Effect of Mathematics Puzzle Instructional Strategy on Mathematics Students’ Achievement

Agboro, Edirin

Department of Science Education, Delta State University, Abraka, Delta State, Nigeria

ABSTRACT: The research investigated the impact of a mathematics puzzle instructional strategy on student achievement. The research employed a quasi-experimental design featuring a pre-test post-test non-equivalent control group. It possesses a factorial structure of 2x2x3. The study comprised 362 mathematics students picked from six randomly selected mixed secondary schools. The assessment tool utilised was the Mathematics Achievement Test (MAT). The instrument had a reliability index of 0.82, as determined by the Kuder-Richardson (k21) formula analysis. The data were analysed using descriptive statistics of the mean to address the study issues, while independent sample t-tests and Analysis of Variance (ANOVA) were employed to evaluate the proposed hypotheses. The study’s findings indicated that mathematics students instructed using a mathematical puzzle strategy achieved higher scores than those instructed with traditional lectures strategy; additionally, no significant variation in the performance of male students taught with the puzzle strategy, nor a notable interaction effect between instructional method and gender on achievement. The study concluded that the puzzle instructional strategy is more effective in enhancing mathematics students’ achievement compared to the lecture method. Furthermore, the puzzle instructional strategy is not biassed by gender. It is recommended that both teachers and students receive adequate training to develop the necessary skills for implementing this strategy and that they be encouraged to utilise it in teaching and learning. Additionally, the faculties of education in universities and Colleges of Education should revise their curricula to ensure that pre-service teachers are trained in the skills required for its application.

KEYWORDS: Puzzle Instructional Strategy, Sex, Mathematics, Achievement,  Quasi-experimental Design.

1. INTRODUCTION

Mathematics is a paramount subject globally, as proficiency in mathematics is essential for the effective comprehension of numerous disciplines, particularly in technical and scientific fields. Davies and Hersh (2012) regard mathematics as the most critical subject, not only for achieving academic qualifications but also for equipping students for future endeavours and influencing their career choices. Meefor (2014) encapsulated the significance of mathematics by asserting its relevance to all aspects of the universe, from the minuscule to the immense. Mathematics indeed intertwines with the daily existence of individuals as they interact with their surroundings. In Nigeria, mathematics is accorded  significant  emphasis within  the  curriculum and educational policies. The policy decision which made the study of mathematics a compulsory core subject is contained in the National Policy on Education (FRN, 2013). This decision of making mathematics a core subject is based on its importance in various fields of Science and Technology. This suggests that everyone in the community needs to understand mathematics. Also, competency in mathematics is a requirement to be obtained for any course of study in higher institutions of learning. For one to be successful in life, one need to acquire the basic mathematical knowledge needed in one’s chosen career or vocation. With this, one can say that mathematics is the foundation of all subjects and vocations. Hence it is made a compulsory subject studied at pre-primary, primary and secondary levels of education.

Notwithstanding the significance of mathematics, it has been noted that pupils exhibit inadequate performance in mathematics in internal and external examinations. Over the years, examination bodies specifically, the Junior Secondary School Certificate Examination Reports (2017 to 2022), have been reporting a downward trend in the performance of students in mathematics. Also, research findings like those of Adebayo (2015); Programme of International Student assessment (PISA), 2018); Okebukola (2020), Mensah, (2020), Mwangi (2021) indicated the unsatisfactory performance of students in mathematics. This predicament has been attributed to teachers’ continued reliance on conventional teaching methods, primarily the lecture approach. To support this assertion, Betiku (2001), Adeyemi (2020), and Mwakapenda (2020) noted that mathematics is among the courses that are most inadequately taught, largely despised, and perceived by pupils as abstract and tedious. All these affect students’ achievement in mathematics at the Basic Education Certificate Examination.

Experience and observation indicate that mathematics, which necessitates critical skills and active student engagement, is delivered through the lecture method/strategy. Lecture approach is a methodology that makes the teacher a dispenser of knowledge instead of someone who guides the students in the teaching learning process. Lecture method according to Okebukola (2019), Njoroge (2020) Mensah (2022) and Mwangi (2022) make students passive, non-thinking and assume information receiving role. This method also encourages students to learn through rote and memorisation process. When students memorises concepts taught, they tend to forget what have been learnt easily since the concepts learnt is stored in their short-term memory (Atakpo, 2024). There is no doubt that the lecture method is a very ineffective way to get students involved in schoolwork, because the use of the method does not provide adequate learning experience which leads to poor achievement. To solve this problem, there is need to reverse the trend from the traditional teaching methods (predominantly lecture method) to a more efficacious strategy such as the activity-based instructional strategies.

