A scoping review was conducted to examine the existing knowledge regarding the teaching strategies for mathematics subject from various perspectives. A total of 30 previous studies were surveyed to identify the best mathematics teaching strategies as well as their effectiveness. The reviewed articles and reports were published between 2017 and 2021 and can be accessed through Google Scholar and NECTA websites. From this review, we identified twelve (12) teaching strategies that were confirmed by previous scholars to be effective in teaching and learning mathematics subjects. As mentioned in section 1, these strategies were tested in classroom or school settings to assess their effectiveness, and the findings are summarized in section 4.
Since the problem of poor performance in mathematics cuts across different countries and levels of education, many studies have been performed to address it. The meta-analysis of those studies shows that the major factors for students’ poor performance in mathematics are the students’ and teachers’ negative attitude toward the subject, large teachers’ workload, inadequate teacher’s competence in both content and pedagogy, poor classroom practices, inadequate teaching and learning resources, inadequate knowledge of the linkage between mathematics and real life experiences and poor recruitment and preparation of mathematics teachers for a teaching job. (Veresova &Mala, 2017)
Attitude refers to a way someone thinks and feels about something.(Northwest,2017). Previous scholars have pointed out that developing a negative attitude toward mathematics is a process and does not occur abruptly! (Mata,Monteiro, & Peixoto,2012);Veresova &Mala, 2017) .When children start schooling, they are usually free from any fear, and they generally have a positive attitude toward learning with self-motivation about schooling. However, depending on the school orientation and their first schooling experience in their first days of schooling, children may start losing motivation to study and slowly develop a negative attitude toward learning and school. In mathematics, students start to develop fear, anxiety and negative attitudes when they experience consecutive failures in class work and assessment or when they fail to relate what they learn in class with their life experiences. As reported by (Webel & Dwiggins, 2019) and (M. Y. Mazana, Montero, & Casmir, 2018), negative community attitudes and beliefs about math also have a negative impact on students’ performance, as they often affect how mathematics is taught in schools.
There are several reasons for massive failures in mathematics in Tanzania. However, the authors of this study believe that effective teaching strategies can help to ease the situation by addressing most of the challenges and improve students’ performance. Therefore, this scoping review is intended to gather information from various scholars on effective strategies for teaching mathematics as reported by different experts from different classroom settings.
2.2 Scoping Review of the Proposed Strategies
The National Examination Council of Tanzania has a tendency to prepare candidates’ item response analysis reports to give feedback to students, teachers, policy makers and all other education stakeholders about the candidates’ performance in each subject. This report is in preparation every year and for all subjects and is written based on what was observed during the marking of students’ examination scripts. This report gives a detailed explanation of how students attempted each question that was asked, clarification of what was expected from students, samples of both the best answer and the poorest answer or solution that was given by students and recommendations for improving students’ performance.
For example, the 2021 report for mathematics subject pointed out that the major factors that contributed to average and weak performance were the candidates’ failure to apply correct formula, rules, theorems, properties and procedures; formulate expressions, inequalities and equations from word problems; perform correct mathematical operations; and draw diagrams and graphs as well as interpret figures correctly (NECTA, 2021). This report recommends several teaching techniques for improving students’ performance in mathematics, such as the use of teaching aids and real objects, which will help students link the concepts covered in class with the real world. Unfortunately, the majority of teachers do not invest enough time to go through these reports and implement the given recommendations. To avoid similar mistakes in the future, mathematics teachers are required to design and deliver their lessons in a manner that will promote a meaningful understanding of the concepts and enable students to gain such skills.
A meta-analysis by Turgut, 2018) examined the effect of cooperative learning techniques on students’ mathematics achievement in Turkey by referring to 47 articles. Basically, a cooperative learning strategy allows students to have face-to-face communication while working together as a team in performing a given task to achieve a certain learning target. In this approach, learning results from each group member’s contribution with just little teacher support and interventions. However, for this approach to work properly, the teacher is supposed to help students develop their interpersonal and intrapersonal intelligence to have productive groups. The findings from this study indicated that cooperative learning techniques increase mathematics achievement, and this effect is the same at the elementary, middle school, high school and undergraduate levels.
Cooperative learning can also be achieved through peer tutoring, which includes a range of approaches that enable learners to work together either in pairs or in small groups to provide each other with explicit teaching support. A study by (M. and C. (2019) Mazana, 2020) confirmed that peer tutoring in mathematics has similar academic benefits for both primary and secondary education. Peer tutoring can take the form of either cross-age tutoring, peer-assisted learning, reciprocal peer tutoring or a gallery walk. In cross-age tutoring, a teacher can assign an older learner (e.g, higher class levels) to take the tutoring role and be paired with a younger tutee or tutees (lower class levels) and guide them on how to address some mathematical problems.
