Factors Affecting Students' Mathematical Achievement

1: Analyze the impact of personal, social, economic and political factors on the development and progression of numeracy Learners

2: Explain the impact of learners’ literacy and language skills on the development and progression of their numeracy skills

3: Explain how different communication approaches can affect the learning of numeracy processes and skills

4. Identify the skills, knowledge, and understanding that can be assessed in numeracy

5: Analyse approaches to initial and diagnostic assessment to identify the mathematics and numeracy skills and aspirations of numeracy learners

6: Analyze the use of assessment tools in numeracy teaching and learning

7: Analyze numeracy teaching approaches and resources, including technologies, for suitability in meeting individual learners’ needs

8: Analyze the impact of using technology on learner engagement, motivation and success in numeracy teaching and learning

9: Identify the numeracy skills and knowledge needed by learners across contexts and subjects, and for progression purposes

10. Explain the importance of encouraging learners to make links between their mathematical and numeracy development and their other personal development

11: Explain the boundaries between own specialist area and those of other specialists and practitioners (my own specialist area is childcare)

12: Analyze numeracy learning opportunities to determine how teaching and support needs may be shared among learning professionals

13: Explain how to liaise with other professionals to provide specialist knowledge of how to include numeracy in vocational and other subject areas

14: Explain how to liaise with other professionals to promote the inclusion of wider skills in own specialist area

1. Personal factors

Self-Directed Learning

This is one of the personal factors that affect the student’s mathematical achievement. To learn mathematics requires extensive understanding of mathematical concepts, making connections between concepts, and getting solutions to unstructured problems. Unfortunately, the system of learning mathematics is neither perfect nor well-structured to enable students to think mathematically. In learning mathematics students have to play active roles. Self-directed learning plays a critical role in the learning of mathematics. A student with this trait is intuitive in learning by knowing their needs, getting objectives right, recognizing their resource needs for learning, and assessing their learning (Knowles 1975). The role of the teacher is simply engagement in students’ organization and initiation of their self-directed studies instead of directing their learning (Strommen and Lincoln, 1992).

Arithmetic Ability

The learner ability to tackle mathematics problems is another predictor. This ability includes mathematical manipulation knowledge and conceptualization of the problem for its meaning and implication. The arithmetic ability allows the learner to do interpretation, analysis, and synthesis of the mathematical facts and figures (Kaeley, 1993). The high mathematical reasoning of the learner enables him/her to get a solution to complex problems, exploring new methods and understandings, and getting logical conclusions.

Various studies have confirmed arithmetic ability as a critical factor on learner mathematical success. According to Conradie (2014), there is a high correlation coefficient with math success for those learners exhibiting arithmetic ability. Another study by Schiefele and Csikszentmihalyi, (1995) confirmed the same where the learner achievement scores were strongly correlated by the level of arithmetic ability. These studies revealed that mathematics ability is a significant predictor of a learner math achievement.

Motivation or Concentration

The complexity of mathematic logic, interpretations and mathematical problem solving and conceptualization, requires a highly motivated learner. Most mathematics learners today are faced with the challenge of the need to have discipline in studies, high concentration and both internal and external motivation. Broussard (2004) did a research on 123 first grade and 130-second grade math learners to find out the relationship between classroom motivation and academic achievement. Their findings were consistent with previous studies where they found motivation be one of the contributors of higher mastery in mathematics.

Beside the internal motivation of a learner, teacher’s role in creating learner motivation should also be factored in. The teacher plays a key role in motivating the learner by acting a role of instructor and creating a learning environment for learners to engage in mathematical reasoning tasks and be able to view mathematics as a subject of exploration, verification, and reflection.

Arithmetic Ability

Social Factors

Gender

Various researchers have conducted studies to determine the influence of gender on the performance in mathematics. However, out of all gender has been the most researched. One example of such studies is by Agyei and Eyiah-Bediako (2008), through their meta-analysis, they established that males showed the greater capability to do better on mathematics that involves problem-solving while females do better in calculations. However, they observed that male and female did not differ much in mathematics understanding in both genders. There is another research which established how females get better grades in mathematics than males (Liu and Tau, 2013).

Other studies have tried to explain how gender differences in mathematics are becoming insignificant in various countries. On the other hand, other researchers have established that as the learner performs well with higher grades, gender differences become apparent with males getting higher math grades males (Campbell, 1995; Ercikan, McCreith, and Lapointe, 2005). An instance of this study got a conclusion from Third International Mathematics and Science Study that the mathematics grades of each gender group showed no much difference at both lower and middle school. This is contrary to the last final year in secondary school which showed gender differences in math performance. In addition, attitude and perceptions differences between genders are considered a factor to consider. The study found that female tends to have a negative attitude towards mathematics and thus don’t have interest. It is argued that the boy does mathematics competitively to master the concepts while girls learn by way of rules and cooperation (Innabi and Dodeen, 2018; Webster and Fisher, 2000).

Scholarly literature has determined how gender contributes to performance differences in achievement of higher grades in mathematics. For this reason, instructors are advised to take interest in those differences teaching, designing their classes and class culture and how they communicate during learning.

