### Theoretical Framework

The research will be underpinned by a range of theories and perspectives (based on cognitive psychology). The literature has shown that students have math anxiety usually because of an unfounded fear of math, which creates demotivation (Geist, 2015; Ramirez et al., 2013). Areas such as self efficacy, intrinsic and extrinsic motivation, expectancy theory and locus of control will be considered as the framework for this proposal.

The nature of motivation is such that it explains why one starts an activity, the direction one takes to accomplish the task, why one tries so hard at it, and how one persists in the activity. When one is learning in a classroom setting, Byrnes (2001) suggests that there are three goal structures that motivate a student to learn – individualistic, competitive, and cooperative. Thus, students set an individual goal in order to produce something for themselves, such as an A grade. They consider doing better than others in their class, and when working together, they want their groups to succeed. Transmuting this to students and math, one can say that individually, a student may want to be the best they can in order to impress others with their knowledge or they might have an individual goal in mind, such as to be first in class. Competitively, the teacher may encourage competition in class and the student may want to participate at the school level or national level in math olympiads. This motivates them to challenge themselves and develop proficiency in the area.

This speaks to intrinsic and extrinsic motivation, since student may be intrinsically motivated to do well for their overall grade and may also be extrinsically motivated to receive praise and gain rewards. If teachers can see what and how a student is motivated, then they can use this in all of the subjects being taught to the student, such as mathematics. Ryan and Deci (2000) believe that if a student is intrinsically motivated, it is easy to make them extrinsically motivated and thus this can be used to create competition and social comparison. As Droe (2013) suggests, effort should be praised in order to encourage learning goals rather than praising talent as this only encourages performance goals, hence, students who try hard at math should receive further encouragement.

The expectancy-value theory says that behavior is a function of the expectancies one has and the value of the goal one is working towards (Wigfield, 1994). Thus, the characteristics of students must be considered by educators so math can be taught in a way that is appropriate for the students’ levels of concentration, awareness, and self-control, in order to keep them motivated (Burak, 2014).

It then portends that a student’s locus of control must be examined if they are to be motivated by teachers. One’s internal locus of control suggests a person who believes they can direct their own lives while those with an external locus of control believe they are controlled by outside forces (Fournier, 2010). Tella, Tella, and Adeniyi (2011) found that the better a student achieved in one subject, the less they are able to settle for mediocre results in others and therefore, would attempt to enhance their performance in all subjects. So, developing the internal locus of control in students can lead to higher functioning learners. They found that students with an internal locus of control use more effort in their academics and thus perform better than their counterparts. A students’ self-efficacy, means they feel they have the tools and abilities to follow procedures that will ultimately produce the desired outcome. This then means if students believe they can do something, they are motivated to first try and progress to the end.

### Significance of research

The purpose and overall aim of this research is to consider the benefits a positive result would have on the teaching of math and the results for students.

### Literature Review

Technology has been used in mathematics for millennia evidenced by the abacus, which was first invented by the Chinese in 500BC to help with counting (Samoly, 2012). Today however, with the advancement of technology, educators have gone further by seeking to integrate current technology in the classroom to help with math. Traditionally, it seems that most students dread mathematics as a subject and some struggle with it seriously (Andrews & Brown, 2015; Lyons & Beilock, 2012), having preconceived ideas that it will be difficult and impossible to do.

Vahedi, Farrokhi, and Bevrani (2011) defined math anxiety as the negative associations, evasion behaviors, and experiencing feelings of inadequacy and pressure when required to use math in school and real life. In an article called Overcoming Math Anxiety (2007), it was discussed that anxiety about math may not actually have to do with aptitude at all but rather involved the lack of role models, and the notion that women and minorities were bad at math. Thus, it was considered a social problem. The article was supported by Geist (2015) and Ramirez, Gunderson, Levine and Beilock (2013), who also found that math anxiety, which started as early as age 7 or 8, was compounded by a lack of verbal skills for understanding math problems as well as a lack of teacher confidence in his/her math ability.

Undertaking math problems, according to Lyons and Beilock (2012), was discovered to be akin to a neural pain response and therefore was a subject to be avoided. This however, has future implications as math- and science-based careers are then avoided, leaving gaps in the economic structure (Andrews & Brown, 2015).