Alternatively, a teacher can plan for peer-assisted learning, which is a structured approach for mathematics in which students who are good at math can be assigned sessions of 25 –35 minutes two or three times a week to help their peers understand some mathematical concepts. Likewise, a teacher may plan for reciprocal peer tutoring in which learners alternate between the role of tutor and tutee. This is also a very good approach since it makes every student busy and committed to preparing what he/she will present to peers. Presentations of peer tutoring tasks can be in the form of gallery walks, activity circus or learning stations . Generally, peer teaching or peer tutoring can be of great help to both students and teachers,especially in schools that have no or few mathematics teachers.
Another study by (Tambunan, 2019) compared the role of problem-solving strategy and the use of scientific approaches in developing students’ higher-order thinking skills, such as communication, creativity, problem solving, and mathematical reasoning skills. Teaching through the problem-solving approach in mathematics means that students are assisted in learning through problems, questions or challenging tasks that are often in word format and have no clear rules or formulas for arriving at the solution. On the other hand, scientific approaches in mathematics focus on helping students observe, question, experiment, associate, and communicate mathematical ideas. The findings from this study indicated that problem-solving strategies are more effective than scientific approaches in developing students’ abilities in mathematical communication, creativity and reasoning.
In addition, (Tokac et al., 2019) performed a meta-analysis to examine the effects of game‐based learning on students' mathematics achievement. These researchers analyzed data from 860 studies that focused on the effects of computer games on student mathematics achievement. These studies were found in various databases, such as ERIC, Psyc INFO, Wilson, Google Scholar, JSTOR, and ISI Web of Science, and they were in the form of empirical studies, peer‐reviewed journals, book chapters, theses and dissertations, and conference papers. Overall, the findings indicated that video games are a slightly effective instructional strategy for teaching mathematics across lower levels. The use of games benefits visual, audio and kinesthetic learners who learn best by seeing and performing various tasks during the lesson.
Other studies by (M. and C. (2019) Mazana, 2020) investigated the impact of metacognitive strategies and self-regulating processes in learners’ achievement on solving math word problems. It specifically analyzed the impact of the linguistic factor and the number of steps and arithmetic operations that learners need to apply during the process of solving math word problems. Their study used a sample of 233 students from two urban schools in Kosovo. Almost half of these students were exposed to metacognitive instructions, while the other half were included in control classes in which they performed tasks without having been given any specific guidance, based exclusively on traditional methods and respective textbooks. All the learners were tested in math word problems twice, before the intervention and after it. The study found a statistically significant difference between the pretest and the posttest results among the two groups of students. They concluded that metacognitive strategies and self-regulating processes that learners use to control their actions, to reason, and to reflect are some of the main resources that influence their success in solving a math word problem.
Additionally, (M. Y. Mazana et al., 2018) mentioned the issue of students’ limited knowledge on effective learning and examination strategies or techniques as a factor for persistent failure in mathematics. Their study found that most students lack learning and examination strategies such as speed and accuracy, which limits their ability to understand mathematical concepts taught in class and to handle mathematics exams. This implies that in most mathematics lessons, students just adopt surface learning approaches that are not capable of imparting to them meaningful understanding of the concepts and that they might fail due to a particular study habit. Their study suggests that both teachers and students should work together to design and develop the best study techniques that will enhance a deep understanding of mathematics lessons. Mathematics teachers must help their students gain a deep conceptual understanding. To confirm that students have truly mastered a concept, they should be able to show all the detailed steps in a process, explain why those steps occur, and connect the process to related concepts. A deep mastery of concepts will also help students develop the math skills that are necessary for progression and innovation in STEM-related fields.
A need to establish special interventions that reduce math anxiety and/or reduce the negative impact of math anxiety on achievement was also proposed by Ramirez, Shaw and Maloney (2018). These researchers presented a review of past studies that investigated the association between math anxiety and math achievement, factors that can cause math anxiety, characteristics of students that can increase their susceptibility to math anxiety, and efforts that educators can take to remedy math anxiety. Their study indicated that math anxiety can result from poor math skills, genetic predispositions or socioenvironmental factors such as negative math-related class experiences, home experiences around math and how they interpret their previous math experiences and outcomes of their efforts in solving math problems. The paper addresses several mechanisms that teachers may use to help students develop self-concepts and build a strong positive attitude toward the subject.
