Humor, motivation and achievements in mathematics in students with learning disabilities

Abstract This study examined the association between humor, motivation, and achievements in mathematics in students with learning disabilities. For this study, 80 sixth-grade students with learning disabilities who attend integrated classes in a general education school were tested using three instruments: a questionnaire about incorporating humor in mathematics instruction, a questionnaire about motivation, and a mathematics achievement test.The findings of this study show improved mathematics achievements and motivation in students with learning disabilities when humor is incorporated in mathematics classes. In addition, students with learning disabilities who were taught mathematics with humor scored higher on motivation and mathematics achievement at the end of the school year compared with the beginning of the school year. We conclude that incorporating humor in mathematics instruction can be recommended. The expected positive effect on motivation and achievements in this special population could have a positive impact on a variety of other pedagogical phenomena, such as dropout rates, academic achievements in other subjects, and social interactions.


Introduction
Modern teaching seeks more advanced and innovative methods of instruction to make learning the required curriculum easier and less stressful for students. Incorporating humor in the mathematics classroom is one example of such methods. Mathematics is of particular interest as it is considered one of the more difficult subjects for school-children to master, and this difficulty is often more pronounced in students with learning disabilities (Kuperman, 2006).
Humor is known to have a positive impact on people: it can improve intrinsic resilience, mood, and self-image. Humor can also facilitate non-threatening relationships in various contexts (including learning), support development of cognitive abilities, and improve creativity (Hendriks, 2021;Sover, 2009). One way to promote success in mathematics is to increase student motivation. Motivation means a student is stimulated to learn and achieve a goal. Accordingly, highly-motivated students are driven to understand the material and respond to questions (Maimon, 2008). If incorporating humor in mathematics classes improves students' motivation, their achievements will also benefit.
The present study set out to examine the association between attitude to incorporating humor in mathematics instruction and the motivation and achievements of students with learning disabilities at the start and end of the intervention.

Humor: Definition and features
The term humor usually relates to statements or actions which make people smile or laugh. Although humor is part of many areas of people's life, it is most common in social interactions with other people (Gazit, 2011) and is indispensable when it comes to maintaining relationships (Van Praag et al., 2017).
Humor is also an important defense and survival mechanism (Sover, 2009;Steir-Livny, 2021) and it shows up in many contexts and takes many forms (Alatalo & Poutiainen, 2016). Usually, it is deliberate rather than random, and people tend to generate humor as needed in almost any area, e.g. financial, political, social, cultural (Sover, 2009;Steir-Livny, 2021). A person's ability to use humor and even self-deprecating humor correlates with higher self-esteem and ego-resiliency (Herzog & Stervey, 2008).
Humor has positive internal and interpersonal effects (Sover, 2009) that are achieved by reducing stress and anxiety and creating a positive atmosphere (Gazit, 2011). It facilitates nonthreatening relationships, in sexual, and in hostile contexts, for example, and it can defuse or prevent stress. Use of humor is perceived as an indicator of positive mood, reducer of anxiety and depression, and improver of cognitive abilities (Herzog & Stervey, 2008). As an equalizer and trigger of fellowship, humor can unite members of a group irrespective of their group status. In this way, it can eliminate the gap between teacher and student (Ostrover, 2009).
Humor also has an important role in communication among groups of peers, as a measure of popularity, e.g., adolescents who display a sense of humor have higher social status (McGee & Shelvin, 2009).
Humor has an important cognitive role in class as it can enhance attention by creating time-out for a shared laugh and by fostering learner creativity. Arbel (1997) and Hendriks (2021) have shown that humor skills indicate high intellectual ability and creativity, and other studies show that humor in class is associated with benefits such as improvement in student motivation, classroom climate, and students' positive perceptions of teachers (Alatalo & Poutiainen, 2016;Bolkan et al., 2018;Van Praag et al., 2017).
However, caution is necessary; teachers must be sensitive to their class and students. Difficult to understand or offensive humor should be avoided, at least partly because some students can have difficulty interpreting humor correctly (Ostrover, 2009). Therefore, teachers should think about making humor they use in class accessible to all students by avoiding sarcasm, and idioms or abstract language, which are harder for students with learning disabilities to understand. This difficulty is the result of normal development of humor in children being related to their social, cognitive, and linguistic development. We may therefore assume that the delayed development often associated with learning disabilities may interfere with the normal development of humor, and that this can affect how one understands and engages in the emotional interaction that experiencing humor requires (Semrud-Clikeman & Glass, 2008).