By considering whether technology through blended learning would assist students in increasing their ability to do math, the authors of this proposal hope to find a way forward in decreasing or eradicating anxiety and making mathematics a subject like any other, whereby students will be motivated to solve math problems and improve their self-concept through the integration of blended learning.

There is extensive research on the benefits of blended learning for students since the 1990s. In the 21st century, blended learning means the integration of the face-to-face classroom with online or e-learning (Saliba, Rankine & Cortez, 2013; Poon, 2013), so that students can be flexible in their approach to learning (Chase, 2015).

One benefit is that of improved learning outcomes. Lim and Morris (2009), López-Pérez, Pérez-López and Rodríguez-Ariza (2011) and Poon (2013) all found that by offering the option of a blended approach into a traditional learning environment, students were able to achieve higher scores than their colleagues in traditional enrollment. Lim and Morris (2009) discovered their participants were able to achieve higher grades through more motivation and involvement, while López-Pérez et al. (2011) saw a decrease in dropout rates and improvements in exam marks. Francis and Shannon (2013), Larson and Chung-Hsien (2009), and Poon (2013) found the same, in that students were able to study at their own pace and thus, were able to self-regulate learning, which increased their achievement. Yasar Kazu and Demirkol (2014) studied students doing a Biology course in 12th grade (17 and 18 year olds) in two groups similar to this proposals research design and students in the blended learning environment were more academically successful than their colleagues in the traditional environment. They also improved their post-test scores.

Literature tells us that blended learning can be cost effective also. In one study, traditional instructor-led training was twice the cost of its blended delivery (Lothridge, Fox, & Fynan, 2013), and Maloney, Nicklen, Rivers, Foo, Ying Ying, Reeves, Walsh, and Ilic (2015) and Aasen (2013) found that blended learning had a lower cost because of already established methods through which learning could occur, such as YouTube and Schoology.

Blended learning was also seen to be more flexible and less stressful, which increased student satisfaction (López-Pérez et al., 2011; Montrieux, Vangestel, Raes, Matthys, & Schellens, 2015). Web based lectures were evaluated more positively for achieving better results and for independent learning, even with those students with poor backgrounds and low self-efficacy. These students however, had an internal locus of control and so were able to use the lectures as reinforcement of what was done in class. El-Khalili and El-Ghalayini (2015) discovered the same as they considered achievement and satisfaction, finding that students found a blended approach more suited to the development of higher order thinking skills. One concern though was about low-achievers, who may not have had the study skills to use the blended approach productively (Montrieux et al., 2015).

As several researchers have established, the benefits of blended learning can be summarized by looking at what students think about the process – blended learning, inclusive of online learning has more advantages than traditional learning (Larson & Chung-Hsien, 2009; El-Khalili & El-Ghalayini, 2015; Montrieux et al., 2015).

The future of blended learning is obviously one that needs further research and the literature suggests two approaches could be addressed. Lim and Morris (2009) suggest investigating macro issues such as the blending mix for different delivery methods, and assessing individual learner characteristics to improve motivation. Estelami (2012) believes educational technologists need to consider the type of course being made blended, as some are more effective when the student-lecturer interaction is maintained. All the literature however, suggests blended learning is effective as a learning mode.

### Summary of literature

The literature informed the project by using research to galvanize the relationship between blended learning and scores in different subjects. The body of research claims blended learning is beneficial to learners and thus should encourage further investigation.

### Methodology

### Research Design

The blended learning experience will be formulated using the ‘math program’ of the Tranquility Government Secondary School. To carry out this study, the students will be divided into two groups—one group will take part in online subject-related activities and the second group of students will not. The second group is referred to as the control group. The sample size for each group will be 30 and to strengthen internal validity they will be randomly chosen from both of the Form 4 classes. The teaching methodology will consist of a combination of face to face classes together with 35 activities designed to reinforce the concepts being learnt in the classroom, and based on the Schoology platform. A website will be created for students to complete the activities and will be entirely voluntary. The website will contain two types of activities.