Activity based instructional strategies are instructional strategies adopted by the teacher to guide students as they participate actively in the teaching learning process. It is organized to enrich the knowledge of the content matter, take away fatigue, boredom and develop creative abilities among the students. When activity-based instructional practices are employed in instructional process, there is healthy change in the class atmosphere, students’ knowledge is enriched and their minds broaden as regards the content matter. The use of such strategies leads to avoidance of boredom in certain abstract concepts in mathematics and helps develop creative abilities in students. It also brings about different styles in teaching learning process, thereby increasing the development of interest among students for the subject through stimulation of thinking and development of reasoning ability. Incorporating such activities in the teaching/learning processes also helps in the development of social and moral values such as cooperation, team spirit, tolerance and respect for others (Atakpo, 2020). In addition, these activities enable students learn different methods of solving problem in a concrete way and development of mathematical attitude, that is preciseness, accuracy, in-depth thinking and reasoning power.

One of such instructional strategies that make use of activities is the puzzle instructional strategy.  A puzzle is a logically designed problem-based activity constructed to teach and test knowledge of the students in a creative, fun and recreational learning environment. According to Oxford English Dictionary (2002), a puzzle is a game that tests knowledge and intelligence while Alloway (2020) sees puzzle cognitive tasks which requires the use of problem solving, critical thinking skills and reasoning to solve a particular problem. Hamari (2022) sees puzzles as creational activities which provides fun and challenging ways for individuals to exercise their cognitive abilities, relax and experience a sense of accomplishment. According to Lee (2019), they are instructional tools utilised in education to offer a demanding and interesting method for fostering students’ problem-solving, creativity, and critical thinking skills. Kim (2020) perceives puzzles as cognitive challenges necessitating the application of problem-solving, critical thinking, and reasoning skills to attain a goal. The utilisation of puzzles in the instructional-learning process is called puzzle instructional strategy. The puzzle teaching technique is a method that employs problem-based activities to educate and assess students’ knowledge. This technique requires students to systematically arrange components to derive a solution to a given problem. The implementation of puzzle instructional strategy facilitates the construction of a comprehensive and adaptable knowledge base, enhances problem-solving abilities, fosters self-directed learning, cultivates lifelong learning skills, promotes effective collaboration, and stimulates intrinsic motivation, as students actively engage in the educational process. Jaramillo, Losada, and Fekula (2012) assert that the puzzle teaching strategy cultivates several essential student skills, including vocabulary, reasoning, spelling, and problem-solving abilities. One good quality of puzzles is that they cannot be solved by rote and thus are highly beneficial in helping students think. Michalewiz and Michalewiz (2008), were of the view that puzzles are engaging and thought provoking. Engaging in puzzles is associated with the enhancement of professional skills, as they necessitate abilities like as logic, spelling, and object manipulation for resolution. Many firms utilise puzzles as verbal reasoning assessments during job interviews to evaluate candidates’ problem-solving abilities. This is due to the belief that puzzle-solving aptitude correlates positively with the creative thinking skills essential for addressing innovative real-life challenges.

Numerous problems are employed in the instruction of various topics, including Sudoku, Picross, logic grid puzzles, Scrabble for English, and numerical and mechanical puzzles for physics; nevertheless, the researcher is specifically focused on the application of mathematical puzzles. Mathematical puzzles provide a fundamental component of activity-based educational methodologies. Mathematics Puzzles can be utilised in mathematics instruction as they often do not entail competition among participants; rather, the solver must identify a solution that meets the specified criteria to resolve the issue. Puzzles offer learners the chance to engage in a relaxed environment. They render education enjoyable (Education World, 2016). Zablocki (2013) posited that exposing students to puzzles is advantageous for several reasons, including the introduction of intellectual humour, enhancement of comprehension and creativity, expansion of vocabulary, provision of self-directed learning opportunities, and facilitation of peer bonding. According to Bragdon and Gamon (2002), the use of puzzles in education enhances students’ critical thinking and problem-solving abilities. Puzzles as a resource provide teachers the ability to engage and maintain learners’ interest in the classroom. Consequently, it can be asserted that the utilisation of puzzles is advantageous for students in cultivating their creative and analytical skills, as it promotes active engagement in the educational process. Student participation in this classroom setting facilitates mathematics learning in a calm atmosphere, free from worry and enriched with enjoyment. When this occurs, children can fully utilise their learning potential and cultivate essential academic abilities. The primary motivations for students’ interest for puzzle-based learning are that puzzles are educational and demonstrate effective problem-solving principles in an engaging manner. When puzzle is used in teaching of mathematics the methodology is called mathematics puzzle instructional strategy.

