The Challenges Faced by Secondary School Students

Introduction

This paper aims to examine literature which discuss the reasons algebra is challenging to secondary school students and how teachers can plan their teaching strategies to overcome negative stigma about Algebra. Mathematics is the area of curriculum am interested in because it is a fundamental area within every country’s education system in the world. According to Adeeko et al. (2020), mathematics is the backbone of technology and science and is an inevitable tool for the survival of human beings. Phonapichat, Wongwanich and Sujiva (2014) noted that mathematics as an instrument can be used to teach and train students to solve different problems and develop the ability to think. One area of mathematics that is particularly intriguing for me is algebra. This area is defined by Usman and Musa (2015) as a mathematical dimension which employs numbers and letters. Combining figures with letters confuses students, especially when the values of letters change or when letters replaces one another at intervals.

My interest in this specific aspect of math is its role as a doorway to future career and educational prospects (Silver, 1997). Algebra plays a vital role in a person’s ability to make connections, reasoning, communication and problem solving abilities. Iji, Abakpa and Takor (2015) says that algebra is a language through which different aspects of mathematics are communicated. According to Bala and Shaafiu (2016), advancements in algebra has made it possible for mathematical modelling and abstraction to have relevance. Many secondary school students find algebra particularly challenging. This is especially because of their attitude towards the aspect of mathematics. Bala and Shaafiu (2016) state that student attitude towards algebra is key because it shows an individual’s reaction and perception to executing different tasks. These authors claim that students’ attitude towards tackling algebraic problems determine their interest and success in this field and because of their negative attitude towards algebra, low performance is often witnessed. Teachers are advised to find appropriate teaching strategies which can create a positive attitude and make it easy for all students, including those with learning disabilities to understand algebra.

Causes of poor performance and negative stigma in solving algebra

Tolar (2007) claim that many students are not proficient in algebra and commit errors while attempting to tackle algebraic problems. This in turn lowers their access to both educational, as well as economic opportunities. A study conducted by UNICEF and NIE (2014) indicate that students perform lowest in algebra as compared to all the other areas of math. Moseley and Brenner (2009) opine that many students often get confused as they try to solve algebraic problems, especially because of their negative attitude and stigma towards this aspect of math. Of importance according to these authors is how the students get confused as they try to interpret algebraic equations comprising of numbers and letters and how to use variables in representing unknowns. As a result, they find it difficult to solve and learn algebra (Anthony et al., 2012).

Pre-Conceived ideas from students’ personal experiences

Authors like Peter and Olaoye (2013) and Krishner and Awtry (2004) believe that most students have pre-conceived notions concerning algebraic equations and what they represent. Their interpretations are thus based on the experienced they have and end up wrongly assuming that algebraic equations and their symbolic notations are related. These authors opine that students operating algebraic expressions usually respond to familiarity with certain visual notional designs during decision-making rather than relying on the existing mathematical rules. Students fail to reason concerning the general goal and concepts in a problem and instead find an implied procedure in the equations which they apply directly. The result is that algebraic equations cause great confusion in students.

The lack of in-depth content understanding and knowledge of algebra in teachers

According to Strand and Mills (2014), teachers introducing students to algebra have the responsibility to help them develop a strong foundation which they can later use to construct more sophisticated algebraic solutions. These researchers found that most students often fail to reach basic or the primary algebraic literacy which later become a barrier for them to venture into fields like businesses, technology, engineering and sciences. According to Strand and Mills (2014), one of the reasons that students fail to grasp basic algebra is because of the approach which is used by teachers during the introduction to algebra. These researchers claim that some approaches used by teachers lead to early frustration in understanding algebraic content and they end up developing a negative attitude towards this aspect of math.

Difficulty encountered while solving algebraic equations

Tambychik, Subahan, Meerah and Aziz (2010) found that students may develop difficulty in understanding mathematical concepts like procedure, facts, and formulas because of the lack of capacity to visualize the concepts and problems. Therefore, they lack strategic understanding and knowledge and become inefficient in terms of logical thinking which are critical in tackling algebraic problems. Many students do not have the knowledge of the procedure or process followed in solving algebraic problems. Additionally, some may have some knowledge about algebra but lack understanding of the basic mathematical structure (Adeleke, 2007).

Lack of confidence to tackle algebraic equations

According to Mohd and Mahmood (2011), many students are not sufficiently confident to tackle algebraic problems yet confidence is key in finding the needed solutions and mathematical achievements. The lack of confidence lowers their morale and as a result put little effort and perseverance in solving algebraic equations.

Learning difficulties

In a study conducted by Greg and Fiore (1999), some students have a challenge or difficulty in relating symbols with the correct referent. These students have difficulty in understanding the meaning behind different variables. They see expressions only as objects. They end up feeling tense and anxious when solving algebraic problems and manipulating numbers. Greg and Fiore (1999) claim that this type of anxiety which students experience when solving mathematic problems is a psychological condition which occurs when one expects or experiences the loss of self-esteem. This anxiety prevents them from learning and understanding basic mathematical concepts. As a result, the performance of such students is affected negatively. Evidence shows that many teachers fail to take into consideration learning difficulties in different students when developing teaching plans or when thy in panel meetings to discuss appropriate strategies which should be used to teach mathematical concepts.

