refer to algorithmic tasks that are not related to the underlying concept or meaning. These tasks can be executed using explicitly stated procedures or ones that are evident based on prior instruction, experience, or task placement. They leave little room for ambiguity regarding what needs to be done and how it should be done. There is no need for a connection or explanation of the concept as the main emphasis is on producing accurate answers rather than fostering mathematical understanding. This aligns with Higher Level Demand 3.

Processes with Connections involve using broad general procedures to develop a deeper understanding of concepts. These tasks can be represented in various ways, such as visual diagrams, manipulatives, symbols, or problem situations. The connections between these representations help build meaning around the concept. While following a procedure is necessary, it is not enough for success; students must actively engage with conceptual ideas.

Doing Concepts

and Processes requires complex and non-algorithmic thinking in mathematics. Through this task, students explore and investigate the nature of concepts and relationships. It involves accessing relevant knowledge, reflecting on actions, and exploring concepts through non-algorithmic activities. This task also requires self-monitoring or self-regulation of thinking.
- 4. - International Review of Social Sciences and Humanities, Vol. 3, No. 2 (2012 139-147 (2012), 147 143 -

The task necessitates the analysis of limitations that may restrict potential strategies and solutions. The task is unpredictable because of the type of solution process needed. The main focus of this component (the levels of cognitive demand) is the cognitive thinking processes in which learners engage during observed lessons. In a constructivist classroom, learners are anticipated to think at a high level, actively participating in their own learning. Alongside analyzing the levels of cognitive demand, the data analysis members also observed how students interacted with the teacher.

They took notes on these observations. The study discovered that in a sample of Botswana School, the levels of cognitive demand in classroom teaching were as follows: 7.3% of the lessons required learners to recall a fact, which is essentially memorization. Additionally, 85% of the lessons involved procedures without connections, while 23% incorporated procedures with connections. Only 3% of the students were actively exploring and investigating the nature of the concepts and relationships.

According to the video, teachers typically ask questions in most lessons and allow the entire class to respond. This is consistent with Arthur's (1998) research, which found that teachers frequently lead classroom discussions, especially during extended question and answer sessions involving individual students or the whole class (p.

314). When only teachers ask questions and students solely provide answers, learning tends to focus on the teacher rather than the learner.

Based on the discussions, it is clear that teachers in Botswana predominantly employed procedural teaching methods, resulting in students relying on memorization of facts. This approach discourages critical thinking and the construction of personal knowledge, as the teacher is solely responsible for providing the content. Previous researchers like Fuller and Snyder (1991), Arthur (1998), Tabulawa (2004, 1998), and Thenjiwe Emily Major et al. (144 and 1997) have also noted the prevalence of memorization in Botswana classrooms.

According to Arthur and Martin (2006), the majority of teachers in Botswana tend to ask factual questions and limit students' opportunities for using their reasoning and imagination (p. 195). Their research indicates that lessons primarily focus on recalling facts and procedures without applying them to real-life situations, suggesting that students are not actively constructing their own knowledge but rather being spoon-fed by their teachers. The National Commission on Education of Botswana (1977) concurs with these findings, asserting that learning in Botswana primarily involves memorization and recall of facts, which does not contribute to the learning process. In order to achieve Vision 2016's goal of providing quality education in Botswana that prepares individuals for national and global changes, it is necessary to incorporate theories like constructivism as they encourage learners to explore and develop their own solutions to problems.

According to available data, learners in Botswana need more than just memorization and imitation of teachers to succeed in a world filled with social, political, and economic turmoil. Henningsen and Stein (1997) argue that mathematical tasks

are crucial for students' learning as they contribute to their understanding of mathematics. These tasks also provide the opportunity for students to develop critical thinking skills across various subjects. However, if learners only receive tasks that encourage memorization, they are operating at the lowest level of cognitive demand identified by Stein et al. (2000). At this level, students simply memorize formulas without applying them to real-life situations. For example, during a video observation, a teacher introduced the concept of "area" by asking learners to provide a definition.