Mathematics Puzzle instructional strategy is a strategy that uses problem designed base activity to teach and test the knowledge of students (Agboro, 2019). In this strategy, students are expected to organize pieces together in a logical way for them to arrive at the solution to a posed problem. In doing this, students are given some problems which are puzzle based to solve. Puzzles possess the advantageous trait of being unsolvable through mere memorisation, hence effectively stimulating critical thinking in students. Engaging in puzzles can be associated with the enhancement of professional capabilities, as they necessitate abilities such as reasoning, spelling and manipulations of objects for them to be solved. In using this methodology, the teacher informs the students how to solve the various puzzles using the puzzle sheets in order for them to generate the needed figures. The students, as teams, will be asked to complete the empty puzzle boxes and make sure that they generate the needed numbers as the case may be. These activities involved in solving puzzles enables them construct their own knowledge.

Researches have pointed out that for students to learn effectively, teachers need to design lessons that are both relevant and authentic, so that students can build their own knowledge on top of what they already know about the subject. Furthermore, learners must take an active role in their own education if they are to achieve academic success (Ajaja & Eravwoke, 2010). Based on the qualities of puzzle instructional strategy and the lapses associated with the use of lecture methods, the researcher is of the view that mathematics puzzle instructional strategy could be given a try in the teaching of mathematics. It is for this reason that the study is being carried out.

The existing literature indicates a scarcity of empirical studies examining the use of puzzles to enhance learning in formal educational environments, specifically in mathematics. A limited number of studies were undertaken in foreign nations. Research on puzzles in international contexts includes a comparison of puzzle-based and traditional lecture methodologies on students’ performance in human anatomy and physiology laboratories, an examination of the efficacy of puzzles in enhancing vocabulary acquisition and retention among Palestinian tenth graders, a survey of NP-Complete puzzles, and an analysis of the impact of information technology versus puzzle-based teaching methods on the educational advancement of third-grade math-physics students in Urmia’s first district. Additionally, studies on the application of puzzles to enhance mathematics instruction in Nigeria encompass the relationship between mathematical puzzles and students’ performance in plane geometry. Impact of two puzzle-based instructional methodologies on primary school pupils’ learning results in social studies in Ondo State, Nigeria; influence of puzzles on educational advancement of students; and the effect of puzzles on the comprehension of challenging topics.

Literature reviewed on the effectiveness of the use of puzzle in teaching other subjects (Human Anatomy and Physiology and Vocabulary) and not mathematics indicated that the use of puzzle has positive effect on students’ achievement. Generally, majority of the reviewed empirical studies indicated that the use of puzzle improves learning and retention. Specifically, empirical studies showed that puzzle promote learners’ achievement ( Stetzik, Deeter,  Parker& Yukech, 2015; Essie & Ado, 2017), and Aminu and Appolos  (2016) looked at its effect on the learning of difficult concepts. The findings of these researchers further strengthened the desire for the study, in a subject where students find difficulties learning.

Some research findings have shown that girls and boys perform differently in different aspects of mathematics (Owduni & Ogundola, 2013). Others show that as students go higher in their education, sex differences favour increases in mathematics achievement by males (Stemler, 2000). The literature on sex differences gives evidences that sex issues have an impact on students; achievement in mathematics and so this becomes an important issue that teachers and every educator should pay attention to when designing mathematics instruction and delivery.  Recent studies, have shown that the use of puzzle has positive effect on students’ achievement, literature shows that puzzle instructional strategy influenced both male and female achievement equally (Adedoja, Abidoye, & Afolabi, 2013).

A clear explanation of the significance of the mathematical puzzle instructional strategy, its applicability to teaching and learning, and a summary of research findings on the impact of the approach on student accomplishment have all been attempted. Considering the relevance of puzzle instructional strategy in enhancing students learning the results of studies in other fields and countries, conducted in the past, this study is therefore an attempt to determine its effects on mathematics students’ achievement, mathematics in Delta state. The study will also determine if students of varying sexes achieve differently on achievement.

