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Most research has focused solely on understanding high school or college students' mathematical creative thinking abilities while understanding younger students' creative thinking in mathematics was ignored. These studies of older students have focused mainly on students' creative products rather than creative processes. The authors of the present study investigated four young elementary school students' creative processes through eye-tracking (ET) and stimulated recall interview (SRI) techniques while they engaged in multiple representations (MRs) of mathematical problems. Our qualitative case study revealed what phases four elementary school students' creative processes in MRs involve and how they achieve original ideas. The results revealed that neither Wallas' (1926) creative process of mathematicians nor Schindler and Lilienthal's (2020) creative process of a high school student could fully explain the creative processes of four young elementary school students in the present study. The findings from the present study emphasize that four young students' creative processes are difficult to predict as it is non-linear compared to professional mathematicians' creative process, but young students' creative processes can be demystified through ET and SRI techniques. The present study also emphasizes the importance of external factors (e.g., teachers, peers, environment) for the four elementary school students to get different perspectives to achieve creative ideas in mathematics.

While it is well-documented that students of color and students from low-income communities have often been denied access to a challenging education in mathematics in the United States, less is known about how teachers of color have overcome their deprived educational backgrounds to become teachers of mathematics who implement inquiry-based instructional methods as a means to improve their students' learning and mathematical identities. In this article, we use a sociopolitical theoretical framework to examine how seven elementary school teachers of color characterized their experiences as mathematics students, themselves as teachers of mathematics, and their mathematical identities after experiencing significant professional development in mathematics. All the participants in this study had experienced extensive professional development support in mathematics over a sustained period of time. We demonstrate through the teachers' narratives that, given the deprived mathematics education that the majority of the participants experienced as PK-12 students, having opportunities to participate in significant and focused PD in mathematics over a sustained period transformed how teachers viewed themselves as teachers and positively impacted their mathematical identities.

The purpose of this systematic review is to reveal the research findings that suggest instructional practices to foster the creativity of students in mathematics. Although several studies have investigated the effects of various instructional practices influencing the mathematical creativity of students, little is known about how the findings of this collective body of research contribute to the understanding of what instructional practices should be integrated into a mathematic classroom to further foster the mathematical creativity of students. In this systematic review, the knowledge of instructional practices that foster the mathematical creativity of students were categorized under two main factors including: 1) discipline-specific instructional practices and 2) general instructional practices. The discipline-specific instructional practices were problem-solving, problem-posing, open-ended questions, multiple solution tasks, tasks with more than one correct answer, modeling/model-eliciting activities, technology integration, extendable tasks, and emphasizing abstractness of mathematics. The general instructional practices were providing students with ample time to think creatively about real-world related mathematical problems in a judgment free and collaborative classroom environment so that they take risks to share their mathematical ideas and use informal words. Integrating all of these instructional practices into mathematics classrooms can provide opportunities for students to discover their potential creative abilities in mathematics.

The purpose of this meta-analysis was to examine the effects of Cognitive Behavioral Therapy (CBT) interventions as a clinic-based treatment on students' mathematics anxiety level. A total of 7 studies containing 14 effect sizes were selected for inclusion in the present meta-analysis. Results indicated that the overall effect size was moderate to strong (g = -0.76 with SD = 0.04). The implication from the present study is that CBT can be a useful intervention to reduce students' mathematics anxiety.

The purpose of this study is to observe the changes on pre-service teachers' cognitive (i.e. fluency, flexibility, and originality) and affective outcomes (e.g. perceptions towards creativity-directed tasks, beliefs about the nature of mathematics) related to mathematical creativity after they participated in a creativity-focused mathematics method course. The pre-service teachers (n = 40) were randomly assigned into two groups as the intervention (n = 21) and the control (n = 19). The results revealed that the pre-service teachers who received the intervention developed all of the cognitive and affective outcomes more than the pre-service teachers in the control group (p < 0.05). The implication of these findings is that integrating creativity-directed tasks into mathematics education college courses can better equip pre-service teachers to develop mathematical creative abilities in their future students.