Instead of defining the word, the teacher provided the learners with a formula for finding the area of a square. Some shapes were drawn on the board and the teacher solved one as an example, then asked the learners to use the formula to find the areas of the remaining shapes. While most learners were successful in using the formula to find the areas, it remains to be seen if they can apply this knowledge in real life situations. While the procedure may be correct, it is important to determine if the learners were able to make connections to real life.

The analysis of the data reveals that the majority of tasks assigned to learners primarily focused on low levels of cognitive demand instead of promoting mathematical understanding. This emphasis on generating correct answers rather than fostering the development of knowledge and critical thinking may be attributed to factors like an examination-oriented curriculum. In Botswana, teachers tend to provide factual information and assign lower level tasks to students rather than encouraging them to actively engage in thinking and constructing their own understanding. This is potentially influenced

by the centralized curriculum and the pressure to cover the syllabus within a specified time frame, leading to a teacher-centric approach.

Arthur and Martin (2006) recognized that in Botswana, students' examination success enables them to pursue further education (p. 192), which leads teachers to rush through the syllabus. Tabulawa (1998) further supports this notion, stating that teachers' beliefs about students and the objectives of education directly impact their teaching style. Teachers perceive themselves as the primary conveyors of knowledge, while students are seen as passive recipients who are required to memorize and demonstrate knowledge during exams.

The high teacher-to-student ratio may result in a focus on delivering information rather than encouraging learners to develop their own understanding. In a constructivist learning environment, learners thrive by actively constructing their own knowledge. Teachers facilitate higher-level thinking skills, allowing students to go beyond giving simple factual responses. In addition, in a constructivist classroom, learners are encouraged to enhance their understanding through analysis, prediction, justification, and defense of their ideas.

According to Cobb (1999), constructivist learning theory suggests that knowledge acquired by learners themselves is more flexible, transferable, and useful compared to knowledge provided by experts and delivered by an instructor or other delivery agent (p. 15). Constructivism emphasizes knowledge construction rather than knowledge reproduction, which aids learners in retaining what they have learned. International Review of Social Sciences and Humanities, Vol. 3, No. 2 (2012), 139-147 145.

According to constructivists, the second highest level of cognitive demand involves using procedures to gain a deeper understanding of concepts or ideas. To fully grasp the content, learners need to focus on higher order thinking skills and

developing a deep understanding. Constructivists believe that learners become critical thinkers when they are actively engaged in the learning process and encouraged to apply concepts to real-life situations. This allows learners to make meaningful connections.

When learners are given the opportunity to practice within the teaching/learning environment, they can use their experiences to generate new information. This is different from solely receiving facts from an authoritative figure. The teacher's role is to facilitate this process. In mathematics, the highest level of cognitive demand requires complex and nonalgorithmic thinking. Students should be encouraged to explore and investigate concepts and their relationships. Assignments should aim to help learners understand how these concepts connect to real-world situations.

To help learners grasp the concept of 'area' in practical terms, it is important for teachers to give them opportunities to apply this knowledge in real-life situations. To achieve this, educators should provide tasks that encourage exploration, discovery, and application of these concepts. According to Richard (as cited by Simon, 1995), mathematics teachers must provide a framework and plans that enable students to explore and inquire while still allowing them to take initiative and control. It is essential for teachers to create tasks and projects that inspire students to ask questions, present problems, and set goals.

In order for students to become active learners, we need to provide structured plans that guide exploration and inquiry. It is the responsibility of every teacher to create activities that require a high level of cognitive demand. Using prior knowledge as advocated by constructivists is essential for achieving this. Henningsen and Stein (1997) argue that connecting new information with what students already

know is important for engaging them in higher-level thinking processes. The study found that teachers were not assigning tasks that required higher levels of cognitive demand. These findings support the idea that teachers in Botswana classrooms often ask for factual information without promoting critical thinking.

The text highlights that in Botswana classrooms, students are not typically required to explain the process or relationship between multiple events (p. 276). This indicates that teachers in these classrooms primarily assign tasks with low cognitive demand, contradicting constructivist theory principles. Additionally, constructivist theory emphasizes recognizing each learner's individuality and their unique ways of learning. Therefore, as a facilitator, the teacher should understand the strengths and weaknesses of each student and provide opportunities for them to build knowledge based on their own experiences.