This factor has been determined to contribute largely to mathematics development and progression of learners. Various studies have been conducted to determine how this factor influences learners with some focusing on the parent’s economic level in terms of annual income. They found that the level of parent income has a relationship with the learner’s performance in mathematics (Eamon, 2005; Hochschild, 2003).

Other studies have established that parents who are better of social-economically tend to be more involved in the education affairs of their children. Involvement of a parent in their education and especially in mathematics, help learners have a positive attitude towards education thus higher development and progression in various education disciplines (Epstein, 1987). Thus it is believed that low social-economic status negatively impacts development and progression in mathematics. Because of this, learners access to education resources is limited which create learners distress in homes (Ali et al., 2013). Therefore, social-economic status is a factor to consider when teaching mathematics as factors that affect the learner’s development and progression.

Motivation or Concentration

Parents’ Educational Level

This factor has been investigated to provide how it impacts the learner progress in mathematics. To most learners, their parents serve as role models and guide to excel in academics. Parents have a role of encouraging and motivating their children to pursue higher educational excellence. They also offer support and educational resources to their children. Therefore, the educational achievement of a parent, and in this case in mathematics, are indicators of attitude and values which the parent instill to their children by creating a learning environment at home which children depend on for learning and achievement.

There number of studies which determined the relationship between the parent's educational background and their children excellence in education (Coleman, 1995). For example, it was observed that those children whose parents attained less in education they are likely to perform poorly in education compared to those who attained higher education (Campbell, Hombo, & Mazzeo, 2000). These researchers have shown that parent’s educational background and level have an impact on the learner attitude and the development and progression of the learner in education and their mathematics success.

Ethnomathematics

This is the study of the relationship between one's culture and mathematics. Often the connection between the two is the key to overcoming this problem in mathematics (Siemon et al 2012). It is concerned with the how a specific group of people perceive mathematics. It is important for the educator to communicate mathematically in the classroom set up. It is also important in educator’s understanding of the importance of the deriving the relationship between mathematics and culture in teaching.

The home background and culture of a learner are crucially considered as one of the factors influencing the learning experience of the learner. The experience of the instructor in making connections between the learner’s background and culture in the classroom help learners to better their mathematics experience. Being able to link the culture and mathematics is beneficial to both the learner and the educator on how to see the world beyond mathematics.

Social-cultural norms

These factors include the language use, styles of communication in the classroom, and classroom rules. These aspects of social-cultural norms are affected by the educator. It is important to establish the norms for different classes and the environment (Mottier Lopez and Allal, 2007). The teacher roles are defined by these norms which largely affect the learner development and performance in mathematics. The educator has to choose the right norm for various classes depending on the environment.

Gender

Education support system laid down by the government has impacts on the education. The decisions made by the government of the day have a direct impact on the running of the education system and thus the effect on the learners. Poor decisions that are affected by the education stakeholders have a far-reaching effect on learners as well as educators. The effects of the general performance in education also affect how the learner’s performing in mathematics.

2. Learning mathematics goes hand in hand with the student ability to communicate using a particular language being used in teaching. The language barrier is a concern for understanding mathematics especially those who use it as a second language in learning (Ilany and Margolin, 2010). In teaching mathematics, educators have to recognize the cultural and linguistic diversity that is evident in the environment of the classroom (Abedi and Lord, 2001). Although not very clear, studies have explained that the numeracy capability and arithmetic processing of a learner are shaped by different language experiences and cultural factors like mathematical learning (Tang, Liu, and Clarke, 2006).

Learners use language to define and express mathematical concepts and in learning and teaching. Different language backgrounds of learners may influence their mathematical development and progression (Miura et al., 1994). For instance, mathematical concepts and terms defined and explained in Chinese are well understood by Chinese indigenous than those who use it as a second language. This is because the concepts and terms are expressed through everyday words, just like ordinary written and spoken the Chinese language. Therefore, there is higher language competence in indigenous Chinese learners’ thus higher grades in mathematics. A study focused on English language learner’s mathematics performance (Bernardo and Calleja, 2005). The results showed that there is a performance difference between English language learner and non-learners in mathematics. Therefore, therefore the literary competency of a learner is a factor in determining the development and progression of a mathematics learner.

3. Participation and problem solving

The educator should engage learners when teaching mathematics. The communication between the two is critical to ensuring the learner understand the mathematical concept. Also, the educator should engage the learners in solving mathematical problems in math class and their application in life. The learners should be encouraged to conceptualize the mathematics skills gained in class to derive new meanings and applications. Through problem-solving and one on one engagement, learners are trained to communicate mathematically. According to the Hsu (2013), good problem solvers "monitor and reflect on the process of mathematical problem solving" (p. 52) and adjust their use of strategies as needed. "Such reflective skills are much more likely to develop in a classroom environment that supports them" (p. 54).

Social-Economic Status

One-on-one communication with the learners

The educator may need close one-on-one contact with the learner. This communication approach becomes important, especially where they learner failed to understand the math concept in class and need a farther explanation. For weak and non-indigenous language learners this communication approach is better for their understanding of mathematics (Westwood, 2008). The learner contact with the educator is important in making the missing mathematical connections.