Theory of humor
The importance of humor and the need for it in the classroom is better understood through the theories of humor. Three classical theories explain humor: the incongruity theory, the superiority theory, and the relief theory (Lintott, 2016). According to the incongruity theory, attributed to the philosophers Cicero, Kant, and Schopenhauer (Kulka, 2007), a comical situation emerges when a person senses an incongruity in a specific situation. In other words, a sense of something out of the ordinary or an accidental contrast between expectations and the actual event makes the person perceive the situation as comical. According to the incongruity theory, the comical situation arises when ideas that are contrasting or incongruous get connected (Sover, 2009).
The fundamental premise of the superiority theory-attributed to philosophers Plato, Aristotle, and Hobbs (Kulka, 2007;Stone, 2021)-is that the comical side of a situation derives from one party feeling superior to the other. This theory explains the more aggressive aspect of humor, in which humor is generated in order to belittle the object of the joke. This makes laughter a judgmental reaction, as the person laughing feels superior to the the subject of laughter. Note that this theoretical explanation conflicts with the notion that humor is an equalizer and unifier (Lintott, 2016;Sover, 2009;Stone, 2021).
According to the release or relief theory, attributed to Freud (Kulka, 2007), laughter is used to relieve tension between people, and the funny situation is created by a tension-triggering situation. According to this theory, the main function of humor is to reduce tension and trigger the relief of getting this tension defused.

Incorporating humor in the classroom
The benefits of humor are multifaceted-humor can contribute to positive, comfortable, empathic communications, effective interpersonal relationships, better teamwork, and conflict defusing. All these effects are pertinent to the teaching environment (Bolkan et al., 2018;Zamir, 2007). Social cohesion is another of the effects of humor, as it allows people to unite around issues or topics (Zamir, 2007). This is another aspect that can be applied in the classroom.
On the academic side, Kuperman (2006) shows that humor can improve students' ability to absorb and remember. Humor can also increase motivation to learn, so that students absorb the material better. In a reading comprehension study, Tang et al. (2019) found that humor improved understanding of texts. Humor in teaching can also increase students' creativity, by opening them up to other, more unusual perspectives.
Humor does have its drawbacks-when it is perceived as inappropriate to the instructional purposes and is used merely for fun, it can impair the learning process by causing students to mock learning because they perceive it as frivolous (Baid & Lambert, 2010). In some cases, students might perceive a comical situation as demeaning or hurtful (Baid & Lambert, 2010).
Another criticism of incorporating humor in class is that it requires special skills, and not every teacher is able to convey a humorous message successfully. As a result, teachers may inadvertently find themselves conveying an incorrect or inappropriate message (Banas, 2011). In some cases, humor can create an antagonistic, distrustful environment that compromises teachers' communication channels with their students and interferes with learning (Baid & Lambert, 2010).
As noted above, students with learning disabilities may have difficulty grasping humor. This can be ascribed to the known association between humor and academic and social competence (Semrud-Clikeman & Glass, 2008) as this competence could be lower in this group. Accordingly, using humor to teach this population must be carefully considered in order to benefit from its use.

Motivation to learn
Motivation is the process of triggering, directing, and maintaining goal-achieving behavior (learning), and it reflects the sum of reasons that make a person behave in a certain way in a given situation. There are two sub-categories of motivation, intrinsic (curiosity, mastery, and selfperception of learning abilities), and extrinsic (as in the need for social recognition, and for feedback and assistance from the teacher). Motivation is a key component of learning at all ages and levels: students who are motivated to study mathematics are driven by the need to achieve a goal, such as understanding the material or answering questions. Studies have shown that students who set themselves curriculum mastery targets and who perceived a task as interesting, challenging, and important tended to engage in more meta-cognitive activities, applied more cognitive strategies, and put more effort into the task (Maimon, 2008;Pintrich & DeGroot, 1990).
Students with a positive self-image-the ones who believe in their own abilities and efforts-will usually be more motivated and will progress in a given subject despite difficulties encountered. Indeed, motivation is the process that drives students to maintain appropriate goal-oriented behavior (Maimon, 2008;Pintrich & DeGroot, 1990).

