Literature Review
Teach Ourselves: Technology to Support Problem Posing in the STEM Classroom
Beal, C. R. (2012). Teach Ourselves: Technology to Support Problem Posing in the STEM Classroom. Creative Education, 03(04), 513–519. doi:10.4236/ce.2012.34078
In this article researchers tried to address low achievement, performance an interest in science, technology, engineering, and mathematics (STEM) fields by American students. Repeatedly students from America score well below nations of similar economic development in STEM areas. This lack of achievement in STEM areas is even more striking when you consider changes in social media and technology that allow for much more creativity by the user in a shift toward Web 2.0.
In a Web 2.0 world, education changes from a passive consumer model to a content creation model. Unfortunately, Web 2.0 has proliferated in student’s non-school lives, it has not caught on in the classroom. Most students spend the majority of time answering questions posed and created by others, or what is known as the traditional model of education.
The author then discusses the need to integrate problem posing into the classroom. Problem posing is when students generate problems, questions and products by using what they already know or seeking new information from available sources. Teachers report that using problem posing created higher levels of interest and engagement as well as reduced math anxiety. At the same time, using problem posing requires more effort in grading individual projects and better classroom management by teachers.
To determine if problem posing is a worthwhile endeavor, researches developed Teach Ourselves, a web-based STEM application. This application allowed students to generate problems of their own, or to work on premade problems, with a higher level of points possible on the student made problems. If students start a problem and fail, they are presented with help materials. Also, classmates are allowed to give each other feedback with thumbs up or a flag type of system.
224 middle school students were studied. Over course of the study students created 961 new original problems. The number of problems accepted by the instructors for each student ranged from zero to nine. Interestingly, 14.3 percent of the sample did not produce any problems that were accepted by teachers. Meaning, these students created problems, but they were unable to complete the process to proficiency. Also, many students chose to work on the problems already created, and simply focused on doing more of these problems to offset the higher point value of the student-created problems.
In summary, the data collected in this study shows that students learned a lot from generating their own work, even though not all of them were able to complete these problems fully. Additionally, this study suggests two things. Middle school students would prefer to answer premade problems. The second item, students learn a lot from coming up with new content or problems on their own. Now the trick to find a balance, where students are producing content but also being successful.
How do Students’ Mastery and Performance Goals Relate to Math Anxiety?
Furner, J. M., & Gonzalez-DeHass, A. (2011). How do Students’ Mastery and Performance Goals Relate to Math Anxiety? Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 227–242.
The goal of this paper is to dissect and analyze the causes of math anxiety. Specifically, how math anxiety is related to teacher practices and how to reduce anxiety amongst students through a mastery oriented classroom. Consider most students do not start school with math anxiety. Therefore, math anxiety must be related to math instruction, classroom practice, school structure or some combination thereof.
Teacher practices that increase student math anxiety include, assigning the same work for everyone, covering the book start to finish, giving written work every day, accepting only one way to complete a problem, and giving math work as punishment for misbehavior. These classroom practices can be compounded by a teacher who is not trained in math or does not want to be teaching math. Teachers outside of their normal role or subject matter often convey through their voice, tone and methods that math is hard and something to be avoided at all costs. All of this followed by students going home to parents who convey their disgust and difficulty with math.
Additional to teacher practices, the types of goals students set for math, lead to differing levels of anxiety. Mastery goals are goals that have growth and improvement at heart. Students who set mastery goals tend to have less anxiety. Teachers and schools need to make it clear to students the importance of showing growth and improvement versus goals aimed at getting good grades. Mastery goals encourage students to focus on growing instead of focusing on a grade or being compared to other students. This can also lead to a decrease in negative behaviors by students.
When a culture of mastery has been established, teachers need to provide tasks are reasonably challenging, emphasize understanding and improvement and connect to the real world. Real world connections make the material more authentic and perceived as valuable to the student. To build mastery focused classrooms teachers should also consider allowing some student choice and use cooperative learning.
When evaluating students to reduce math anxiety, it is best to use standards based grading versus bell curved, “standard” grading methods. Differing methods of evaluation may include “standard” models of testing, portfolios and performance assessments.
Gender Similarities in Math Performance from Middle School through High School
Scafidi, T., & Bui, K. (2010). Gender Similarities in Math Performance from Middle School through High School. Journal of Instructional Psychology, 37(3), 252–255.
The goal of this paper is to build upon work done by Hyde et al (2008) which found gender similarities in standardized test performance. According to Hyde et al (2008) there is no statistical significant difference between gender and math ability, despite strong cultural stereotypes. These findings often fly in the face of beliefs held by parents, teachers and even girls themselves.
Hyde et all (2008) only focused on ten states and this study uses nationwide data providing a much larger sample. In addition, this analysis modified the work done by Hyde et all (2008) to indicate differences in gender achievement based on race, socioeconomic status and math level from middle school onward.
Scafidi & Bui, 2010 used data from the National Education Longitudinal Study. The NELS offered data on 24,599 eighth graders. These students were then retested in their tenth and twelfth grade years. This data was then used to incorporate the above characteristics of race, socioeconomic status and math level. Only 9,813 girls from the NELS had complete data and were used for this examination.