Use of Practical samples

The instructors need to develop practical communication approach in teaching mathematics. Mathematics is a science of practice where learner gain and understand more when practical sample math are demonstrated by the instructor (Siemon, 2015). The learner analyzes the practice samples given by the instructor to gain an understanding of tackling similar mathematical problems. The instructor has to make the teaching of mathematics realistic by applying real-life events to solve mathematical problems while making it easier for learners to conceptualize and understand.

Use of audiovisual and graphics

There are times when the understanding of a mathematical concept by learners becomes difficult. The educator has a responsibility for ensuring the learners understand and are able to apply the mathematical skills in real life. To achieve this, the instructor use chalkboard, charts, projectors, or animations of the concept (Willis, 2010). These tools play a critical role of presentation of visual examples which are easily understandable by the learners.

4: The educators have responsibility impart mathematical skills, knowledge, and understanding to the numerical learner (Siemon, Beswick and Brady, 2015). The learner’s evaluation is important to for the educator to know how effective the learning has been to the learners and also to identify the areas of weaknesses that need more attention. Following areas the assessment areas that the learner is expected to have mastered (Bolton, 2005).

Knowledge of numbers and figures;

A learner has assessed the ability to manipulate numbers and figure in different mathematical problems. They have also tested the application of the numbers and figure in the real-life problems of counting and number manipulation.

Understanding relationships between numbers;

Learners are expected to understand the relationship between number operations, and the way in which they behave. This assessment involves arithmetic only. The leaner is assessed the understanding of behaviors’ of and relationships between the operations. The test areas include algebra as well as arithmetic.

Interpreting mathematical information;

Mathematics is about interpretation, solving, and analysis of information given about a problem. The learner has assessed the ability to read, understand, and interpret the mathematical information provided to come up with an expected solution.

Parents’ Educational Level

Ability to remember;

The ability of the learner to remember mathematical concepts and models is critical for the success in mathematics. The learner is also expected to remember mathematics formulas which they apply in problem-solving.

Visual perception of information;

The math syllabus also includes statistics, graphs, and drawings. The learner is expected to have the visual judgment of mathematical data, graphs, and drawings to derive the meaning. In the assessment, the learner is provided with information, data, or drawings from which he/she is expected to derive the meaning or solution.

Ability to organize information;

Mathematics is a subject of methods and logic of flow. The learner is tested with the ability to think logically while organizing the work in a logical order I deriving solution. Without clear derivation of the solution, the method will not be clear thus losing the mathematical logic behind the problem.

Argumentation and logical thinking;

The ability of the learner’s mathematical explanations of the concepts and derivation of the solution logically are critical in learning mathematics. Mathematics also require logical reasoning of the learner in the interpretation and analysis of complex problems.

Calculation skills;

Basically, mathematics is about calculation and number manipulation. The learner is expected to have mastered calculation skills and ability. In the assessment, the learner is tested with the skills to solve mathematical problems involving calculations.

Language skills;

The learner literacy competency is important in learning mathematics. The learner is expected to describe concepts in math and definitions, for instance in statistics and interpretation of data.

5. There is no single initial and diagnostic assessment that is sufficient on its own as there is a range of methods and approaches. The information obtained from a particular method is evaluated for quality. When the educator is able to know the learners and their preferences, he/she is able to know the appropriate assessment methods (Wallace, 2007).

Learners are supposed to undergo an initial assessment at the course entry. This is the process where the learner learning and support needs are addressed to enable the design of the individual learning plan. The assessment determines the beginning of the learner learning program.

The identified learning needs include the skills, knowledge, and competence the learner is expected to have acquired in the course program. On the other hand, support needs are the assistance the learner requires to go through learning barriers in the course program.

The initial assessment is a critical process at the first stage of the learning cycle as shown by the figure below. Failure to address the learning needs in the initial assessments, the learning plan and program will not address the learner’s needs. Therefore, the training program is unlikely to be of benefit to the learner.

Ethnomathematics

The learner is at the center of the whole system which is driven to identify their needs. The learner needs to actively be engaged at every stage of the learning cycle.

The initial assessment is the first engagement that commences when the educator comes into contact with the learner and continues until the learner learning plan is completed. Throughout this process, the leaning and support needs are also identified in the learning plan. The initial assessment is not confined to a single session but rather it is spread over a number of days to weeks.

To get learning and supports needs of the learner, a wide range of learner information is collected and analyzed. The list below provides information for analysis in the process of initial assessment. The depiction of the list is the interlocking of information form the image of the learner.

1. Career preferences and suitability

The career orientation of the unemployed learner is identified when joining the learning program. This helps the learner to orient their learning to specific learning areas or options. This is depended on qualifications, abilities, interests, subjects, skills, knowledge, etc. Undecided learners after initial assessment are taken to a series of activities that will assist them to decide.

2. Qualifications and achievements

The learner qualification and achievements are tested to measure their ability levels. These indicate the strengths of the learner in areas of mathematics which inform on their career. The information on qualifications is important in identifying the areas of learner weaknesses. For instance, the previous low grades on GCSE math and English may an indication of basic skills that need to be focused on more in the initial assessment.