Moreover, studies show that teachers’attitudes and beliefs about mathematics, such as the usefulness of mathematics, the way mathematics should be taught and learned, the difficulty or ease of mathematics, and gender ability in mathematics achievement, affect their own attitude toward the subject, which in turn has a significant impact on students’ performance. (Peteros et al., 2019). Generally, the literature has confirmed that students’ and teachers’ attitudes toward school and learning are important predictors of students’ academic achievement. A study by (Eliseo P Marpa, 2019) pointed out that teachers’ behaviors may increase the student's math anxiety if they put too much pressure on the student. This kind of pressure seems to be the common challenge faced by the students in their daily learning process, and it originates from their teachers and family members who place very high expectations for students to excel in mathematics. Competitive pressure from peers and friends also tends to increase students’ anxiety in learning mathematics.
While we all encourage students to work hard in their studies, the study found that too much emphasis on attaining excellent results in examination creates a potential worry, fear and anxiety that ends in emotional or psychological disorders.Their study calls for all parties to establish good mechanisms for controlling and minimizing the high-performance pressure. Unfortunately, some of the mathematics teachers relate with their students in a too strict manner, which results in a significant fear of asking for clarification when they do not understand or volunteer to answer a question. This results in total hatred of both the teacher and the subject. To avoid this problem, mathematics teachers are supposed to use a variety of techniques that will make their students feel at ease throughout the lesson. Among such techniques are the use of interactive/student centered approaches of teaching, use of differentiated tasks, giving personalized constructive and timely feedback, motivating or awarding the high achievers and the most improved students, encouraging the low achievers as well as focusing more on students’ ability to solve problems rather than getting good grades.(Xia, 2020). In addition, mathematics teachers should plan their lessons in a way that will help students make connections between the concepts taught in class with real life application.
Another study conducted by (Spooner et al., 2019) emphasized the need for teachers to help students learn both a progression of foundational skills (e.g., early numeracy) and how to apply these skills within the content of their assigned grade levels. These researchers pointed out that students need instructions that focus on foundational mathematics skills, such as number sense, while applying these skills to higher levels. The issue of imparting numeracy skills to children was also emphasized by (Tout, 2020), who described numeracy as a critical awareness that builds bridges between mathematics and the realworld, with all its diversity. This researcher suggested that for students to gain numeracy skills, teachers should use a problem-solving, investigative, open-ended approach when teaching and use real texts and real situations to make connections between mathematics and the real world.
In addition, we found another strategy for teaching mathematics that insists on designing mathematics lessons in a way that will help students make connections between mathematics concepts covered in class with real life experiences. This recommendation was proposed by, Siregar & Surya, 2017), whose study found the level of mathematical connection ability of most students to be very low. Their study therefore calls for mathematics teachers to design and apply deeper teaching strategies that will enable students to establish a meaningful connection between classroom mathematics and life experiences. These scholars also recommended further research to examine what causes the lack of mathematical connection ability of junior high school students in Indonesia. This recommendation can also work in other countries, including Tanzania.
The use of technology in teaching and learning mathematics has been mentioned by several scholars as a possible means of improving students’ achievements. Among such scholars, (Abramovich et al., 2019) pointed out that curiosity and motivation can also be supported by the use of digital tools as instruments of action learning. Another study by (Etcuban & Pantinople, 2018) found that the use of the mobile application in teaching mathematics to Grade 8 students somehow helped to enhance students’ achievement and learning. This study therefore recommended that the administrator enforce and include the use of the mobile application in carrying out learning to its maximum, and teachers should equip their learners with the latest technological skills so that they may compete globally. As explained by (Eliseo Perante Marpa, 2020), integration of ICT in mathematics is not merely using computers for typing and printing questions, searching and delivering lessons via PowerPoint but rather using ICT in teaching various topics in mathematics and encouraging students to use technology in mathematics learning.
The use of effective assessment strategies is also key to improving students’ math grades. Mathematics teachers should have a high ability to assess their students before, during and after classroom teaching, which is an important predictor of mathematics achievement.(Alfaro & Joutsenlahti, 2020). Assessment in mathematics should focus more on authentic assessment rather than just rote learning, as in multiple-item tests or passive test taking. Authentic assessment focuses on making students demonstrate the various skills and concepts they have learned in class and explain when it would be appropriate to use those facts in mathematics computations or in solving a real-life problem.