Anxiety is the most common mental health problem that occurs with Autism Spectrum Disorder (ASD), and due to creating a more inclusive learning environment, children with ASD are placed in general education classrooms. Thus, addressing anxiety problems for children with ASD in school settings become critically important. This systematic review and meta-analysis investigated the current qualities of studies and the effects of school-based interventions for reducing anxiety in children with ASD. The study included six studies with a total of 165 participants. A random-effect meta-analysis yielded a moderate overall effect (g = - 0.58, 95% CI [- 0.96, - 0.20], z = - 3.01, p < 0.05) with no significant heterogeneity, Q (5) = 7.31, p = 0.20. Findings of the systematic review indicated that school-based interventions for anxiety problems are still in the early stages, and studies showed significant issues with adaptations of current clinical-based interventions and anxiety measurements to use in school settings for children with ASD. Interpretation of these findings and implications are discussed.

Although algebraic reasoning has been considered as an important factor influencing students' mathematical performance, many students struggle to build concrete algebraic reasoning. Metacognitive training has been regarded as one effective method to develop students' algebraic reasoning; however, there are no published meta-analyses that include an examination of the effects of metacognitive training on students' algebraic reasoning. Therefore, the purpose of this meta-analysis was to examine the impact of metacognitive training on students' algebraic reasoning. Eighteen studies with 22 effect sizes were selected for inclusion in the present meta-analysis. In the process of the analysis, one study was determined as an outlier; therefore, another meta-analysis was reconstructed without the outlier to calculate more robust results. The findings indicated that the overall effect size without an outlier equaled d=0.973 with SE=0.196. Q=20.201 (p<0.05) and I[superscript 2] =0.997, which indicated heterogeneity of the studies. These results showed that the metacognitive training had a statistically significant positive impact on students' algebraic reasoning.

The purpose of this meta-analysis was to examine the effects of writing intervention on students' mathematical attainment based on their achievement (mathematics standardized test scores) and their attitudes toward mathematics (mathematical motivation and interest). Twelve studies with 19 effect sizes were selected for inclusion in the present meta-analysis. Results indicated that the overall effect size equalled 0.42. The small sample size (12 studies) in the present meta-analysis limits the generalizations that might be made regarding the overall impact of writing intervention on students' mathematical attainment. However, the implication from the present study is that integrating writing into mathematics classrooms can be a useful instructional strategy to increase students' mathematics success.

In the current investigation, research studies (n = 30) conducted from 1965 to 2018 were synthesized to examine the mathematics achievement-creativity relationship and the range of factors that could have moderated this relationship. The meta-analysis included sample size of 11,418 and revealed that there was an overall moderate and statistically significant (r = 0.47, p < 0.05) positive correlation between mathematics achievement and creativity. The investigation further revealed that the relationship was constant across sample location but stronger when the relationship was examined with mathematical creativity (r = 0.53, p < 0.05) than with general creativity. Findings from studies conducted after 2000 indicated a stronger relationship between general creativity and mathematics achievement than did findings from studies conducted before 2000. The relationship was the strongest when creativity was measured through the Mathematical Creativity Test (MCT) compared to other measures of general or mathematical creativity. Lastly, the relationship was stronger for elementary and middle school students than for high school students. Possible explanations for these findings in relation to existing theories and the implications for future research are provided.

Teachers need to develop a variety of pedagogical strategies that can encourage precise and accurate communication--an extremely important 21st century skill. Precision with STEM oral language is essential. Emphasizing oral communication with precise language in combination with increased spatial skills with modeling can improve the chances of success in STEM courses and later in making STEM career choices. The participants were 14 middle and high school teachers who participated in a week of professional development (PD). The Aural/Spatial Interactions and Invariant Components of Vocabulary for STEM Content Area Specialists (AS-STEM) was administered to teacher groups to examine how STEM discourses influenced AS-STEM success. This study compared language differences among groups that were more versus less successful at representing unseen 3-D objects by drawing 2-D depictions from oral descriptions from peers. The groups that were more successful, able to produce more accurate depictions, used (a) language type merging that was more coherent and less frequent, (b) language precision that appeared to convey meaning effectively, and (c) validated shared meaning regularly and established these shared meanings efficiently. Thus, teachers who were able to merge language types using precision and jointly took ownership of the tasks were more successful. We trust that this work translates into practice through the awareness teachers had from participation in and discussion of the activities.