3. Ability and potential

Previous educational qualification and achievements of some math learners may not be enough reflection of their skills. There are various causes of low abilities and potential ranging from school dropout, missing of classes due to illnesses or disability. Therefore, academic qualifications may not be a true indicator of success in mathematics. The actual ability of the learner needs to be a good assessment to know these weaknesses.

4. Prior learning and experience

This assessment aim at ensuring that the learner does not waste time on the already covered program. This is because the learner may have attended the program earlier and this may slow him/her down. In a math program, the learner may have done some of the units thus for them to cover it again is a waste of time.

5. Basic Skills

It is important to note the learner who needs basic skills and support in learning the math program. The level of their skills should be known to identify specific areas that they need assistance to perform well in mathematics.

6. Learning difficulties

Social-Cultural Norms

This assessment will identify the difficulties which might be obvious or not and which require the prior attention of the educator. When identified, they are addressed in the individual learning plan.

7. Interests

Interest and hobbies of a learner are important in making clear and informed judgment learning choice. This will help the educator to come up with engaging and motivating learning programs suited to learner interests and hobbies.

8. Learning Style

The educator needs to come up with the innovative way of engaging the learner during math learning. Leaners have different preferences in the style of learning including practice, reading, listening etc. Therefore the educator awareness of such needs of the learner, he/she is able to incorporate them for the good of the learner.

9. Personal circumstances

In a class of many leaners, there exist varied circumstances of learner personal problems that the educator needs to be aware of. Such persona problems may include social like homelessness, behavioral, or substance addiction. Other problem may be on medical grounds which need close attention during learning. These and other personal problems need be identified in the initial assessment of the learner so that the educator will plan ahead.

The Information Collected can be used to:

1. Place the learner in the mathematical program which is suitable to their ability
2. Work to towards the learner achievement in mathematics
3. Place the learner in an appropriate position to learn mathematics
4. Be able to support the learner in their learning needs

The learners too have responsibilities after an initial assessment which includes:

1. Have a better understanding of their mathematics options
2. Identify what they need to learn
3. Identify their weaknesses in mathematics
4. They feel valued and motivated to learn mathematics
5. Take part in their learning plan
6. Become responsible for their learning
7. Have a bottom line for their learning process

1. Documents and recordsprovide a basis of learner achievements which include qualifications, achievement records, references, and rewards.
2. Self-assessmentoffers the learner a platform to evaluate their strengths and weaknesses. The task collects the view of the learners about their abilities.
3. Discussions and interviewsis an orientation approach between the learner and the educator. Both get to know each other. The instrument is important for giving previous feedbacks for deeper interviews.

Assessment tools used to set initial objectives and diagnostic assessment of literacy, language, and numeracy (LLN) skills.

The educator uses structured group and individual activities during induction to the program which allows learners to apply their skills. They are provided with an opportunity to write freely on there are of interest. In this case, the learners are at the center of the assessment process by virtue of freedom to write their mind and mathematics interests.

Observation provides a broad view of the learners and their performance in mathematics. This method gives the learner insight into strengths and abilities.

The learner information from the information from the initial and diagnostic assessment process is used for the development of learning goals and objectives. It is also used to derive appropriate teaching, strategies for learning, and resources for use in teaching mathematics. The information is recorded in the learner’s learner plan, session plans, and schemes of work.

For effective use of assessment data:

• Learner’s needs and priorities should be well addressed during planning.
• Time wasting should be avoided.
• Give learners tasks that will motivate them not frustrate them by tasks beyond their thinking.

The assessment data should be used by all staffs supporting the learners. Through this, the learning is differentiated by taking into account the strengths and needs of the learners.

There are varieties of tools for student assessment. The following are the general categories of assessment including Checkpoints, Survey of Knowledge, and Observation.

Government Education Policies

Under this category, the assessment tools are the basis for evaluating the learner’s understanding of the math unit. These tools help the learner to identify their understanding, know the areas of weakness, and assist in decision making concerning the student progress.

i. Homework

The homework assignments assess the learner’s development in concepts and skills. The purpose of homework is to bridge the gap between children’s learning at school and at home.

Advantages

a. Children develop time management and study skills: It tracks the learner's schedule of learning at home.

b. Students can engage in their studies: engage learners more in their studies because the time at school may not be sufficient enough to do some learning tasks.

c. Teachers can keep track of progress: the educator is able to track the learning progress of the learner and also identify areas of weakness.

Disadvantages

a. Use learner free time

b. The learner may feel “burnt out” due to excess homework

c. It is rarely valuable

ii. Reflection

When the learner is assigned mathematical reflection questions, the educator is able to assess the learner’s development of conceptual knowledge and reasoning skills. Reflection is used to review the past of the unit, thus help the learner to remember the past, internalize it and get the bigger picture of the unit.