Teaching mathematics: Approaches and means
Mathematics instruction is a long-standing concern in education and its principles are under constant readjustment due to poor student achievements in the subject. Poor achievements have triggered questions such as how to integrate new educational technologies in mathematics education, and how to emphasize the practical application of mathematics (Geary, 2004).
These adjustments also reflect different approaches to the psychology of learning that were prevalent at different periods. Consider, for example, changes in the United States between the 1920s and the 1970s: (a) the "drill-and-practice phase" (1920-30, influenced by behaviorists such as Thorndike), followed by (b) the "meaningful arithmetic" phase (1930-50, influenced by Gestalt psychologists), and finally (c) the "new math" phase (1960-70, influenced by Bruner and Piaget) (Martinovic, 2018).
Mathematics as a school subject has a central place in the official Israeli curriculum (pre-school to high-school) and is a required subject for matriculation (Chiu, 2009;Fischbein, 1997;Ministry of Education, 2006). The established goals of the elementary-school mathematics curriculum in Israel are: (a) acquisition of concepts and structures in arithmetic and geometry; (b) development of the required skills in each of the topics: arithmetic and geometry insight, mastery of mathematical skills, problem solving, investigation assignments, understanding properties and associations between concepts, learning and using mathematical language; and (c) preventing failure, or a sense of failure, and getting students to like the subject. But, to succeed in mathematics education, a child's functioning both in mathematical topics and in other subjects must be taken into account.
Mathematics is considered one of the toughest school subjects to master and is one of the greatest obstacles to gaining a high-school diploma in Israel. The reality of mathematics education reveals dissatisfaction with both content and methods: mathematics education at all levels and stages usually emphasizes technical acquisition of knowledge using repetition, practice, and exams, and often, neither the instruction process nor the textbooks leave room for independent thinking, creativity, or experiential and relevant learning (Gazit, 2011). Therefore, mathematics should not be difficult or too complex to understand. But it seems that learning mathematics from pedestrian textbooks and from teachers, who are sometimes inadequately trained, can make learning mathematics traumatic for many students (Markovitz, 2003).
An Israel State Comptroller audit (State Comptroller, 2014) states that both the inappropriateness of the curriculum for the educational reality and the dirth of suitably-trained teachers of the subject has led to low achievements in mathematics among Israeli school children. These challenges and lower achievements are compounded for students coping with additional difficulties, as are students with learning disabilities.