Sotiriou, Lazoudis and Bogner (2020) note, however, that there are many forms of technologies today which can be used by teachers to help low achievers in the classroom. These technologies, ranging from less to the most powerful computers and software can be used in addition to the pencil and paper approach to help those with learning difficulties gain a positive attitude in learning and understanding basic algebraic concepts (Sotiriou, Lazoudis and Bogner, 2020). According to theorists like Block (1971) and Bloom (1974), people who are different, especially those with varying levels of learning ability can reach equality or higher performance/achievement outcomes when given the needed time and resources.

How to plan effective algebra lessons for secondary school pupils

Minimizing students’ abstract reasoning

According to Start et al. (2015), one of the methods which teachers can use to improve students understanding of algebra and get rid of the negative attitude associated with this topic is by engaging them in the analysis of algebraic strategies and reasoning. These authors believe that unlike elementary math such as arithmetic, tackling algebraic problems need abstract thinking. Therefore, students must use multiple and complex information during the process of algebraic reasoning and challenge their working memory. Teachers should learn how to minimize students’ abstract reasoning by allowing them to see solution steps and problems at once. Teachers have a duty to help their students to learn efficiently. This can be done by using algebraic representation structures which can allow the students to see the underlying mathematical relationships and features. When students pay attention to algebraic structures, they can make connections between problems, representations and solution strategies. This approach can help simplify algebraic problems and allow the students to find solutions, as well as develop a positive attitude towards this topic. When students recognize structure, they can understand the meanings and characteristics of problems and algebraic expressions even when the problems are in graphic, verbal, numeric or symbolic forms (Start et al., 2015).

Using the Mastery Learning Approach (AMaLM)

Guskey (2015) notes that AMaLM is an approach that rely on properly-defined algebra learning objectives. In this approach, algebraic concepts are arranged into simple or smaller sequential units. Learning materials are subdivided and a test is given at the end of each unit to evaluate how much students have understood. If the students lack a mastery level or grade of between 80% and 90%, then they are given more teaching and time until they reach the required mastery grade, also determined through a retest. This approach captures most elements of appropriate and successful teaching because the teacher gives students specific and frequent feedback using formative tests and diagnostics and by regularly correcting their mistakes along the learning process and period. In AMaLM, teachers examine students’ achievements in algebra using criterion-referenced tests. Evidence shows that this approach is important because it allows teachers to assess the progress of all students each time they start a new unit (Guskey, 2015). As a result, students develop confidence when they start new learning. This author believes that this model offers an advantage because it allows teachers to produce robust gains in students’ overall achievement and gives the students the chance to master vital concepts before the introduction of new content.

Davrajoo et al. (2010) claim that math teachers need to inculcate this situational experience that students should develop their understanding of every mathematical concept. This model allows teachers to observe, assess and involve students in the learning process as they complete different tasks. Teachers can also pose questions to their students to promote reasoning and mastery of concepts. According to Davrajoo et al. (2010), the AMaLM model helps improve the performance of students and lowers their anxiety as they tackle mathematical problems and algebraic equations.

The concrete-to-representational-to-abstract sequence of instruction (CRA)

According to Witzel, Mercer and Miller (2003), students can comprehend abstract concepts easily when they first learn and also understand the various precursor concepts in a solid or concrete manner. These authors opine that teachers can simplify their students understanding of the various abstract concepts by transforming complex concepts into pictorial representations and concrete manipulations. These researchers claim that this approach can improve students’ chance for success, especially in challenging areas like algebra. The result is that their graduation rates can improve. The use of concrete-to-representational-to-abstract approach is recommended by these researchers as a method of teaching secondary school students challenging mathematical concepts easily. Witzel, Smoth and Brownell (2001) support this approach by saying that it shows a lot of promise when issuing algebraic instructions. The latter authors opine that this approach makes the instructions accessible to all students, particularly to those with experiencing difficulties. This approach allows such students to use concrete materials to develop representational concepts abstract thought, following what these authors call the concrete-to-representational-to-abstract instruction sequence. This instruction begins with the use of manipulative objects which are displayed to help solve algebraic problems. Students who develop concrete understanding of the topic work with similar concepts with the help of pictorial representations and develop abstract understanding later. Witzel, Smoth and Brownell (2001) believe that representational knowledge can be a practical approach and step for the students unable or unwilling to use objects to solve mathematical problems.

Using the indicator approach

Nyman (2015) discussed the importance for teachers to be observant concerning student engagement in class while teaching challenging subjects like algebra in secondary schools. According to Nyman (2015), engagement is a student’s effort directed towards and investment in learning. This author states that engagement is active negotiation that takes place through speech and gestures, an indication that a student either understands what is being taught or is not. This author opines that student engagement is based on the notion that interplay between teachers and students shapes the general instructional practice. One of the engagement indicators which teachers can look for in the classroom is verbalizing thinking. Nyman (2015) believes that this indicator can be seen when students convey the willingness to share ideas concerning contents of the topic being taught. For instance, when they want to use a mathematical language or attempt to express what they known by asking questions.