In their study, DeVries, Zan, Hildebrandt, Edmiaston, and Sales ( 2002) argued that teachers need to change their perspective from being the central figure in the learning process to placing the child at the center. They noted a prevalence of spoon-feeding in many classrooms, with students being passive consumers of mathematical concepts rather than active participants. This limited knowledge construction and created a teacher-centered learning environment.

According to Thenjiwe Emily Major et al. (references [1] [2]), teachers being dominant in the teaching and learning environment in Botswana will lead to a lack of deep and critical thinking skills among students. The authors argue that knowledge is not passively received but actively developed by students themselves. Therefore, they promote constructivism, which urges learners to build their own knowledge using their past experiences. This approach enables students to apply theory to practice and establish significant links

between their learning and the real world.

The text cites multiple education sources, such as articles by Arthur (1998) and Arthur and Martin (2006), along with a study conducted by Chu, Chow, and Tse (2011). These sources offer insights into various aspects of education, including the cultural construction of primary school teachers in Botswana, dynamics within postcolonial classrooms in Botswana and Brunei Darussalam, as well as effective teaching methods for improving students' skills.The sources include Cobb's article "Applying constructivism: A test for the learner as scientist" from Educational Technology Research and Development in 1999, DeVries et al.'s book "Developing Constructivist Early Childhood Curriculum" from 2002, an article titled "Constructivism as a Paradigm for Teaching and Learning" from the Educational Broadcasting Corporation in 2004, and Freire's book "Pedagogy of the Oppressed" from 1970. The link to the last source is http://www.thirteen.org/edonline/concept2class/constructivism/index.html.The following publications and their respective authors are mentioned in the text:

- B. Fuller and C. Jr. Snyder: "Vocal teachers, silent pupils? Life in Botswana classrooms" in Comparative Education Review, 35(2) (1991), pages 274-294.
- M. Henningsen and M. R. Stein: "Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning" in Journal for Research in Mathematics Education, 28(5) (1997), pages 245-249.
- Hausfather: "Where is the content? The role of content in constructivist teacher education" in Educational Horizons, 80(1) (2001), pages 15-19.
- S. Hmelo, E. Cindy, R. G. Duncan, and C. A.

Please note that the last author is left incomplete in the original text.. Kennedy, and J.B Silverman, Instructional tasks in science classrooms:
A framework for cognitive engagement in authentic scientific inquiry,
Science Education ,86(1)(2002),
1-22.
7.Wood,R.H.MillarandI.Treagust,Learningthrough models,
Paper presented at the annual meeting of
the National

Association for Research in Science Teaching,St.Louis,(1993).
8.C.E.ThompsonandS.Kinoshita,Makingintentionsexplicit:Teachers’viewsabout
usinga constructivist approach to teaching mathematics,
Mathematics EducationResearch Journal ,7(1)(1995),32-46.
9.D.F.Steele,Aconstruct!Visita approach to mathematics teaching
and learning byfourth–grade teachers,
UnpublishedPhdDissertation,(1995),
UniversityofFlorida

The book "Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development" was written by A. Henningsen and E. A. Silver in 2000 and published by Teachers College Press in New York [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13][14][15][16]. It is referenced as source number 17 in the study mentioned in the International Review of Social Sciences and Humanities, Volume 3, Number 2 (2012), pages 139-147[18][19][20][21]. Additionally, there is an unpublished document from 2011 that examines the learning process in Botswana and evaluates the quality of sixth-grade mathematics teaching and its impact on student achievement.

R. T. Tabulawa published research on geography students' role as constructors of classroom knowledge and practice in Botswana in the journal Curriculum Studies in 2004 (volume 36, issue 1, pages 53-73). In addition to this, Tabulawa also discussed teachers' perspectives on classroom practice in Botswana and its implications for pedagogical change in an article published in the International Journal of Qualitative Studies in Education in 1998 (volume 11, issue 2, pages 249-268). Another publication by Tabulawa featured in the International Journal of Educational Developmentin 1997 examined the relationship between pedagogical classroom practice and the social context in Botswana (volume 17, issue 2, pages189-204).