Firstly, to help students better understand the key ideas, individual activities will consist of fill-in-the-blank, multiple-choice quizzes, crosswords and related words. Secondly, there will be activities to encourage participation and cooperation (for example whatsapp and wikis). The teachers will coordinate the discussion forums and encourage students to create and constructively critique their peers’ contribution. The web activities will be designed as study tools and there will be immediate constructive feedback on why a response was incorrect. Teachers will receive immediate feedback on which areas of the program students need help with and will reinforce these areas in class.

1. Participants

The participants would come from two form four classes namely group a and group b attending the Tranquillity Government Secondary School Port of Spain Trinidad and Tobago. Group a would be the experimental group and group b would be the control group. Each group would comprise of 30 participants. The mean age of the participants would be 15 years.

2. Procedure and Measures

Sampling method Instrumentation

Instrument 1

The same math test (pre-test) will be given to the two sets of students.

Instrument 2

The same math test (post test) will be given at the end of the semester to the students from both groups.

Instrument 3

SPSS will be used to analyse the data. Or the Excel tool pack will be used to analyse the data collected. A within T-test will be done to determine whether the difference between the pretest and posttest is significant. A between T-test for the post test between both groups will also be considered.

Data Collection

Both test results will be collected from the teachers and then by the researchers.

Analysis: Use of statistics 1. Descriptive statistics Descriptive statistics will be used to summarize information about the sample. Calculation of the mean, median, mode, range and the standard deviation will be done. The average mark from both groups will be compared but more than that the standard deviation will be a more accurate measure of spread for comparing both groups since, although the average may be the same, one may show more variation.

2. Inferential statistics

T-test Inferential statistics will include a within – group t-test or independent samples t-test would be used to compare the results of the math scores for both groups. The advantage of using this test is that it can be used for small groups. In this case n=60. This has to be further divided into two groups, namely the experimental group and the control group. Another advantage is that it works well with two means–so they are good for ratio data, and the like. It shows easily whether they have significant differences. Two major assumptions of this test are that, firstly, both groups are sampled from populations with the same variance – “homogeneity of variance” and secondly, both groups are sampled from normal populations – assumption of normality, although this can be frequently violated with little harm. It is applied to a relatively small number of cases and was specifically designed to evaluate statistical differences for samples of 30 or less. The z-test would be capable of testing where n > 30.

Protection of human rights

Clearance for access to the school will be sought from the school principal and a letter from UTT would be required. From an ethical standpoint it should be noted that only data will be gathered and that no student’s name will appear anywhere in the document. All students are volunteers and can refuse to proceed even after they have started the process.

Expected results and discussion

It is expected that the students who partake in the research would have a higher average math score than was previously obtained and also a higher percentage increase than the control group. Also the T-test should show a statistically significant difference between pretest and posttest for individual scores. If these expected outcomes are achieved then, perhaps, longitudinal research can be done where an entry math test can be given to all students. The results of the study may have serious implications for the future of education in Trinidad and Tobago. For example, pilot testing may be done in schools struggling with math and based on the results policy may be enacted to roll out blended learning nationwide. Furthermore the research may be done with other subjects as well thereby increasing the academic status of the country. One way of ensuring internal validity will be to make sure that the syllabi are identical for both classes and that the tests given are similar. In terms of ensuring external validity a challenge would be the difficulty in measuring the effect additional math lessons would have on the overall outcome of the results. Perhaps future research could look at what is the best age to begin integrating technology such as blended learning into the classroom which may then guide educational policy.

A positive school-wide result could make a strong case to encourage blended integration in all schools. Part of the educational budget can then be used for testing out other types of technology integration.

Instructional design considerations

There is software already on the market to help students with math, such as Smart Tutor educational programs and Learning RX. The use of these online sources have improved math when used as a supplement to classroom learning, as students are able to go back to material they did not quite understand (Osmanoglu, Koc, & Isiksal, 2013). Suppes, Holland, Hu, and Vu (2013) found in their study that the hypothesis that a computer-based math course would increase the scores of their student participants was supported, when used as a companion to traditional classroom based learning. They saw that immediate feedback and reinforcement, concrete assistance from the software, and an individualized program of learning was viewed as positive by both students and teachers and hence, encouraged the policy that blended learning be incorporated into the math syllabus in the curriculum.

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