The results of this study show no correlation of gender to test scores. Moreover, there is no correlation between test score and race, socioeconomic status or math level. The results suggest that common stereotypes about girls and math ability are a myth and stand against scientific research. It is impressive that girls compare similarly to boys on standardized math tests, given all of the social stereotypes regarding female math ability in our society.
Based on these finding and those of Hyde et al (2008), it is imperative for teachers and parents to inspire and nurture girls’ math abilities. Additionally, critical skills such as perseverance and doing well in math must be celebrated, so girls can go to prepare themselves for careers and fields that require strong math skills. Careers that require high level math ability pay more, which is a strong selling point.
Cooperative Learning vs. Direct Instruction: Using Two Instructional Models to Determine Their Impact on Student Learning in a Middle School Math Classroom
Duff, Jenna. “Cooperative Learning vs. Direct Instruction: Using Two Instructional Models to Determine Their Impact on Student Learning in a Middle School Math Classroom.” Education Senior Action Research Projects, May 9, 2012. http://scholar.valpo.edu/sarp/5.
Often math is not a favorite subject of middle school students. The most common method of instruction is direct instruction. The teacher is the information giver and the student sits in class and tries to absorb as much information as possible. This sequence continues for a while, then a test is given. The author of this paper had a goal to determine if there was a difference in learning with direct instruction versus cooperative learning.
The goal of cooperative learning is to move from wrote instruction to using your interpersonal skills and manipulating objects and tools to learn. There are five parts of cooperative learning:
•Interdependence-relying on other students
•Face to face interaction- discussion and externalization
•Individual work – completing work on their own
•Communication and social skills – being able to express ideas to others
•Group work-challenging ideas and delving deeper to material
Cooperative learning should be used when the following are present:
•Learning goals are highly important
•Mastery and retention are important
•A task is complex or conceptual
•Problem solving is desired
•Divergent thinking or creativity is desired
•Quality of performance is expected
•Higher-level reasoning strategies and critical thinking are needed
The study included fifteen students in the sixth grade. These students are in the eleven to twelve age range and included seven boys and eight girls. Work on this paper was collected over two chapters of math. One chapter was dedicated to direct instruction and the second chapter was dedicated to cooperative learning.
In the end the teacher was surprised that grades were higher at the end of chapter for the direct instruction unit. However, from survey results the cooperative learning activities and lessons were more enjoyable to the students and students made more connections to their lives. These connections are invaluable and should not be taken lightly.
Beal, C. R. (2012). Teach Ourselves: Technology to Support Problem Posing in the STEM Classroom. Creative Education, 03(04), 513–519. doi:10.4236/ce.2012.34078
In this article researchers tried to address low achievement, performance an interest in science, technology, engineering, and mathematics (STEM) fields by American students. Repeatedly students from America score well below nations of similar economic development in STEM areas. This lack of achievement in STEM areas is even more striking when you consider changes in social media and technology that allow for much more creativity by the user in a shift toward Web 2.0.
In a Web 2.0 world, education changes from a passive consumer model to a content creation model. Unfortunately, Web 2.0 has proliferated in student’s non-school lives, it has not caught on in the classroom. Most students spend the majority of time answering questions posed and created by others, or what is known as the traditional model of education.
The author then discusses the need to integrate problem posing into the classroom. Problem posing is when students generate problems, questions and products by using what they already know or seeking new information from available sources. Teachers report that using problem posing created higher levels of interest and engagement as well as reduced math anxiety. At the same time, using problem posing requires more effort in grading individual projects and better classroom management by teachers.
To determine if problem posing is a worthwhile endeavor, researches developed Teach Ourselves, a web-based STEM application. This application allowed students to generate problems of their own, or to work on premade problems, with a higher level of points possible on the student made problems. If students start a problem and fail, they are presented with help materials. Also, classmates are allowed to give each other feedback with thumbs up or a flag type of system.
224 middle school students were studied. Over course of the study students created 961 new original problems. The number of problems accepted by the instructors for each student ranged from zero to nine. Interestingly, 14.3 percent of the sample did not produce any problems that were accepted by teachers. Meaning, these students created problems, but they were unable to complete the process to proficiency. Also, many students chose to work on the problems already created, and simply focused on doing more of these problems to offset the higher point value of the student-created problems.
In summary, the data collected in this study shows that students learned a lot from generating their own work, even though not all of them were able to complete these problems fully. Additionally, this study suggests two things. Middle school students would prefer to answer premade problems. The second item, students learn a lot from coming up with new content or problems on their own. Now the trick to find a balance, where students are producing content but also being successful.
How do Students’ Mastery and Performance Goals Relate to Math Anxiety?
Furner, J. M., & Gonzalez-DeHass, A. (2011). How do Students’ Mastery and Performance Goals Relate to Math Anxiety? Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 227–242.
