The study adopted a pretest-posttest, non-equivalent control group in a quasi-experimental setting.

The research design is symbolically illustrated below:

Figure 1 : Pretest—Posttest control group research design.

O₂ X₁O₂ (E)

O₃ X₂ O₄ (C)Where X₁ represents BBLS (treatment).

X₂ represents CST treatment

O₁O₃ = Pre-test measures

O₂ O₄ = Post-test measures

The target Population was all Senior Secondary School Two (SS II) Students in Oyo State, Nigeria.

Using simple random sampling technique, one school was chosen from eight randomly selected local government areas to make a total of eight schools. 30 Senior Secondary School Two (SS II) students were randomly selected from each of the schools to make a total of two hundred and forty (240) students for the study.

Three instruments were used for data collection:

1) Achievement Test in Mathematics (ATM);

2) Cognitive Style Test (CST);

3) Mathematics Attitude Questionnaire (MAQ);

The test items covered the three levels of cognitive domain of remembering, understanding and thinking as shown in Table 1 .

Note: The figures under Remembering, Understanding and Thinking are numbers of items.

The ATM was validated based on the contents of topics incorporated into the instructional design to see how the research instruments covered a representative sample of the content.

The CST is a reasoning test for measuring how students choose and analyse set of pictures of common objects, animals, plants or artifacts for the purpose of classifying them. The modification and revalidation were done by Onyejiaku, F. O. (1980) to reflect Nigerian environment. There is paucity of interaction effect of cognitive style studies, brain-based learning strategy and related fields. Bouiri, O. et al. (2021) & Abdelhadi et al. (2019) point out that cognitive style studies in engineering education are scare and seem to focus on the student’s cognitive level, congitive operation personality traits, mental skills and learning styles. Bouri et al. (2021) opine that the cognitive style test also known as thinking styles assessment or learning styles tests helps to understand your preferred cognitive processing styles. It can guide personal learning strategies, enhance cognitive skills, and improve communication and collaboration in a team setting. The language students use in categorizing these phenomena presumably reflects their style of categorization. The statements made by the students regarding the way he/she perceives the pictures and classifies any two together could be categorized into three thus:

a) Analytic Descriptive (AD)—Students here place objects together based on their shared or common characteristics which are directly discernible. Example, in a card containing a man, a bed and a chair, students here placed together bed and chair because “they are made of wood.”

b) Categorical Inferential (CI)—Students here place together objects on the basis of super-ordinate features which are not directly discernible (abstract) but are inferred. Example, students here will place a bed and chair together because “they are for relaxation”.

c) Relational Contextual (RC)—Students here place together objects on the basis of feature establishing a relational link between them. Example, students here will place together “the man and the bed” or “the man and the chair” on the ground that, “the man can sit on the chair” or “sleep on the bed.” This is in line with the findings of Pinna and Deiana (2018) and Wang and Guan (2022) which showed that coloured words may enhance performances. Although colourful numbers may induce more cognitive load for participants, there are different colours to process and hence may enhance performance of cognition. By implication, this number presentation strategy shows that although it adds colour information unrelated to mathematical computation, it may help learners focus on the information required for answering. In effect, categorizing students into Analytic cognitive style and non-analytic could empower the teacher to design suitable instructional materials for the two categories of the cognitive style (analytic and non-analytic) towards enhancing optimal learning in the subject.

In this study, analytic style students were those who scored above the median in AD and CI responses and below the median in RC responses. Non-analytic style students were those who scored above the median in RC responses and below the median in AD and CI responses.

Onyejiaku (1980) estimates the reliability estimates of items in the CST to range from 0.62 to 0.72. Onafowokan (1998) also trial-tested the CST using 137 Junior Secondary III students in four secondary schools in Nigeria. The trial-test results showed no ambiguities in the instrument.

This is an instrument of twenty items that elicits information from the participants on their attitude towards mathematics. The instrument is made up of two sections: A and B. Section A is designed to elicit responses in relation to student’s name, age, gender, class and name of school. Section B is made up of twenty items (ten positive and ten negative statements), requesting participants to indicate their attitude towards the study of Mathematics based on a four-point Likert scale. Each participant was requested to tick an appropriate option weighted as follows:

Strongly Agreed (SA) -4

Agreed (A) -3

Disagreed (D) -2

Strongly Disagreed (SD)-1

This rating was meant to reflect how the participants felt about the particular statement.