Research Questions

1. Is there any difference in the achievement scores of mathematics students tutored with mathematics puzzle instructional strategy and those tutored with lecture method?
2. Is there any difference in the achievement scores of male and female mathematics students tutored with mathematics puzzle instructional strategy?
3. Is there any effect of interaction of sex and method on achievement?

Hypotheses

H_01:  There is no significant difference in the achievement scores of mathematics students tutored with mathematics puzzle instructional strategy and those tutored with lecture method

H_02:  There is no significant difference in the achievement scores of male and female mathematics students tutored with mathematics puzzle instructional strategy

H_02:  There is no significant effect of interaction of sex and method on achievement

METHODOLOGY

The design utilised for this study was the pre-test post-test non-equivalent control group quasi-experimental design. The structure is characterised by a 2x2x3 factorial design. The design incorporates two instructional methods (puzzle instructional strategy and lecture method), sex (male and female), and repeated assessments (pre-test and post-test). This design utilised intact classes for grouping subjects, rather than employing randomisation. The variables for this study consist of instructional strategies, specifically the mathematics puzzle instructional strategy and the lecture method as independent variables, along with achievement and sex as intervening variables. This design is deemed suitable as random assignment of subjects into groups was not feasible, leading to the use of intact classes. Johnson and Christensen (2000) state that any design that omits randomisation, a necessary condition for true experimental design, should be classified as a quasi-experimental design.

The study population is comprised of all mixed public upper basic schools’ mathematics students in Delta State. There are four hundred and seventy-one schools (one hundred and eighty-seven in Delta Central, one hundred and sixty-eight in Delta North and one hundred and sixteen in Delta South) and fifty thousand five hundred and twenty-five students in Delta state (Delta State Ministry of Basic Education, 2023). Only public schools were used because they all have almost the same learning environment and they are governed by a central body which is the post primary Education board.

The study sample comprised three hundred sixty-two (362) students from six mixed upper basic schools’, randomly carefully chosen from three senatorial districts, all of whom were Junior Secondary School Mathematics students. Two schools were chosen from each senatorial district. The sample for the study included six Junior Secondary Schools, six mathematics teachers, and six whole classes. The sampling method employed for selecting the schools and classes is simple random sampling (balloting) utilising the withdrawal with replacement strategy. All mixed Junior Secondary Schools in the senatorial districts were enumerated. The names of the schools were inscribed on slips of paper, folded, and placed into an opaque bag. The necessary number of schools was determined using the withdrawal with replacement method of balloting.

The tool utilised for data gathering was the Mathematics Achievement Test (MAT). The mathematics achievement assessment comprises two portions. Section A comprises enquiries regarding the student’s biographical data, whereas Section B consists of 50 items derived from fractions and percentages. The items in section B were chosen by the researcher from Junior Secondary School Certificate Examination (JSSCE) question papers from 2020 to 2022. Section B comprises multiple-choice questions, each with one correct answer and four distractors. Respondents must select one answer for each question in section B.

The instrument content validity assessed via a table of specification. The instrument’s face validity was assessed by three experts: one in scientific education, one in mathematics, and one in measurement and assessment. The researchers examined the Mathematics Achievement Test (MAT), along with the research questions and hypotheses, to ascertain whether the instrument could produce the requisite data for addressing the research questions and evaluating the hypotheses. It was recommended that two items be reframed, which was subsequently executed, leading to approval for data collection.

A pilot study was done to assess the instrument (MAT) reliability by evaluating its consistency. The instrument was administered to twenty JSS II students from a public school, who were not part of the study sample, after they had been instructed on the topic. Data were gathered and analysed via the Kuder-Richardson (k21) algorithm to ascertain the reliability coefficient. The formula was employed due to the instrument being an accomplishment test, awarding one mark for a correct response and zero for an incorrect answer. The examination of the collected data yielded an r-value of 0.82 for the achievement test. The instrument was deemed credible due to a value exceeding 0.70. Wiseman (1999) asserts that any instrument having a dependability value of 0.70 is deemed dependable.