Advantages

a. Enhance the learner concentration and focus which important qualities

b. The learner is able to think critically, creatively, and also develop meta-cognitive skills

c. The learner is able to develop the action plan to follow in future with the development of skills

d. The learner is able to examine the feeling towards the subject through thinking within the subject and context

e. Reflection is supportive in personal development, creating self-awareness, and analytical skills

Disadvantages

a. Sometimes a lot of time can be wasted in the reflective process and this may eat time for learning in class

iii. Notebook

Other teachers also approach the learner’s assessment by requiring the keeping of organized notebooks for homework, math class note, definition of terms and formulas, and assignment. At the end of each mathematic unit include a checklist of how to organize their notebooks for educator’s feedback. The educator can also assess the learner understanding along with learning the unit by summary examination or notes.

Importance of math notebook

It is important for learners to keep their books organized with classwork. This will allow the learner to be able to organize their work for reviews later. The educator is also able to review the work of the learner regularly to know their mathematical development. The family is also able to do follow-ups on the learner progress in math school.

This category includes the following check-ups, quizzes, unit tests, self-assessments, oral and written presentation, journals and questioning.

These are individual short assessment tools. The questions in this tool are complex and require more skills to solve compared to quizzes and unit tests. Administering this questions to the learners provide a basis for measuring their mathematical understanding of the concepts and skills of the unit. The results from this assessment assist the educator to plan for additional instructions in the unit.

In each unit, the educator provides one partner quiz. These questions are more detailed and complex than checkups questions because they further explain the concepts learned in class. the learner is expected to apply the knowledge from the unit and get insight to the new situations. In making partner quizzes, the following assumptions apply:

• Learner do them in pairs
• The permission to use learning resources to solve the problem
• The educator has the input into the learners’ works

These are tests that are provided at the end of each unit as an individual assessment. The learner’s ability to apply, refine, modify, and extend the math knowledge gained in the unit is tested. The test is skill oriented while others require problem-solving abilities and knowledge of the entire unit. The scoring method and rubric used by the educator take into account the various dimensions of the units in the test.

The learner does self-assessment after every unit the measure their understanding of the unit and identifies areas of weakness. They also provide the examples used in class for a deeper understanding of mathematics. This assessment is used as a self-reflection of the learner. To many this exercise is difficult but it becomes apparent to them after the educator’s feedback.

The unit project can take the concepts of more than three units and is mostly used instead of unit test or to supplement them. The projects are more performance-based compared to other tests. The learners are free to use the learning materials to research on the project independently. The educator can use the learner’s project work to add on their disposition towards mathematics. The learner is guided by the project guide, examples, and scores rubrics from the educator.

The learner’s assessment can be culminated by the classroom activities which use the power of the learner understanding through the presentation of what he/she have learned the unit. The learner uses a combination of visual presentations and written information as may be applicable to the unit in the presentation. Presentations are tools for testing the learner thinking process, reporting ability, and defending of the solutions and recommendations. However, this assessment should not only be used to culminate assessment activities. To the learners, it is required a lot of practice to be able to translate logic and problem-solving processes into written language.

Importance of written assessment

1. The learner is able to demonstrate the level of their knowledge
2. The assessment test on the learner ability to articulate their thinking
3. The learner is able to explain their thinking. In this case, they argue out their points of view.
4. It takes less time to make learner assessment
5. The educator can provide the feedback to the learner

However, a written assessment can cause learner stress and anxiety. This may cause low concentration and memory during the exam. It is also argued that a written assessment is not an affair way of testing the learner’s knowledge. Nevertheless, the written assessment remains the main tool of learner assessment in mathematics.

The mathematics syllabus provides the educator with the opportunity to assess the learner understanding by observing of group works and class discussions. The educator has chances to observe the learner when he/she is doing math exercises in the classroom where the learner is exhibiting the knowledge, math disposition, and working habits. The observation assessment of learners is important in that some learners are able to express their understanding verbally than in formal written assignments.

Importance of observation

1. The learners are in their own natural state and their reaction is genuine.
2. A greater behavior can be expressed by the learner
3. The learners can reveal a lot especially if not aware of what the educator is about

The educators have a wide range of resources at their dispensation to use in facilitating the learning of mathematics. To achieve the teaching of objectives the following resources are used interactively:

1. Projectors for display of the visual presentation

The educator can use projectors to give visual presentations of mathematical concepts. This visual aid helps the educator in explain complex concepts which otherwise would have been difficult to explain using other resources like a chalkboard.

1. More efficient note-taking

Learners may be unable to concentrate by just listening to the lectures and note-taking. Use of projectors to present mathematical models during lectures offers a more interactive way of engaging the learners and able to have a broader view of the lecture while note-taking.

2. Presentations keep learners engaged

The learner plays an interactive role with projections on the wall than just lectures. They are easily engaged in the lecture than an oral presentation. Learners are easily taking part in the presentation thus increasing their understanding of mathematics.

3. Interactive projectors also make it easier to teach dynamically:

The learners are able to ask the questions in the process of the lecture. It allows freezing and unfreezing of the lecture during the presentation. The increase in interaction between the lecture, educator, and learner makes the class lively and the understanding of the learner is increased.

1. The projector is bulky when compared to a chalkboard
2. When compared to the chalkboard, the projector is expensive
3. Projector requires a power supply to function compare to chalkboard which does not need any power to function

These are the books certified by the curriculum development for use in learners’ training. The mathematics course books are used by the educator and learners in the classroom.