The Brain-based Instructional Materials in Mathematics ( Olaoluwa, 2009 ) are developed based on the findings of the following researchers, Jensen (1998) , Nunley (2004) . Their findings show greatest gain in achievement and attitude with the manipulative materials (right hemispheric) while the textbook approach (left hemispheric) resulted in the least gains. Sweller (2020) defines Cognitive load theory in the classroom as the application of an instructional theory that is based on human cognitive learning functions. Cognitive Load Theory (CLT) is an instructional design theory that reflects our “Cognitive architecture” or the way that we process information. During learning, information must be held in your working memory until it has been processed sufficiently to pass into your long-term memory. These materials are designed in consonance with cognitive load theory

1) NKPM—Needful knowledge package in Mathematics;

2) SKACM—Students’ Knowledge Acquisition Card in Mathematics;

3) WLTM—Weekly Learning Terrain in Mathematics;

4) ISCP—Index Card Study profile in Mathematics;

5) SECM—Self-Evaluation Card in Mathematics;

1) “NKPM” (Needful Knowledge Package in Mathematics): The brain is pattern seeking. When new information enters the brain, it searches for familiar pattern and prior knowledge. Once it is located, the information makes an attachment to a neuron that creates an electrical spark, called a synopsis to another neuron. It is from the synoptic connection that dendrites, the brain’s road map of knowledge are grown. “NKPM” is designed to enable students make meaningful connections and consolidate the gaps between the prior knowledge and new information. Copies of the “Needful Knowledge Package in Mathematics” for the current topic or mathematical concept are distributed to the learners to glance through within a few minutes.

2) “SKACM”: (Students’ Knowledge Acquisition Card in Mathematics) is designed to capture and retain students’ attention to a greater extent throughout the learning episode. It is given to the students before the commencement of the lesson. The students are instructed to write the “summary” of important facts they are able to acquire from the lesson. This is done twice before the end of the lesson: The teacher instructs the students to complete part of the “SKACM” during the “brain-downshifting” period of the whole learning episode. The latter part is completed at the end of the lesson.

3) “WLTM”: (Weekly Learning Terrain in Mathematics) is designed to engage the students in active processing. The teacher engages the learner in active processing by guiding the learner to gain insight into the problem. The learner needs to use three skills—order, structure and relate to the new information (at his own pace) to process new information and create mental pattern as favoured by the structure and functions of the brain. The learner needs to order, structure and relate to the new information. Copies of the “Weekly Learning Terrain” in Mathematics are displayed at strategic places in the classroom and on the Mathematics Bulletin Board for students to interact with.

4) “ICSPM”: (Index Card Study Profile in Mathematics) is designed to cater for all the categories of learners, viz. fast learners, slow learners and other prominent individual differences that may exist among the students. Copies of “Index Card Study Profile in Mathematics” that are relevant to the present or current topic which is about to be taught should be made available in a shelf in the classroom. These cards contain key facts, mathematical concepts and definition of terms relating to the current topic. Students will be instructed to go at will to the shelf and explore from the enriched learning environments created within the four walls of the classroom.

5) “SEC”/“Q & S”: (Self-Evaluation Card/Questions & Solution Card). This is designed for spot assessment. The teacher is expected to release the feedback before the commencement of the subsequent lesson. The outcome of the “Q/S” or Students’ performance determines whether the teacher needs to maintain the status quo in the use of his strategies or mandatory to improve upon his strategies towards the actualization of an improved learning outcomes in the subsequent lesson. “SEC” cards containing questions and solution space are expected to be given to the students at the appropriate time. All cards in “Q” portray questions that are drawn from Mathematics concepts or topic (s) to be taught. All Cards in “S” portray detail (step-by-step) solution (s) to the questions in “QS”.

The BCIM were given to two Mathematics experts and one Educational Technology expert in the Department of Science, Mathematics and Technology, University of Ibadan, Ibadan Nigeria for face and content validation in terms of language clarity to the target audience, content coverage, and relevance to the stated objectives.

The teacher does his teaching with optimum utilization of the “Prime Times” in mind. The brain learns best at the beginning and at the end of a learning episode—“Primary-Recency Effect” or focused, diffused and focused times in a learning episode. In a 40-minute period, students’ attention is strongest for the first 20 minutes, then the brain needs “down time” for approximately 10 minutes (Brain’s downshifting is like a camera that has a reduced focus). The next ten minutes is the next best teaching time (closure).