MathForward™, developed in 2004-2005 in cooperation with the Richardson (TX) Independent School District, was implemented nationwide in 2007. The program integrates TI technology and professional development while focusing on student achievement and teacher efficacy. This study investigated the effect of the MathForward™ program on student achievement scores of Algebra I students from a southeast Texas high school. The specific purpose of this study was to understand whether there was an effect on students' STARR mathematics scores, accounting for teacher professional development and years of experience. To do this, structural equation modeling (SEM) in M-plus was employed. The result of the present study showed that our model fits well to the data and the explained variance of students' mathematics achievement (R(superscript 2) = 0.14).

Research has shown that most children with emotional disturbance (ED) are struggling to use communication skills and they may tend to use inappropriate behaviours as a form of communication to disclose their needs. A function-based communication intervention might be an effective approach to decrease inappropriate behaviours of children with ED. The purpose of this single-case multiple baseline reversal design (ABAB) study was to examine the effectiveness of the function-based communication intervention for on-task and disruptive behaviours of an 8-year-old student with ED. Functional behavioural assessment (FBA) was conducted and based on the findings of FBA, a colour-coded communication system, was implemented during reading and math classes. The findings indicated that function-based communication intervention was effective in increasing on-task as well as decreasing disruptive behaviours. Furthermore, the function-based communication intervention improved communication between the teacher and the student that resulted in decreasing disruptive behaviours in a general classroom setting. The generalisability of the findings due to the limited number of participants was an important limitation for this study. Future directions, as well as implications for practices, are discussed.

The primary purpose of this current study was to identify knowledge of special education and mental health professionals in anxiety‐related problems of children with autism spectrum disorder (ASD) in four Different Categories: Separation Anxiety (SA), Uncertainty (U), Performance Anxiety (PA), and anxiety Arousal (AA). Three hundred eighteen participants across the United States (199 special education teachers, 97 school counselors, and 22 school psychologists) participated. The finding indicated that special education teachers and school counselors have significantly less training and expertise to identify anxiety symptoms in typically developing children and children with ASD than school psychologists (p <.05). Moreover, school counselors have significantly limited knowledge in identifying and treating anxiety issues in children with ASD (p <.05). Findings showed that school counselors could not determine precisely whether symptoms of uncertainty events existed because of anxiety issues or ASD characteristics. School psychologists and special education teachers identified the uncertainty of children with ASD as characteristics of children with ASD, not anxiety symptoms. Implications were discussed. Practitioner points: Schools can play a significant role in delivering support to anxiety issues of children with autism spectrum disorder (ASD).School psychologists have more knowledge in identifying anxiety symptoms of children with and without ASD, but it is still limited.Special education teachers and school counselors have significantly limited knowledge in identifying and treating anxiety issues in children with ASD. [ABSTRACT FROM AUTHOR]

The purpose of this study was to reveal both the effects of problem-posing interventions on the mathematical creative ability of students and how students' creative self-efficacy in mathematics was related to their mathematical creative ability. Elementary school students (n = 205) were randomly assigned to one of two groups: problem-posing or control. Results showed the mathematical creativity for the problem-posing group increased (p < 0.05) more than for students in the control group (d = 0.77). Results from the Confirmatory Factor Analysis showed that mathematical creativity was a higher order factor that included mathematical creative ability and mathematical creative self-efficacy as first-order factors. Among the implications for this is that integrating problem-posing activities into elementary school mathematics instruction can foster mathematical creativity.