Learning disabilities: Definition and features
The controversy regarding the definition of a learning disability has produced several accepted definitions. Learning disability has been defined as late or disturbed development in any of the following: speech, language, reading, spelling, writing, and arithmetic, due to impaired brain function. This definition excludes causes such as intellectual disability, sensory impairment, and educational or cultural factors (National Joint Committee on Learning Disabilities, 2013). According to the Diagnostic and Statistical Manual of Mental Disorders (DSM-V), a person is diagnosed with a learning disability when achievements on individually administered standardized tests for reading, arithmetic, and writing are significantly lower than expected by age, level of education, and IQ, and when these learning problems interfere with academic achievements or other routine activities that require reading, writing, and arithmetic skills (APA, 2013). The US National Joint Committee on Learning Disabilities (NJCLD) has added that these disorders are internal, are assumed to derive from a central neurological dysfunction, and that they can emerge at any age. Although a learning disability can emerge concomitantly with other disabling conditions (such as sensory impairment, intellectual disability, emotional or social disorder, or external conditions such as cultural differences, or inadequate or inappropriate instruction), learning disabilities are not the direct result of these conditions (National Joint Committee on Learning Disabilities, 2013).
According to the United States Individuals with Disabilities Education Act (IDEA) (2018): "Specific learning disability means a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, that may manifest itself in the imperfect ability to listen, think, speak, read, write, spell, or to do mathematical calculations, including conditions such as perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia. Specific learning disability does not include learning problems that are primarily the result of visual, hearing, or motor disabilities, of intellectual disability, of emotional disturbance, or of environmental, cultural, or economic disadvantage." Several points emerge from a synthesis of these different definitions. First, the source of the disability is primary (neurological/cognitive) and not environmental. Second, sensory and emotional disorders, as well as physical disabilities and intellectual disability do not count as causes of learning disability. And third, a marked gap between IQ and academic achievements is material to the condition (National Joint Committee on Learning Disabilities, 2013). In addition to this, it is necessary to distinguish between developmental learning disability and academic learning disability. Developmental learning disabilities are identified at pre-school age. They include delayed acquisition of fundamental skills, and attention, memory, language, perception, motor, and thinking disabilities. Academic learning disability includes impaired reading, writing, spelling, and arithmetic skills, and these are usually acquired during early stages of learning in school (National Joint Committee on Learning Disabilities, 2013).
Students with learning disabilities can have specific disabilities called specific learning disabilities in mathematics that make it harder for them to learn arithmetic. Specific learning disability in mathematics is a specific learning disability that involves difficulty processing numerical and mathematical information despite a normal IQ. Originally, specific learning disabilities in mathematics were believed to be limited to difficulty grasping numbers and quantities, but in time it was understood to include visual, spatial, and verbal difficulties in other mathematical areas. Its definition was revised, therefore, to include a broader group of individuals with learning disabilities (Menon et al., 2020). Today it is evident that students with specific learning disabilities in mathematics have persistent problems implementing basic arithmetic and mathematical facts, and that these problems are not a result of low intelligence or poor education. These problems are often associated with impaired processing of numbers and quantities (Haberstroh & Schulte-Körne, 2019).
Recently, researchers identified impairments in cognitive processing mechanisms that are associated with specific learning disabilities in mathematics. The two most widely studied factors are working memory and cognitive control. Individuals with specific learning disabilities in mathematics exhibit clearly impaired use of suitable arithmetic procedures, which has been ascribed to weaknesses in manipulations of quantities in working memory. These persons also have a consistent pattern of visual-spatial and verbal impairments. Impaired cognitive control also affects problem-solving and performance in several areas of mathematics, for example, in comparing magnitude, logic, and word problems. According to this view, number processing and word problem solving rely on multiple neuro-cognitive components that are deployed by overlapping and unique brain systems. Impairment in any one of these components could be a cause of specific learning disabilities in mathematics (Menon et al., 2020).
Indeed, students with specific learning disabilities in mathematics show substantially reduced performance on a wide range of basic numerical tasks, including judging size and quantity, mapping symbols and representations, mathematical problem solving (Menon et al., 2020) as well as impaired ability to make abstractions, which is fundamental to understanding arithmetic. They also show impaired ability to make discoveries and draw conclusions independently, impaired ability to make generalizations and apply the rule to similar cases, and impaired symbolization and ability to tell the wheat from the chaff. Spatial awareness impairments may make it harder to distinguish sizes or understand spatial concepts (Margalit, 2003;Montague, 2005).