For every lesson throughout the six-week course of treatment, the experimental (Puzzle instructional strategy) group students were made to participate in the solving of puzzles and followed by the mathematics teacher teaching of the concepts in the recommended examples in their textbooks using the following steps

Step I: Gaining attention:  To gain students attention, the teacher first of all ask students what they know about puzzle and its types, present the puzzle sheet to the students before introducing the concepts to be studied. The idea that will be studied will be explained by the students. Finding out what they already know about the idea that will be taught is the goal of this.

Step II: Informing learner of the objective(s):The students were informed of the objectives to be accomplished by the conclusion of the lesson.

Step III: Stimulating recall of prerequisite learning: Students were asked to solve the puzzles from the puzzle sheet given to them in groups. The puzzle activity proceeded as follows:  the students first of all solve and complete the empty boxes on the puzzle sheet and generate the words that match each answer. Thereafter with the provided words representing each solved figure, they make a complete sentence that makes sense or meaning. It is expected that this analogy activity will lead to conceptual understanding. The aim is to encourage participation.

Step 1V: Presenting the stimulus material: students were asked to bring out all the figures that they were able to generate during the time of solving their puzzles. The aim is to encourage participation.

Step V: Providing learning guidance: From the generated figures of the students, the teacher selects and bring out a problem for the students to solve in groups. The aim is to encourage participation and critical thinking.

Step VI: Eliciting the performance: Teacher goes round to see if students’ workings are correct. The aim is to encourage participation and foster understanding.

Step VII: Providing feedback about performance: Teacher corrects the students based on what he/she discovered at step VI. The aim is to foster understanding.

Step VIII: Assessing performance: Learners were made to solve more of the problems as a result of the feedbacks individually. The aim is to activate retrieval and make reinforcement possible. This was done by providing students with homework and class work from the textbooks and puzzle sheets given to them. The work were assessed and feed-back provided.

Step IX: Enhancing retention and transfer/ Drawing of Conclusion: Teacher explains all the necessary procedures required in solving the problems putting into consideration all the mistakes made by learners at all the other stages. Also, the teacher will ask the students to relate what they have learnt with real life situation. The aim is to provide varied practices and promote understanding and retention. To draw conclusions, the teacher elucidates the principles taught while considering students’ reactions. Educators pose enquiries, respond to students’ queries to evaluate comprehension, and encapsulate the lessons. The detailed steps for each topic are presented in Section B of Appendix IV.

In the control group, the instructors exclusively imparted the concepts as outlined in the textbook through the lecture approach, adhering to the following steps:

In the instruction of the ideas of fractions and percentages via the lecture technique, the following stages were implemented for each topic presented:

Step I: Gaining attention: To capture students’ attention, the teacher initially requests an explanation of the idea to be studied. The objective was to assess their existing understanding on the idea to be instructed.

Step II: Presenting the stimulus material: Teachers writes out the equation to be solved based on the topic. The aim is to foster understanding

Step III: Providing learning guidance: From other equations written on the board based on the concept to be studied, the teacher selects and bring out a problem for the students to solve and there he asks questions. The aim is to encourage participation and critical thinking.

Step IV: Eliciting the performance: Teacher goes round to see if students’ workings are correct or not correct. The aim is to encourage participation and foster understanding.

Step V: Providing feedback about performance: Teacher corrects the students based on what he/she discovered at step IV. The aim is to foster understanding.

Drawing of Conclusion VI: Teacher explains all the necessary procedures required in solving the problems and putting into consideration all the mistakes made by learners at all the other stages. Teachers will pose enquiries, respond to students’ queries to evaluate their comprehension, and summarise the teachings.

METHOD OF DATA COLLECTION

At the end of the treatment which lasted for six weeks, the investigator administered the Mathematics Achievement Test was administered on both the control and experimental group students.

RESULTS

Research Question one

Is there any difference in the achievement scores of mathematics students tutored with mathematics puzzle instructional strategy and those tutored with lecture method?

Table 1: Descriptive statistics showing the comparison between the control and experimental group students’ mathematics achievement test scores.

________________________________________________

Groups                       N   Mean      Mean Diff           SD        

Mathematics

Puzzle Instructional 119 28.278                               8.074

strategy

7.27

Lecture Method

Group                       243  21.008                             8.038

________________________________________________

Table 1 shows that the experimental group students had a mean score of 28.278with a standard deviation f 8.074and a mean score of 21.008 with a standard deviation of 8.038 for the control group. The mean difference between the two sets of scores was 7.270, favouring the experimental group students. This shows that a difference exists between the groups in their mathematics scores. To determine if the difference is significant, H₀₁ was tested.