Data collected were analyzed using Descriptive Statistics of means scores, standard deviation and Analysis of Covariance (ANCOVA) with the pre-test scores as covariates. Initially, students in both the experimental and control groups were pre-tested on the Achievement Test in Mathematics. Statistical analyses showed no significant difference in pre-test scores of the students.

Results of Findings

Table 2 shows that the mean value (2.51) of students taught using Brain-based Learning Strategy is higher than that of the students taught with conventional method (2.23). This implies that students taught with Brain-based learning strategy performed better than those taught with Conventional Method. This shows that there is significant difference in the academic performance of the two groups. Therefore, the null hypothesis is rejected.

Table 3 showed that the experimental group had a mean value of 4.38 in the pre-test attitude and a mean value of 23.47 in the post-test attitude making a pre-test and post-test mean gain in the experimental group to be 19.97 but the control group had a mean value of 3.27 in the pre-test attitude and posttest of 19.33 with a pre-test and post-test mean gain of 16.07. This result showed that the disposition of students in the experimental group towards Mathematics was higher than the control group. This may be attributed partly to the effect of the treatment.

*Significant at P < 0.05.

Hypothesis 1: There is no significant main effect of treatment on students’ achievement in Mathematics.

The result in Table 4 shows a significant main effect of treatment on students’ achievements in Mathematics (F_(1:510) = 760.93: P < 0.05). This clearly indicates that there was a significant difference in the post-test achievement mean scores of students exposed to the treatment and those exposed to the CTS. In line with this result, Ho₁ was rejected.

The table shows that both the treatment and cognitive style had significant main effect on students’ achievements in Mathematics (000*).

To find out the magnitude of the difference between the experimental and control groups, Multiple Classification Analysis was computed and the results are presented in Table 5 below.

This table shows that students exposed to the BBLS obtained the higher adjusted post-test achievement mean score ( $\bar{x}$ = 29.44) than those taught using the CTS. The table also indicates that 67.2% of the variation in students' achievements in Mathematics was accounted for by taking the independent variable (treatment) and the moderator variable (cognitive style) together.

Multiple regression 0.820 Multiple r. squared 0.672.

Hypothesis 2: There is no significant main effect of cognitive style on students’ achievements in Mathematics.

The results in Table 5 shows a significant main effect of cognitive style on students’ achievement in Mathematics (F_(1:510) = 26.69; P < 0.05). Thus, students with varying cognitive style levels differed significantly in Mathematics achievement. Therefore, the Ho₂ was rejected.

To find out the magnitude of the difference in mean scores between the analytic and the non-analytic groups, Multiple Classification Analysis was computed.

The table shows that analytic cognitive style group obtained higher achievement mean score ( $\bar{x}$ = 21.61) than the non-analytic cognitive style group ( $\bar{x}$ = 17.15).

The effect size or eta squared for each factor is an indicator of the strength of these effects. Table 5 indicates that treatment contributed 74.6% (or eta squared) to the variance observed in students’ achievements in Mathematics. Beta-weights or standardized coefficients are calculated to “wash out” the effect of the units of measurement. We can see that (0.703) has a slightly stronger “pull” on experimental group than the control group (0.132).

Hypothesis 3: There is no significant interaction effect of treatment and cognitive style on students’ achievements in Mathematics.

Figure 1 reveals a significant interaction effect of treatment and cognitive style on students’ achievements in Mathematics (F_(1:510) = 6.65; P < 0.50). Therefore, Ho₃ was rejected.

Figure 1 shows the graphical illustration of the nature of this significant interaction.

Findings showed that there was significant interaction effect of treatment and cognitive style on students’ achievement in Mathematics. This result confirms the assertion of researchers ( Awofala, 2002 ; Olajengbesi, 2006 ) that the personal variable of cognitive style interacts with instruction to produce results. This implies that the treatment is sensitive to students’ cognitive style on achievement in Mathematics. In other words, understanding and utilizing the core principles of brain-based instructional strategy to teach students of different cognitive styles in order to achieve the desired learning outcomes becomes inevitable. Also, analytic cognitive style students are very critical in their reasoning more than non-analytic students and are able to distinguish figures as discrete from their background and this may have enhanced their achievements in Mathematics.