Another indicator of engagement is concentration, visible when students appear to be focused when teachers are explaining concepts to them. Teachers can distinguish between the lack of concentration and focused students, an indication that they are paying attention to what is being taught. Students who are interested in algebra will pay attention to their teacher’s explanations and resist distractions like movement in the classroom. Nyman (2015) noted that teachers can also look for excitement and gestures. For instance, when students nod at certain times and when they follow their teachers reasoning with head and eye movements, it shows that they are interested in and understand what is being taught. Answering and asking questions is another indicator that students are engaged in the topic. This also shows the willingness to comprehend the topic. The last indicator is justification and argumentation (Nyman, 2015). This indicator is demonstrated when students show persistence and stand up for what they believe is the right answer or concept. These indicators can show the teachers that the concept being taught is interesting and students understand or are willing to understand. Therefore, a teacher can either improve on or change the teaching strategy being used, especially when dealing with challenging topics like algebra (Nyman, 2015).

Statement on why this is an important aspect to focus on

As indicated by literature, algebra plays a critical role in everyday life. It is a primary math topic which requires the use of logical thinking about numbers instead of simply focusing on computation of the numbers. Literature has also indicated that many students find this topic challenging because of their negative attitude towards the topic. Algebra is particularly challenging to students with learning difficulties. The challenges experienced by students in comprehending algebra and the importance of this particular mathematical aspect in daily life and many technological and scientific fields make this aspect an important area which teaching professionals must focus on. Solutions must be found to determine how teachers can change students’ attitude towards this topic and make them to think both arithmetically and algebraically to find solutions to challenging tasks to algebraic equations since this topic play a critical role as the gateway to numerous future careers in the business, technological and scientific world.

Discussion and how this will inform my future curriculum planning

It is true that most secondary school students develop a dislike towards tackling algebraic equations because of a myriad of reasons and challenges. Students with pre-conceived ideas, for instance, those who have previously heard that algebra is challenging often fail to pay attention to and reason concerning the goal of or need to master algebra. They fail to pay attention to the important concepts being taught in class and get confused. Additionally, it is true that teachers introducing students to basic algebra need to be highly skilled professional mathematics teachers whose strategies cannot scare students away from the subject. These should be teachers whose strategies of teaching this significantly challenging aspect of math is exciting or interesting. Poor teaching strategies might lead students to develop a negative attitude towards algebra and cause frustration in understanding its contents and concepts. Some students, especially those with learning difficulties might lack the capacity to visualize the concepts and problems of algebra. This may also cause a challenge in understanding this topic. Lack of ability to relate symbols with the appropriate referents means that students cannot understand the meaning behind the variables they are seeing. This means that rather than seeing expressions and finding their abstract meaning, they only see them as objects, causing more confusion and stigma.

Therefore, teaching algebra in secondary schools need skilled teachers who can help students to learn efficiently using structures that can allow students to find and understand the underlying mathematical relationships and features and connect between problems, representations and solution strategies. Teachers can also use new proven models such as AMaLM to not only test students’ mastery of algebra but also develop teaching strategies which can help avoid anxiety, ensure important concepts are understood and assess progress. This is important for improving existing teaching strategies or finding new better teaching methods. Furthermore, teachers in this area of mathematics can also use the concrete-to-representational-to-abstract sequence or the CRA instructional methods which enables students to comprehend abstract concepts and learn different precursors that lead to the transformation of complex concepts. For instance, teachers can use pictorial representations and other concrete manipulations to help students understand different algebraic concepts. Some students need more than just verbal lessons. Those with learning challenges might benefit a lot from pictorials and other forms of representations which make the learning process exciting.

Teaching algebra, an evidently challenging aspect of math, requires teaching professionals who are skilled in determining learning indicators ad using them in developing teaching strategies which enhance learning in students. Indicators such as verbalizing, concentration, gestures, justifications and argumentation can help determine whether the students are excited and interested in the topic or not. Teachers can also know whether students understand what is being taught. Therefore, they can improve the existing teaching strategies or develop new ones to ensure that students like and understand algebra. As a teacher, this information will inform my future practice as I not only know what to avoid but also how to improve my teaching process to ensure that students like and master algebra.

Conclusion

To help overcome a negative attitude of students towards algebra require teachers who can help students to develop interest in the topic. Students should not be made to believe that algebra is challenging. Instead, the relevance or importance of this topic in different fields and in solving real life situations should be emphasized. Additionally, teachers should come up with teaching plans which make it easy for students to relate reasoning, communication and problem solving abilities. While developing teaching plans, teachers should consider using new approaches like AMaLM and the CRA to make it easy for every student, including those with learning challenges to comprehend this relatively challenging but very important aspect of mathematics.

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