In order to determine the appropriate statistics to use in testing H₀₁, independent sample t-test was utilised to test the students’ pre-achievement test to determine if a significant difference exist between their pre-test scores. The result is shown in Table 2.

Table 2: Independent sample t- test statistics comparing the difference in mean scores between experimental and control group students at pre-test.

______________________________________________

Groups          N   Mean     Mean Diff.    SD      df   sig(2-tail

Mathematics

Puzzle  

Instructional

strategy        119   5.91                          3.14

0.143                    360        0.694

Lecture

Method   243    5.77                             3.26

Table 2 illustrates that the disparity observed between the experimental and control groups at the pre-test is not statistically significant, as the calculated significance value of 0.694 exceeds the critical significance threshold of 0.05. As a result, the independent sample t-test for students emerged as the suitable statistical method to evaluate H01.

Hypothesis one

There is no significant difference in the achievement scores of mathematics students tutored with mathematics puzzle instructional strategy and those tutored with lecture method.

Table 3: Independent sample t-test statistics comparing the difference in mean scores between experimental and control group students at post-test.

________________________________________________

Groups         N   Mean  Mean Diff.  SD  df  t_{ca l}    Sig(2-tail)

Mathematics

puzzle

instructional

strategy       119  28.28                       8.07                                                                                                                    7.27                    360  8.07     0.000

Lecture

Method    243  21.00                       8.04

Table 3 indicates that the observed difference between the experimental and control groups at post-test is significant, as the computed significance value of 0.000 is less than the crucial significance value of 0.05. The null hypothesis H01, which posits that there is no significant difference in the accomplishment scores of mathematics students instructed using the mathematics puzzle instructional approach compared to those taught via the lecture technique, is consequently rejected.

Research Question Two

Is there any difference in the achievement scores of male and female mathematics students tutored with mathematics puzzle instructional strategy?

Table 4: Descriptive statistics comparing the effect of mathematics puzzle instructional strategy on mathematics male and female students’ achievement test

________________________________________________

Sex        N            Mean     Mean Diff.                         SD

Male      38          28.605                                               8.132

0.481

Female 81          28.124                                               8.092

________________________________________________

Table 4 indicates that the male experimental group students achieved a mean score of 28.605 with a standard deviation of 8.132, while the female students attained a mean score of 28.124 with a standard deviation of 8.092. The average difference between the two sets of scores was 0.481, favouring the guys. This indicates a disparity between the post-test scores of males and females. An independent sample t-test was employed to assess the significance of the difference, testing H02, as illustrated in Table 5.

Hypothesis Two

There is no significant difference in the achievement scores of male and female mathematics students tutored with mathematics puzzle instructional strategy.

Since a non-significant difference was observed in Table 2, independent sample t-test became the appropriate statistics to be used in testing H0_7; and the result is shown in Table 5

Table 5 : Independent sample t- test statistics comparing the difference in mean scores   between male and female experimental group students at post-test.

________________________________________________

Group  N   Mean  Mean Diff.  SD    df    t_cal   Sig(2-tail)

Male      38  28.61                      8.13

                                 0.481                    117  0.30   0.76

Female  81  28.12                      8.092

P> 0.05

Table 5 shows that the observed difference between the male and female experimental groups students at post is not significant since calculated sig. value of is 0.763 is greater than critical sig. value of 0.05. With this, H₀₇ which says that there is no significant difference in the achievement scores of male and female mathematics students taught with mathematics puzzle instructional strategy is, therefore, retained.

Research Question 3

Is there any effect of interaction of method and sex on achievement?

Table 6: Descriptive statistics showing the interaction effect of method and sex on achievement in mathematics.

________________________________________________

Sex                             N  Mean  Mean Diff  SD       

Experimental Male 38   28.60                      8.13                                                                0.48

      Female 81   28.12                        8.09

Control          Male 137  21.98                        7.98                                                                1.32

Female  106       20.66                    8.14

________________________________________________

Table 6 shows that the mean interaction scores of male and female students in the mathematics puzzle instructional strategy (experimental group) are 28.602 and 28.124 respectively with a mean difference of 0.478, in favour of the male students while that of the control group is 21.975 and 20.660 for males and females respectively with a mean difference of 1.315, in favour of the males.  To determine if the differences in interaction scores are significant, H₀₃ was answered using Analysis of Variance (ANOVA), as shown in Table 7.