Advantages of course books

1. Important in guiding the learner through the syllabus
2. Learners have the security of the sense of direction of what it is expected of them
3. The books provide the educator with a guide for lectures such as visuals, activities, and reading which saves time.
4. Include learners testing base and evaluations for learners

Disadvantages of course books

1. The course book may not suit a particular class because of culture, language or nationality.
2. Because of specific pattern and predictability of most coursebooks, they become boring to the learners in they are too strict
3. The course book make educators become less creative when teaching because they tend to use ideas of the book

3. Reference books

These are additional books besides the core textbooks used in the coursework. The educator gives recommendations of the books the learner may use to supplement their math learning.

1. Provide additional knowledge to the learners besides what is provided in the course book.
2. Provide more evaluation and test to learners
3. The reference books are student partners in revising the class work

1. Some reference materials might be misreading with the wrong information as some may not have been approved by the relevant authorities
2. Learners may concentrate more on references than the course book thus they end up missing  critical course information
3. They are not comprehensive in the content

Inquiry teaching

The educator provides the learner with content-related problems which they use as foci to do math research. In other words, the educator gives the learners a problem in which they identify the problem.

The process of inquiry teaching

• presentation of situation
• encourage observation to get a statement of the research objective
• request learners to explain their observations
• encourage test of the hypothesis
• come up with generalization
• debrief the process

Advantages

1. natures the passion and the talent of the learner
2. make learner curious and become engaged in learning
3. the learners are able to ask questions
4. foster a deeper understanding of the mathematical concepts

Disadvantages

Demonstration approach

The educator engages in a learning task other than just teaching to the learners. This teaching approach uses the following method:

• Explanation

The educator explains the mathematical concepts to be learned to the learners.

• Demonstration

The educator engages in the task by doing it while the learner observes.

• Student performance

After the educator demonstration, the learners take a turn to do the task on their own.

• Instructor supervision

The instructor observes the learner as they do the task and make clarifications where necessary

• Evaluation

The instructor gives the feedback after the learners have completed the tasks

Discovery approach

The learner and the educator play active roles in discovery learning. Depending on the role the educator takes, it can range from guided discovery to free discovery.

The steps involved in lesson planning

1. statement of the problem
2. previous knowledge
3. concept to be developed
4. specific objectives
5. teaching aids
6. presentation
7. investigative activities of the learner
8. observation table made by the learners
9. generalization
10. open questions
11. teacher activity

Math-lab approach

The learners are grouped for the assigned task. Then from the groups, they approach the problem, learn, and discover the mathematics all by themselves.

Practical work approach

This approach provides the learner with an opportunity to manipulate concrete objects or activities which aid in understanding the mathematical concept. They can use any environment as the laboratory to carry out their investigation.

Problem-solving

Problem-solving can be explained as a learner-directed strategy in which learners “think patiently and analytically about complex situations in order to find answers to questions”.

8. Technology integration into education today has made a huge impact on the learners’ understanding of mathematical concepts, motivation, and change of attitude. According to Özdaml?, Hürsen and Özçinar (2009) technology have improved the academic performance of learners. This is because technology has the learning capabilities of learners by making them become more engaged in the learning process. Other researchers Carlsen and Willis (2007) stated that “Technology provides an excellent avenue for student motivation, exploration, and instruction”

Today, the world of education is changing by more and more people being absorbed into the modern technology. Thus schools today are adapting to this evolution and have started to integrate technology in the classrooms. Technology in the classroom is a priority as it is more engaging to the learners than ever before with traditional methods of lecturing.

Technology applications in the classroom and for lectures provide a way of convenience and ease in education for both learners and educators. For this and the following reasons, will show why the technology is needed in classrooms.

1. Use of mobile devices like tablets and their applications have enabled digital learning which increases the contact between the learner and the instructor.
2. Through the integration of various technologies and lectures, the learners are connected to different learning styles and they are able to adapt to any that suit them well.
3. Technology integration into classrooms has encouraged interaction between the educator and learners themselves. This culture of interaction builds cohesion and a better learning environment.
4. In the contemporary world and education, use of technology has increased in most aspects of life, especially social life. Most young people have become tech-savvy and use of technology in their learning will do them good in understanding mathematics
5. The technologies combined with traditional ways of lecturing create a better experience for learners and thus enhance their mathematics understanding.

However, technology comes with its disadvantages to users of technology especially learners. Below are the detriments of the technology integration in technology.

1. Use of internet in classroom exposes learners to inappropriate contents. Student finds it easy to access pornographic content and violence.
2. It creates disconnected youths: long attachments to computers has caused social disconnects, especially among the youths.
3. When it comes to testing the learners, with increased use of technology cheating in exams has become rampant among the students.

Importance of using technology in teaching mathematics

• Technology offers an interactive platform for learners. This has enabled fast feedback on the solution to the mathematical problems, testing of hypothesis, links between formulas and graphical interpretation.
• Enables the presentation of mathematical graphics which are attractive and colorful to the learners. These graphical and animations, aids in understanding various concepts in math.
• The technology dynamics like large memories and speed has enabled high-level computations which include statistical data. The speed has made it possible to produce results faster.