Humor, motivation, and achievements in mathematics learning for students with learning disabilities
Students often perceive mathematics as a threatening, difficult to master subject and their significant adults contribute to demonizing the subject. Classrooms are often highly heterogeneous, and in such environments, lower-achieving students lose their confidence and self-esteem and develop low self-efficacy. A mathematics teacher who is aware of this can use humor to improve the climate in class and interpersonal communications (Berg, 2010;Chiu, 2009).
A study by Ford et al. (2012) compared the achievements of students exposed to cartoons before taking a mathematics exam to achievements of students who were either exposed to nonhumorous songs, or not exposed to anything, before taking the exam. They found that the test group's achievements were higher and suggested that exposure to cartoons before the exam reduced anxiety. In another study (Berk & Nanda, 2006), students who took a humorous version of an exam in theoretical statistics performed differently than the students who took the standard version. It, therefore, seems that humor has an appreciable effect on achievements that could be explained by reduced anxiety.
Although high-achievers in mathematics do not need the encouragement of humor, as they are already self-motivated, students having trouble with mathematics can benefit from appropriate motivation-boosting subject-related humor (Bishara, 2005;Duda, 2010).
To many, the mathematics curriculum implies rigid rules and multiple concepts and principles: students are required to memorize rules, terms, methods, relationships, theorems, and formulas, sometimes without being able to understand them. For example, to cope with equations in mathematics students must be able to memorize certain principles, otherwise they will not be able to make progress with the very extensive curriculum. This is doubly difficult for students with learning disabilities, and underscores the importance of integrating humor in mathematics instruction as a way of adjusting the curriculum according to students' individual abilities (Gazit, 2011).
To summarize, teaching mathematics to children with learning disabilities entails many challenges, so it is important to investigate which teaching approaches work best, and which interventions can reduce anxiety and improve motivation and achievements. The literature regarding the association between using humor to trigger laughter and increased motivation and academic achievements shows that humor can directly benefit both student motivation and their achievements. Many students felt that they learned more when they were taught with humor (Wayne, 2021).
As noted throughout this review, humor can eliminate barriers, increase attention, improve thinking, and boost creativity and self-image in both teachers and students. Humor can improve class climate, reduce anxiety, and possibly support motivation and interest in learning mathematics. Humor can also bolster students' abilities and self-efficacy in the face of challenges (such as mathematics), and achievements (Bishara, 2005;Duda, 2010;Margalit, 2003).
At the same time, there may be drawbacks to using humor in teaching, for example, it may interfere with the learning process, discredit both the teaching and learning process, be perceived as offensive (Baid & Lambert, 2010), cause the message to sound inappropriate or be misunderstood, or create a cynical or disrespectful class atmosphere (Baid & Lambert, 2010;Banas, 2011). Students with learning disabilities may also experience difficulty grasping humor due to delayed development associated with their disabilities and the academic and social competence (Semrud-Clikeman & Glass, 2008).
In light of this, the present study examined how integrating humor in mathematics instruction affects motivation and achievements in students with learning disabilities, as this has yet to be studied in this particular population of students. The little research into the integration of humor in teaching students with learning disabilities shows that humor in the classroom can benefit these students and has no negative effects resulting from the differences in the way their sense of humor develops (Semrud-Clikeman & Glass, 2008). The present study may also shed light on the conflicting findings in the literature regarding using humor in the classroom.

Study hypotheses
This study posed four hypotheses: (a) A positive link will be found between attitude to using humor in mathematics class, motivation, and achievements. I.e., the more positive the attitude to humor in mathematics classes, the greater the student's motivation and achievements in mathematics; (b) the experimental group will show differences in attitude to humor, in motivation, and in achievements between the beginning and the end of the year; (c) attitude to humor is a predictor of achievements in mathematics; and (d) motivation is a predictor of achievements in mathematics.

Participants
A group of 80 sixth-grade students (aged 11-12 years) with learning disabilities participated in this study (50% boys, 50% girls). These were students from four different schools in the center of Israel, with about 20 participants from each school. All four schools are general education schools and all the participating children attend integrated classes. The families of these students are mostly middle-income households, with large families (4+ children) where mothers are homemakers and fathers are employed earning an average wage.
Irrespective of and prior to this study, all participants had undergone a psychological evaluation by the Counseling Service in their area. In Israel, this is a process in which a psychologist diagnoses the type of disorder and administers a Wechsler IQ test (WAIS), and a qualified didactic evaluator uses standardized instruments to evaluate reading, reading comprehension, mathematics, and English and also visual-motor, visual, hearing, language, memory, thinking, and attention skills. Participants' evaluations showed extensive learning difficulties including problems with mathematics and language. A review of these students' records showed that their cognitive abilities were within the normal range.

Research instruments
Data was collected using three instruments: a questionnaire for testing attitude to humor in mathematics classes (Gazit, 2018), a questionnaire about motivation (Roeser et al., 1996), and a mathematics achievement test (Haddad, 2018).