Children with autism spectrum disorder (ASD) are at greater risk for experiencing high levels of anxiety symptoms. Recent evidence suggests Cognitive behavioral therapy (CBT) may also be effective for anxiety reduction in some presentations of ASD. This meta-analysis evaluated twenty-three studies. Results yielded a moderate effect size (g = -0.66) for the reduction of anxiety symptoms. Moderators indicated larger effects for studies were achieved with parental involvement (g = -0.85, p < 0.05) than with child-only treatments (g = -0.34, p < 0.05). Short-term interventions generated a smaller effect (g = -0.37 p < 0.05) than either standard-term (g = -1.02, p < 0.05) or long-term interventions (g = -0.69, p < 0.05). Implications for children with ASD are discussed.

The integration of Science, Technology, Engineering, and Mathematics Project-Based Learning (STEM PBL) into educational curriculum has received much attention because of its strength in improving students' affective engagement. We designed the present study to investigate the effectiveness of STEM PBL lessons on 9th grade students' development of affective mathematics engagement. The affective mathematics engagement of two groups of participants (STEM PBL and non-STEM PBL) were compared (N = 147). The results showed group differences in STEM PBL versus non-STEM PBL lessons were statistically significant (t = 5.587, p < 0.001, d = 0.960). In particular, STEM PBL students had greater positive affective mathematics engagement in terms of mathematical self-acknowledgement and value as compared to the non-STEM PBL students. The results of the study indicate that highly situated and integrated instruction has a positive impact on students' perceptions of their affective mathematics engagement.

The purpose of this study is to compare students' mathematics achievement growth rate in Texas science, technology, engineering, and mathematics (T-STEM) academies to students' mathematics achievement growth rate in traditional public high schools. Forty-six schools, 23 of which were T-STEM academies and 23 of which were matched non-STEM schools, were included in this study. A hierarchical linear modeling method was conducted. The result of the present study revealed that there was no difference in students' mathematics achievement growth rate in T-STEM academies compared to students' mathematics achievement growth rate in comparison schools. However, in terms of ethnicity, the results indicated that African American and Hispanic students in T-STEM academies outperformed African American and Hispanic students in comparison schools on their mathematics growth rate.

Gender difference on spatial visualization has been considered an important factor that impacts the gender gap in academic performance in STEM-related disciplines. The purpose of this meta-analysis was to examine the gender difference on spatial visualization between STEM and non-STEM undergraduate majors. Twenty effect sizes representing STEM majors' spatial ability and 14 effect sizes representing non-STEM majors' spatial ability were included in the present meta-analysis. Results indicated that the overall effect size equalled 0.613 (95% CI = [0.444, 0.782]) in STEM and 0.481 (95% CI = [0.359, 0.604]) in non-STEM. These findings showed that the gender differences on spatial visualization were statistically significant in both STEM and non-STEM majors. The gender difference on spatial visualization in STEM was larger than the gender difference on spatial visualization in non-STEM. In addition, male students' spatial visualization ability was higher than female students' spatial visualization in both STEM and non-STEM majors.

Problem posing is the act of creating one's own problems, unlike the traditional practice of solving problems posed by others. Problem posing is not a commonly taught topic. Though some students have difficulties acquiring problem-posing skills, the positive effects are far reaching. A quasi-experimental research design was used to determine the growth in problem-posing and -solving skills in a low socio-economic status rural elementary school. Teachers conducted mathematics learning centres daily while researchers conducted research-based intervention activities for 3 months. A short quiz was administered to students in grades 2-5 (N = 45) pre and post measuring problem-solving and problem-posing changes. A statistically significant difference (p < 0.05) was noted in both problem solving and problem posing. Results indicate that explicitly teaching problem posing in elementary classrooms is a worthwhile endeavour.

The purpose of this paper is to demonstrate Hispanic students' mathematics achievement growth rate in Inclusive science, technology, engineering, and mathematics (STEM) high schools compared to Hispanic students' mathematics achievement growth rate in traditional public schools. Twenty-eight schools, 14 of which were Texas STEM (T-STEM) academies and 14 of which were matched non-STEM schools, were included in this study. A hierarchical linear modelling method was conducted. The result of the present study revealed that there was no difference in Hispanic students' mathematics achievement growth rate in T-STEM academies compared to Hispanic students' mathematics achievement growth rate in comparison schools. However, in terms of gender, the results indicated that female Hispanic students in T-STEM academies outperformed female Hispanic students in comparison schools in their mathematics growth rate.