H_03: There is no significant effect of interaction of sex and method on achievement

Since a non-significant difference was observed in Table 11, Analysis of Variance (ANOVA), became the appropriate statistics to be used in testing H0_10; and the result is shown in Table 7

Table 7: ANOVA statistics showing the effect of interaction of method and sex, on achievement

________________________________________________

Source     Type111       df      Mean     F-cal     F-cri Sig

sum of                  Square

                   Square                         

Corrected

Model      4249.640      3   1416.547      21.768           0.00

Intercept 175740.135  1   175740.135 2700.552        0.00

Groups   3949.345      1    3949.345     60.689            0.00

Sex          21.796         1    21.796         0.335   3.94    0.563

Method*

Sex           0.330           1    0.330           0.120   3.94    0.843

Error    23297.078    358  65.076

Total     225726.000  362

Corrected

Total     27546.718    361

________________________________________________

P> 0.05

Table 7 indicates that no significant effect of interaction of method and sex on mathematics achievement since the calculated sig. value of 0.843 is greater than the critical sig. value of 0.05. With this, H0₁₀ which states no significant effect of interaction of method and sex on achievement in mathematics is retained.

DISCUSSION

Mathematics students instructed through a mathematical puzzle strategy had higher scores on accomplishment tests compared to those taught via the lecture method. This is illustrated in Table 1. A notable disparity was seen between the experimental and control groups for mathematics students overall, as illustrated in Table 3. The notable disparity in accomplishment test scores between students in the experimental and control groups corroborates the findings of previous researchers about the efficacy of utilising mathematical games in instruction. For instance, Hamari (2020). Stetzik, Deeter, Parker, and Yukech (2015), Elham (2016), and Essien and Ado (2017) identified a significant improvement in the application of puzzles for mathematics instruction compared to the lecture method in the Human Anatomy and Physiology II laboratory, Computer Science Basics course, and plane geometry, respectively.

The study revealed that male students instructed using a mathematics puzzle technique attained superior post-achievement results compared to their female counterparts. This discernible change was, however, determined to be insignificant. Table 5 indicates that the disparity in mean scores between male and female students was not statistically significant. This indicates that all students in the experimental group, regardless of gender, were positively impacted by the mathematics puzzle instructional technique, which subsequently influenced their post-test scores. This indicates that the procedure is devoid of gender bias. This conclusion aligns with the results of Alloway (2020), Mensah (2022), Kim (2020), Mwakapenda (2022), Adedoja, Abidoye, and Afolabi (2013), and Essien and Ado (2017), who reported no significant impact of the puzzle instructional technique on student accomplishment by sex.

The study also revealed a non-significant interaction effect between method and sex on accomplishment, as illustrated in Table 7. This indicates that the interaction between method and gender did not affect pupils’ performance in mathematics. This indicates that the maths puzzle instructional technique affected pupils’ mathematics achievement regardless of gender. This aligns with the conclusions of Alloway (2020), Mensah (2022), Kim (2020), Mwakapenda (2022), Akinsola and Animasahun (2014), and Okigbo (2010), who discovered no significant interaction effect of gender on students’ performance in mathematics. Ajaja (2013) and Agboro-Eravwoke (2022) revealed a non-significant interaction effect between sex and mode of instruction on achievements.

CONCLUSION

Since literature has shown the teaching method is important factor to be considered in the teaching and learning process, investigating the methodologies applied in the teaching of mathematics needs to be carried if pre-service teachers trained to do the job effectively and if practicing teachers are to make their teaching effectively. It is only when mathematics teachers are abreast of effective teaching methods/ strategy that they can be open to changes that will help improve mathematics teaching and learning at all levels. Based on the findings of the study, it is therefore concluded that puzzle instructional strategy is more effective improving mathematics students’ achievement when compared with lecture method and puzzle instructional strategy is not a sex biased instructional strategy.

RECOMMENDATION

Since one of the finding has shown that puzzle instructional strategy increased students posttest  scores more than the lecture method, it is recommended that teachers and students should be properly trained to acquire the skills on usage of puzzle instructional strategy and be encouraged to apply it when teaching and learning respectively and the faculties of Education in the universities and Colleges of Education should review their curriculum in-order for pre-service teachers to be trained to acquire the skills needed for their usage.

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