9. Numeracy is about numbers and calculations. Numeracy learners become numerate to develop confidence, willingness, and ability to apply the skills and knowledge across the contexts and various subjects.

The applicability of mathematical skills and knowledge in science cannot be underestimated. The learner needs to do scientific inquiries and communications using mathematic models and formulas. In this instance, the learners apply the skills when they:

• Gather data from various sources through observations and measurements
• Graphically, in terms of tables, and calculations process data
• Identify data patterns and trends
• Calculate numbers and carry out values predictions
• Make a judgment on various scientific data
• Evaluate convenience and reliability of data information

In the field of chemistry, astrology, and physics learners are expected to interpret and arithmetic skills and interpretation of charts and graphs. Learners use geometry, algebra, and calculus to solve chemistry problems, explore the planets and analyze scientific phenomena.

Mastering mathematics comes with benefits of understanding poetry. The poetry learner applies math in identifying the meter of poetry, the word counts in the lines, and the rhyme of the poem. Mathematics can also be applied in a more mundane way by helping the learner plan for the assignment in literature classes. The skills of logical thinking and linear skills help the learner to write clear literature and logically.

The social sciences such as history and geography require review of graphs and charts of various phenomenon. In history the learner review historical charts and graphs for maybe population statistics and populations. In geography, the learner is expected to appreciate the reading and interpretation of the various geographical areas and data which include population, pictures, graphs, and charts. The basic math competence is an important analysis and interpretation of statistical information.

10. To the mathematics learners, they have to realize that, it is a methodical application of matter. The reason being that math makes learners methodical in their personal life development. In this respect, mathematics gives the power of reason, creativity, abstract thinking, critical thinking, problem-solving ability, good communication skills. I everyday life, mathematics is applicable in all walks of life and without it, things will not be the way they are today. It is applied in farming, cooking, carpenter, mechanics, music and other complex activities like engineering.

Experience has shown that learning mathematics makes doing some things enjoyable like playing games and other mathematical activities. The quizzes involving mathematics like puzzles and riddles are entertaining to the open-minded learners and these help learners develop logical reasoning.

Mathematics has facilitated largely in the development of innovations. The more a learner is competent in mathematics, the higher the success in coming up with creative ideas. The rationality that is created by mathematics, help the learner to think beyond the obvious.  Therefore, learners are encouraged to embrace learning mathematics to realize and appreciate the beauty in it.

1. Mathematics is present in everyday life experiences from going to the bank, building, to cooking and cleaning
2. Learning mathematics conditions the learner’s brain to think and analyze problems more effectively
3. Besides technical elements of mathematics, learners are taught methods of reasoning and how to approach them critically. These analytic skills are important way beyond the mathematics into life

11. Codes of ethics

These are set standards for childcare services by the childcare specialists. The professionals are expected to adhere to these set standards as stipulated by Code of practice. These codes are based on general principles of good professionalism (Thompson, Melia and Boyd, 2000). Below are the explanations of various ethical principles of childcare as outlined in childcare code of conduct (Manual of concrete practice, 2016, n.d.).

Every professional childcare has the responsibility to:

1. See a child as an individual with rights and thus need respect and to be valued.
2. Show respect to the child relationship with his/her family and friends, considering other interdependent rights and responsibilities.
3. Contribute to the growth and development of the child to his/her potential in all aspects of life.
4. Offering protection to the extent of your ability including care and rehabilitation to resolve any problem he/she is in.
5. Respect the privacy of the child by maintaining reasonable confidentiality.
6. Avoid discrimination, oppression, and exploitation of any types at all times and uphold equal rights.
7. Show the highest level of integrity, competency, and knowledge. You should also work well with others, contribute to child monitoring and development.

The following are the groups to which the specialist owe a duty of responsibility to:

• Self
• Children
• Colleagues
• Employers
• Profession
• Society

Responsibility for self

As a childcare specialist, you have responsibilities concerning yourself.

• Have skills, knowledge, and experience
• Undertake education programmes and training
• Take part in career appraisals

• Observe professional standards
• Be committed to quality services
• Not to have biased judgment
• Have a good attitude and personal appearance
• Well-behaved
• Maintain required boundaries between personal and professional relationships
• Apply due diligence when taking responsibilities
• Consult where necessary

• Being self-aware
• Observe personal growth and development
• Being mental and physical well-being
• Being optimistic in service provision
• Avoid abuse of substances

Responsibility for Children

• Advocate and respect the right of the child
• Involve the child in decision making affecting them
• Foster self-discrimination in service
• Respect the privacy of children
• Maintain confidence during interaction with the child

• Promote positive relationship and empowering relationships
• Support development of the child
• Design program with a prior understanding of individual circumstances and needs
• Assess the need of the child
• Maintain safety and health of the child

• Services should understand these boundaries
• Maintain an appropriate professional distance
• Maintain good relationship
• Avoid non-work relationships
• Use appropriate language

• Practices that may be disrespectful, degrading, and humiliating to the child
• Negligence and abuse of children
• Report incidences that harm the child
• Bad child behaviors
• Discriminatory practices
• Divulging secret information about the child