Attitude to teacher's use of humor in mathematics classes
A 20-item questionnaire with statements about various aspects of using humor when teaching mathematics. This questionnaire is based on the Gazit (2018) attitude questionnaire. Items were rated on a five-point Likert scale (1 = disagree strongly, 5 = agree strongly). Attitude to using humor in mathematics classes was calculated based on the answers, and a higher score indicates a more positive attitude, e.g.: "Using humor can improve the atmosphere in mathematics classes"; "Using humor can make teaching more effective". Internal reliability of the general scale (Items 1-20) was α = .89. Items were grouped in five categories: nature of mathematics (Items 4, 5), α = .60; attitude to integrating humor in mathematics instruction (Items 1, 8, 17, 18, 20), α = .67; benefits of integrating humor in mathematics instruction (Items 2,9,7,10,11,15,16), α = .69; drawbacks of integrating humor in mathematics instruction (Items 12, 14), α = .69; teacher status and attitude to teacher (Items 3, 6, 13, 19), α = .68.

Motivation questionnaire
A Hebrew version of the student motivation questionnaire (Roeser et al., 1996) translated by Mevarech, Kramarsky, and Ritz, with some questions about mastering tasks and some based on ability-approach and on ability-avoid goal orientation. There are 17 items with a 5-point scale (1 = disagree strongly, 5 = agree strongly) in this questionnaire. A higher score indicates higher motivation. e.g., "I want to do better in mathematics than other students in my class", "I do my assignments because I'm interested in them". A reliability test of internal consistency (Cronbach's alpha) of the general scale and the three sub-scales indicated reliability: general scale (Items 1-17) α = .88, task goal orientation (Items 1, 4, 5, 7, 10, 15) ɑ = .56; ability-avoid goal orientation (Items 3,6,9,12,13,17), α = .90; ability-approach goal orientation (Items 2,8,11,14,16), α = .73. Note that in both ability scales (approach and avoid) certain items were excluded to improve reliability.

Mathematics achievement test
Mathematics achievement data were collected using a mathematics test (Haddad, 2018). The 10 questions in the test are compatible with the Israeli Ministry of Education curriculum for fifth and sixth grade. Score range was 0-100.

Procedure
The questionnaires were administered twice, once at the beginning of the school year (preintervention) and once at the end of the year (post-intervention) to 80 sixth-grade students with learning disabilities who attend integrated classes at four general elementary schools in the center of Israel. The students studied mathematics with teachers who used humor spontaneously in their teaching. Participants responded to two questionnaires (one for attitude to using humor in mathematics classes and one for motivation) and solved a mathematics test to measure their academic achievements. Students were told that their questionnaires would be anonymous and that there is no single correct answer to any of the questionnaire statements. They were asked to select the response that best reflects their position about each statement. Each participant was asked to state their age, gender and class but to refrain from adding their name. Statements were read to the students, and students marked their answers on their answer sheets. The mathematics achievement test was administered next. All three instruments were administered at the same time to all participants.

Data processing
Averages and standard deviations were calculated for the entire experimental group. Associations between study variables were tested using Pearson correlation, and results from the beginning and the end of the year were compared using dependent sample t-tests. In addition, multiple regression was calculated to test the effect of the predictor variables on mathematics achievements.

Association between attitude to using humor in mathematics and mathematics achievements
The first hypothesis proposed that a more positive attitude to humor in mathematics classes would be associated with greater motivation and better achievements in mathematics. To test this hypothesis Pearson correlations between the indices were calculated. Table 1 shows a correlation matrix for attitude to using humor, motivation, and mathematics achievements.
As hypothesized, study findings as shown in Table 1 indicate a significant positive correlation between all tested indices. In other words, a more positive attitude to using humor in mathematics classes correlates with greater motivation and better achievements in mathematics, with the exception of low correlation between task goal orientation and mathematics achievements, which does not show significance.