Previous research identified a strong correlation between mathematics and science performance albeit for small samples of students. Even though there was a high correlation between mathematics and science performance, researchers examining students' STEM achievement investigated mathematics and science achievement separately. The present study brings science and mathematics objectives together to constitute a higher order STEM assessment model. Data (science and mathematics scores) were gathered from 231,966 students (52% female) who were in 11th grade and took the state mandated test in 2013. A second-order confirmatory factor analysis was used to create a STEM assessment model. The fit indices showed indicated it was an adequate model fit for the data. However, the lack of assessments of technology and engineering objectives taught in K-12 make estimating the effectiveness of STEM teaching and learning tenable at best.

The purpose of the study was to explore the development of discourses that emerge as a result of inservice teachers being engaged in a richly situated technological task that incorporated geometric spatial sense development and the engineering design processes. Typically, learning has been approached as a discrete set of tasks to be mastered without regard for how expressed language within context develops. Secondary teachers (N = 26) who attended a week-long residential professional development program at a land grant university learned to use Google Sketch-Up® to design 3-dimensional (3-D) objects that were created using 3-D printers. Data were collected during an aural spatial visualization test that required language be used to describe 3-D objects to others who created 2-D drawings. Digital audio recordings of these interactions were analyzed. Results indicated language emerged through a variety of discourses each characterized by distinct languages: analogous, technical, and clarifying. The discourses were mediated by cognitive negotiation that allowed meaning to ascribe with sense carrying capacity that was occasionally hindered by terminological ambiguity. Implications of this study are that designing and creating 3-D objects using 3-D printers in classrooms may support opportunities for engaging in and practicing engineering design processes while developing disciplinary language, and spatial ability.

MathForward is a program that provides teacher professional development and integrates the use of technology as a tool in the classroom. The present study examined students' mathematics growth from 2012 to 2013 and observed how students' mathematics scores changed after their school implemented the MathForward program. The sample consisted of two years of the State of Texas Assessments of Academic Readiness (STAAR) test data for a total of 563 students. The participants took the first STAAR examination in 2012 at the end of 7th grade and took the second examination in 2013 at the end of 8th grade. In general, regardless of background or student characteristic, pupils increased their mathematics STAAR test scores statistically significantly (p < 0.05) with the Cohen's d effect size of 0.26. Properly implemented, MathForward could be useful in raising the mathematics achievement of students.

The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold misconceptions and have difficulties with inequalities, but college students also possess some of these same misconceptions, thus demonstrating difficulties in solving and interpreting inequalities. This research specifically focused on mathematics pre-service teachers' understandings of linear and quadratic inequalities to determine whether they possess common misconceptions and difficulties with inequalities. Results provided evidence that many pre-service teachers have misconceptions (only one value makes inequality correct, and treating inequality's solution as the same way treating equality's solution) and difficulties (e.g., lack of understanding what inequalities' questions ask to find, having trouble with representing inequalities' solutions, and arithmetic errors) that cause them to misunderstand inequalities.

This study examined the student-level (i.e., gender, home language, and immigration status) and school-level (i.e., school economic disadvantage status) variability of the students' affective mathematics engagement. It was hypothesized that there is a school effect that contributes toward explaining differences in affective mathematics engagement besides the student-level differences. For the sake of the nested structure of the data in Trends in International Mathematics and Science Study (TIMSS), we used the Hierarchical Linear Modeling (HLM) methodology. There were 10,221 students from 246 schools in the study. The results of this study explained 5.3% of variance in students' affective mathematics engagement by school-mean economic disadvantage status, where students' demographic factors explained 1.2%. The present study contributed to a better understanding of the opportunity to learn variables at the student- and school-level in students' affective mathematics engagement. [ABSTRACT FROM AUTHOR]