The goal of this paper is to dissect and analyze the causes of math anxiety. Specifically, how math anxiety is related to teacher practices and how to reduce anxiety amongst students through a mastery oriented classroom. Consider most students do not start school with math anxiety. Therefore, math anxiety must be related to math instruction, classroom practice, school structure or some combination thereof.
Teacher practices that increase student math anxiety include, assigning the same work for everyone, covering the book start to finish, giving written work every day, accepting only one way to complete a problem, and giving math work as punishment for misbehavior. These classroom practices can be compounded by a teacher who is not trained in math or does not want to be teaching math. Teachers outside of their normal role or subject matter often convey through their voice, tone and methods that math is hard and something to be avoided at all costs. All of this followed by students going home to parents who convey their disgust and difficulty with math.
Additional to teacher practices, the types of goals students set for math, lead to differing levels of anxiety. Mastery goals are goals that have growth and improvement at heart. Students who set mastery goals tend to have less anxiety. Teachers and schools need to make it clear to students the importance of showing growth and improvement versus goals aimed at getting good grades. Mastery goals encourage students to focus on growing instead of focusing on a grade or being compared to other students. This can also lead to a decrease in negative behaviors by students.
When a culture of mastery has been established, teachers need to provide tasks are reasonably challenging, emphasize understanding and improvement and connect to the real world. Real world connections make the material more authentic and perceived as valuable to the student. To build mastery focused classrooms teachers should also consider allowing some student choice and use cooperative learning.
When evaluating students to reduce math anxiety, it is best to use standards based grading versus bell curved, “standard” grading methods. Differing methods of evaluation may include “standard” models of testing, portfolios and performance assessments.
Gender Similarities in Math Performance from Middle School through High School
Scafidi, T., & Bui, K. (2010). Gender Similarities in Math Performance from Middle School through High School. Journal of Instructional Psychology, 37(3), 252–255.
The goal of this paper is to build upon work done by Hyde et al (2008) which found gender similarities in standardized test performance. According to Hyde et al (2008) there is no statistical significant difference between gender and math ability, despite strong cultural stereotypes. These findings often fly in the face of beliefs held by parents, teachers and even girls themselves.
Hyde et all (2008) only focused on ten states and this study uses nationwide data providing a much larger sample. In addition, this analysis modified the work done by Hyde et all (2008) to indicate differences in gender achievement based on race, socioeconomic status and math level from middle school onward.
Scafidi & Bui, 2010 used data from the National Education Longitudinal Study. The NELS offered data on 24,599 eighth graders. These students were then retested in their tenth and twelfth grade years. This data was then used to incorporate the above characteristics of race, socioeconomic status and math level. Only 9,813 girls from the NELS had complete data and were used for this examination.
The results of this study show no correlation of gender to test scores. Moreover, there is no correlation between test score and race, socioeconomic status or math level. The results suggest that common stereotypes about girls and math ability are a myth and stand against scientific research. It is impressive that girls compare similarly to boys on standardized math tests, given all of the social stereotypes regarding female math ability in our society.
Based on these finding and those of Hyde et al (2008), it is imperative for teachers and parents to inspire and nurture girls’ math abilities. Additionally, critical skills such as perseverance and doing well in math must be celebrated, so girls can go to prepare themselves for careers and fields that require strong math skills. Careers that require high level math ability pay more, which is a strong selling point.
Cooperative Learning vs. Direct Instruction: Using Two Instructional Models to Determine Their Impact on Student Learning in a Middle School Math Classroom
Duff, Jenna. “Cooperative Learning vs. Direct Instruction: Using Two Instructional Models to Determine Their Impact on Student Learning in a Middle School Math Classroom.” Education Senior Action Research Projects, May 9, 2012. http://scholar.valpo.edu/sarp/5.
Often math is not a favorite subject of middle school students. The most common method of instruction is direct instruction. The teacher is the information giver and the student sits in class and tries to absorb as much information as possible. This sequence continues for a while, then a test is given. The author of this paper had a goal to determine if there was a difference in learning with direct instruction versus cooperative learning.
The goal of cooperative learning is to move from wrote instruction to using your interpersonal skills and manipulating objects and tools to learn. There are five parts of cooperative learning:
•Interdependence-relying on other students
•Face to face interaction- discussion and externalization
•Individual work – completing work on their own
•Communication and social skills – being able to express ideas to others
•Group work-challenging ideas and delving deeper to material
Cooperative learning should be used when the following are present:
•Learning goals are highly important
•Mastery and retention are important
•A task is complex or conceptual
•Problem solving is desired
•Divergent thinking or creativity is desired
•Quality of performance is expected
•Higher-level reasoning strategies and critical thinking are needed
The study included fifteen students in the sixth grade. These students are in the eleven to twelve age range and included seven boys and eight girls. Work on this paper was collected over two chapters of math. One chapter was dedicated to direct instruction and the second chapter was dedicated to cooperative learning.
In the end the teacher was surprised that grades were higher at the end of chapter for the direct instruction unit. However, from survey results the cooperative learning activities and lessons were more enjoyable to the students and students made more connections to their lives. These connections are invaluable and should not be taken lightly.