Comparing attitude to humor, motivation, and mathematics achievements at the beginning and the end of the year
The second study hypothesis was designed to evaluate whether, on average, there was a difference in motivation and in mathematics achievements between measurements at the beginning and the end of the year. A paired sample t-test was used to test this hypothesis. Attitude to using humor in mathematics instruction was the independent variable and motivation and achievements were dependent variables. Table 2 shows average and standard deviation for motivation and mathematics achievements by attitude to using humor in mathematics instruction.
Looking at the average values in Table 2, it seems that on most measures of attitude to using humor in the mathematics classroom (attitude to incorporating humor in mathematics instruction, .53** .30** -*p < 0.05, **p < 0.01, ***p < 0.001 Note: In this table, a higher score means a more positive attitude to using humor, higher motivation, and better mathematics achievements. benefits of incorporating humor in instruction, drawbacks of incorporating humor in instruction, and teacher status and attitude to teacher), the students in the humor group had improved by the end of the year. For motivation, there were similar findings in the ability-approach goal index. i.e., the students in the humor group improved significantly when comparing the beginning of the year to the end. The findings for ability-avoidance goal were the reverse, as expected, such that the students in the humor group showed a decline when comparing the beginning of the year to the end.

Predicting achievements in mathematics achievements based on use of humor
The third hypothesis was designed to test whether the expected difference in mathematics achievements changed with participants' attitude to using humor. A regression analysis was used to test this hypothesis. Mathematics achievements were the dependent variable and the independent variable was attitude to using humor. Table 3 shows the multiple regression values for mathematics achievements by attitude to using humor in mathematics instruction.
Looking at Table 3, we observe that F(5, 74) = 11.72** and the regression shows that the explained variance is R 2 = .44, p < .01, with only three indices (benefits of incorporating humor in instruction, drawbacks of incorporating humor in instruction, and teacher status and attitude to teacher) contributing significantly to the explained variance. This means that higher average scores for benefits of incorporating humor in instruction, drawbacks of incorporating humor in instruction, and teacher status and attitude to teacher correlate with better achievements in mathematics.

Predicting mathematics achievements based on motivation
The fourth hypothesis was designed to test whether the expected difference in mathematics achievements changes with participants' type of motivation. A regression analysis was used to test this hypothesis. Mathematics achievements were the dependent variable and the independent variable was motivation. Table 4 shows the multiple regression values for mathematics achievements by motivation.
Looking at the regression analysis values in Table 4, we observe that F(3, 76) = 10.43***; the regression shows that the explained variance is R 2 = .29, p < .01, with only the ability-avoidance goal contributing significantly to the explained variance. In other words, the higher the average ability-avoidance goal, the higher the average mathematics achievements.

Discussion and conclusions
The goal of the present study was to test for an association between attitude to using humor, motivation, and mathematics achievements in students with learning disabilities. To do so, linear patterns of associations between these variables were tested. This study also examined patterns of predictor variables of explained variance in mathematics achievements.

Association between attitude to using humor in mathematics and motivation and mathematics achievements
The first hypothesis proposed a positive link between attitude to use of humor in mathematics in class, and motivation and achievements, i.e., a more positive position regarding humor in mathematics classes correlates with greater motivation and achievements in mathematics. This hypothesis has been confirmed and is in line with findings from earlier studies that indicate a positive link between humor, motivation, and mathematics achievements (Alatalo & Poutiainen, 2016;Berk & Nanda, 2006;Bolkan et al., 2018;Ford et al., 2012;Kuperman, 2006;Van Praag et al., 2017).
Note that the one exception is a low, non-significant correlation between task goal orientation and mathematics achievements.
Many researchers have attempted to link humor and mathematics. Low-achieving students may feel insecure and unable to succeed and may have low self-esteem. This points to a need for mathematics teachers to improve class climate and interpersonal communication, and humor can be used to help individuals realize their potential (Berg, 2010;Chiu, 2009). Maimon (2008) notes that encouraging students and boosting their motivation is one way to promote success in mathematics. Motivation is what drives students to achieve goals and succeed. Therefore, using humor when teaching mathematics can improve students' motivation and staying power and this may influence their other school subjects. Arbel (1997) notes that humor plays an important cognitive role in the development of attention and concentration and in improving creativity. So, ability to grasp humor, as well as attention, concentration, and creativity are indicators of high intellectual ability and of potential for success in mathematics.