Responsibility to Colleagues

• Good relationships with trusts
• Respect others and be fair
• Recognize other people achievements
• Respect other peoples beliefs, values, and culture
• Be an active team member
• Observe confidentiality of other workers

Responsibility to Employers

• Honor the contract
• Contribute to the attainment of the objectives
• Offer quality service
• Be loyal to the service
• Contribute to the growth of the service agency

12. Albert Einstein had dyslexia and by implication most people think that learner with dyslexia are brilliant. On the opposite, it is not. A research has established that 40-50% of students with dyslexia show no sign of dyscalculia, with about 10% excelling in math. The rest 50-60% have difficulties in learning math. Many of these learners have math language problem but not the math concept. The following are the problems that the educator needs to deal with when teaching mathematics:

1. Dyslexia:
2. Dyscalculia
3. Autism:

The areas of maths that students with dyslexia find most difficult are:

• The language of maths.Some students struggle to read and understand the vocabulary in maths questions, and therefore don’t know what task they are being asked to do.  Many different words can be used to describe the same action, e.g. add, increase, plus, total.
• The learning of maths is very sequential, but to successfully complete many maths problems a very strict sequence must be followed. Learning times tables are all about learning a strict sequence of information.
• Orientation.  Difficulties with orientation and direction can lead to confusion of maths symbols. Some people with dyslexia show weakness in the Coding subtest in the assessment meaning that they struggle to decode symbols accurately and quickly.
• Memory. There are many facts, figures, tables and formulas which have to be learned and recalled accurately.
• A lack of confidence in their own maths ability can exacerbate the above difficulties.

It is important that teachers, and parents, understand how dyslexia can affect the progress of a student in maths and that there are strategies that have been successfully used in teaching maths to students with dyslexia:

• Multi-sensory teaching using concrete objects will help to establish abstract mathematical concepts.
• Students may need specific instruction to help them understand the language and symbols used in maths.
• Appropriate aids such as number squares and calculators should be available, and students should be taught how to use them.
• Computer programmes can be useful to help consolidate learning.

13. According to Forgasz, Leder, and Hall (2017), numeracy should be taken just like literacy skills where it should be integrated into every area of learning. Therefore, there need to come up with strategies to include numeracy in vocational training and other subject areas. To achieve this, professional from different numeracy and literacy backgrounds have to come together and think of how to integrate mathematics into various subjects in schools.

How to liaise with other professionals

• Opinion gathering on the issues

Professionals can provide their opinion which can be considered as a recommendation in developing curriculum for various subjects. These professionals input will show how the inclusion of numeracy in vocational training and other subject areas is important in developing the learner’s logical skills and problem-solving skills. It has been argued that mathematics is as important as life skills as learners develop mental strength which is important in multiple applications in life.

• Identifying fields that need inclusion of numeracy teaching

It is of paramount importance to be specific as to the vocational and subject areas that we need numeracy inclusion. Through this approach, advocacy and prove of logic for inclusion is easier and understandable. This will also help in developing an integrative curriculum for that particular subject incorporating numeracy.

• Working on a curriculum development and integration project together

As numeracy professional and teachers, working for a projecting aiming to promote inclusion of numeracy invocation and other subjects is a good idea. This can be a research or a journal detailing the need and importance for numeracy in various subject areas. Through this project, each professional will have his/her input on various grounds for learning numeracy in vocational training and other subjects. The research may also use scientific research findings and analysis of data to get an informed conclusion.

• Work with vocational trainers and other stakeholders towards the inclusion of numeracy in vocational training

To achieve the goal of inclusion of numeracy in vocational training, working with the stakeholders is virtually inevitable. The input of vocational trainers and teachers is important for more insight on the need for inclusion of numeracy skills in the vocational curriculum. Their opinions also add value to the professional advocacy for such inclusion.

• Pooling up a professional petition to the curriculum development agency for consideration together with professional opinion and recommendations input.

14. Additional diverse skills and knowledge are needed by the childcare specialists. These additional skills will help in exploring other fields of childcare and learning. Therefore, to liaise with professionals become apparently important in promoting wider skills. As a childcare professional, I have a responsibility to make professional networks in my field of specialization for purposes of career development and growth. From these networks more skills to include in the childcare profession maybe hatched.

How to liaise with childcare professional for the inclusion of wider skills

• Work on a project on the skills for inclusion

Childcare professionals can work on a project to develop skills for inclusion in childcare education. The skills developed will contribute to the development of the curriculum which will continue to make it wider and richer in knowledge.

• Requesting for their input in the skills am developing for inclusion in childcare

As a professional childcare specialist, there are skills which I may explore in my line of work which is included in the childcare learning curriculum will promote the program further. But to promote the inclusion of wider skills in childcare need support from other field professionals. Their inputs in the proposed skills help refine the skills to be more relevant and important in the field. To reach out to professionals, the manuscripts are given for some professional for review and opinions.

• Making a consultation with other professionals

When professionals come together, their opinion can be taken into consideration as a recommendation for developing the skills in childcare.

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