Comparing attitude to humor, motivation, and achievements in the experimental group at the beginning and the end of the year
The second hypothesis proposed that the experimental group would show differences in attitude to humor, motivation, and achievements between the beginning and the end of the year. The present study confirms this and points to significant differences on most measured indices between the beginning of the year and its end. This is in line with findings from earlier studies that indicate a positive link between humor, motivation, and academic achievements. I.e., the more humor is used in mathematics instruction, the greater the motivation and the better the academic achievements.
Previous studies have indicated that this positive association between humor and motivation and mathematics achievements, as found in the present study, derives from the fact that effective study of mathematics requires high order cognitive processes.
As discussed by Herzog and Stervey (2008), cognitive processes are both flexible and dynamic, and organize the thinking and actions that solving a mathematical problem requires. Humor is one way to relieve strain and prevent stress, reduce anxiety and depression, and improve cognitive ability, motivation, and consistent achievements. It could also be a contributing factor in the cognitive processes required to solve mathematical assignments, because by promoting the cognitive flexibility it takes to solve problems effectively, it allows the person to both focus on their goal and respond flexibly in a dynamic environment.
It is also possible that humor has a more prominent role in solving mathematical problems when the knowledge required is more extensive, the complexity of the problem is greater and the solution requires multiple steps (Toll et al., 2010).

Predicting achievements in mathematics by attitude to humor
The third hypothesis proposed that attitude to humor is a predictor of achievements in mathematics. The present study partly confirmed this hypothesis on two indices: benefits of incorporating humor in instruction, and teacher status and attitude to teacher, which both contributed significantly to the explained variance. I.e. mathematics achievements were better with higher average scores for benefit of incorporating humor in instruction, and teacher status and attitude to teacher. These findings are in line with other studies that have shown the importance of incorporating humor in the classroom and of positive attitude to the teacher (Kuperman, 2006;Zamir, 2007).
Humor can foster creativity by presenting students with novel or unconventional aspects of a problem (Kuperman, 2006). This is particularly meaningful to students with learning disabilities who often struggle to succeed even though their cognitive potential is normal or near-normal (Margalit, 2003). Incorporating humor in mathematics can be useful as a predictor of achievements, and can be used to increase student attention, and improve teacher and student thinking processes, self-image, and creativity (Duda, 2010).

Predicting mathematics achievements by motivation
The fourth hypothesis proposed that motivation is a predictor of achievements in mathematics. The present study partly confirmed this hypothesis with only a single index (ability-avoidance goal) being a significant contributor to variance. In other words, the higher the average abilityavoidance goal, the higher the average mathematics achievements. These findings are in line with other studies that have shown the importance of motivational instruction to improving mathematics achievements (Maimon, 2008;Pintrich & DeGroot, 1990).
Motivation is a process that directs and drives the behavior that keeps a person on target with a specific goal and this is what happens in motivated students who are driven to achieve goals such as understanding the material, or answering questions. Studies have shown that students who set themselves curriculum goals perceive assignments as interesting and thought-provoking, and also tend to engage in thinking activities, use more cognitive strategies, and express willingness to perform mathematical assignments (Maimon, 2008;Pintrich & DeGroot, 1990).
Students with learning disabilities typically have impaired audio processing, memory problems, language disabilities, and meta-cognitive featured (Gazit, 2011). Therefore, we may assume that teaching mathematics in a way that increases their motivation may benefit their learning processes and contribute to better achievements

Conclusions and pedagogical implications
The present study may have both a theoretical contribution as well as a practical one. This study may expand existing theoretical knowledge about the links between attitude to using humor in class, motivation to learn, and mathematics achievements in students with learning disabilities. This can encourage scientific discourse and research about teaching mathematics. In practice, this study can encourage mathematics teachers wishing to improve their students' motivation and understanding to incorporate humor in class. Intervention programs developed specifically for students with learning disabilities should concentrate on teaching how to implement humor in class.

Study limitations and suggested future studies
As in many studies of this type, this study has a number of limitations. This study examined the patterns of association between attitude to incorporating humor in mathematics instruction, and motivation and mathematics achievements by principally using quantitative methods. Future research should incorporate qualitative methods, such as interviews with students and their teachers, which would provide a broader perspective and validate the present study's findings regarding the link between humor, motivation, and mathematics achievements in students with learning disabilities.