STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 2 STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 3 Acknowledgements I would like to thank the Davis School District for giving this opportunity to me to get a teaching license and I would like to thank Weber State University for providing the opportunity to finish out with a Master’s Degree. I would also like to thank my mother and my grandmother who are so very educational driven that they pushed me to finish this degree. My mother is an excellent educator and an even better friend. My grandmother, who is no longer with us was also an excellent educator and a great example to look to in her life. I would like to thank my chair for being so kind and giving to my situation. Your notes and edits have been so helpful and each change you requested was made and I never felt uneasy about making the changes. I would like to thank my committee as well who made such great suggestions to my teaching and curriculum and I am excited to try them. I would also like to thank Dr. Louise Moulding who truly took my 9th grade writing ability and turned it into what a graduates writing should be. Your blunt and concise comments were always what I needed to hear. You are an excellent educator and I thoroughly enjoyed all of your classes. Lastly, I want to thank my husband and two wonderful children. Even though we are both pushing through school and our life is crazy chaos, it is lovely crazy chaos and I would not want to spend it with anyone else. Soon our two babies will grow up and we will miss them being so little, let’s enjoy this time as much as we can – I love you! STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 4 Table of Contents NATURE OF THE PROBLEM…………………………………………………………………..7 Literature Review………………………………………………………………………….9 Mathematics Self-Efficacy………………………………………………………..9 Mathematics Self-Concept………………………………………………………12 Explaining the Gaps……………………………………………………………..13 Course Repetition………………………………………………………………..16 Postsecondary Remedial Coursework…………………………………………...16 Potential Solution………………………………………………………………..18 Flipped classrooms……………………………………………………19 Application of the flipped classroom………………………………….20 Summary…………………………………………………………………………21 PURPOSE……………………………………………………………………………………….23 METHOD………………………………………………………………………………………..24 Context…………………………………………………………………………………..25 Setting……………………………………………………………………………25 Scope of Project……………………………………………………………………….....26 Procedure………………………………………………………………………………...27 Curriculum………………………………………………………………………28 Evaluation………………………………………………………………………………31 DISCUSSION…………………………………………………………………………………32 Successes………………………………………………………………………………33 STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 5 Struggles and Recommendations………………………………………………………35 Limitations……………………………………………………………………………..36 REFERENCES…………………………………………………………………………………37 STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 6 List of Figures Figure 1. Screen shot of Commons link………………………………………………………29 Figure 2. Screen shot of search bar……………………………………………………………29 Figure 3. Screen shot of Chapter 14 Module…………………………………………………..30 Figure 4. Screen shot of Files link……………………………………………………………...30 STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 7 Abstract Many students struggle in their mathematics course required for their bachelor’s degree. There are many reasons that they may struggle, some include a lack of mathematics self-efficacy and thus they do not have the confidence to complete the course. Other reasons may be that they simply are not prepared to take the course because they are missing important mathematical concepts and skills. To solve this problem these struggling students are given the opportunity to take their required mathematics course for college in the secondary setting as a concurrent enrollment course. This course is then extended to a full year instead of a semester. The two semesters allow the students time to fully learn the material and gain the confidence needed to successfully pass the course. The course is partially taught through a flipped classroom, which helps the students better conceptualize the ideas and gain good mathematics self-efficacy. The curriculum for this course is presented in this project and the discussion states that the curriculum is well prepared. The students are also mentioned in the discussion and they were all successful in passing the course. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 8 NATURE OF THE PROBLEM Students who do well in a mathematics course are more likely to develop confidence that they can do well in subsequent mathematics courses. Self-concept and self-efficacy build this confidence that support one's belief in themselves to do well (Pajares & Miller, 1994). Mathematics self-efficacy is defined as the confidence in one’s self to successfully accomplish a specific task or solve a problem (Hackett & Betz, 1989). Mathematics self-concept taps into the judgments of one’s self as a student. Pajares and Miller stated, “The course-specific [mathematics] self-concept question, ‘Are you a good mathematics student?’ taps different cognitive and affective processes than the [mathematics] self-efficacy question, ‘Can you solve this specific problem?’” (1994, p. 194) When students do not do well in a mathematics course, they do not build the confidence to help them succeed in subsequent mathematics courses. Students develop a low mathematics self-efficacy and mathematics self-concept because of the lack of confidence they gained in their mathematics course (Pajares & Miller, 1994). In addition to doing poorly in mathematics due to low self-confidence, students may struggle mathematically because they simply are not grasping the material like other students. Tall and Razali (1993) discussed that students who struggle are not seeing the process of solving a mathematics problem turn into a concept. The struggling students are then more likely to fail because they can only think about individual processes instead of understanding the mathematics conceptually. Long, Iatarola, and Conger (2009) researched to find the gaps in student mathematics education which supported the idea that students are not learning the material well enough to show they understand the concepts. They identified that students are receiving passing grades without learning the material required for the course. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 9 Struggling students need to receive remediation in mathematics rather than repeating the course. Shepard and Smith (1990) did a research synthesis on grade retention and found that repeating students are more likely to drop out of high school. Even when students complete the requirements to graduate from high school, about thirty percent of the United States college freshman are not prepared for college level mathematics (Long et al., 2009). Students who need remedial post-secondary education can become just as successful as students who do not; however, going through the remedial education can be expensive for both the student and the university (Long et al., 2009). A potential solution to help the students who need remedial post-secondary mathematics education is first allowing the struggling students to attain success, by performing well on mathematical assessments (Tall & Razali, 1993). This will build up their confidence giving them time to rebuild a strong mathematics self-efficacy and mathematics self-concept (Pajares & Miller, 1994). The students also need to learn how to think more conceptually rather than procedurally. This cannot be done by isolating procedures and trying to give them more practice with problems they do not understand. Tall and Razali (1993) suggest “to teach problem-solving strategies in a separate course from those courses teaching mathematical content and procedures” (p. 15). What was unknown and needed to be figured out is a way to modify an existing mathematics course to allow students to attain success and learn problem solving skills by extending a semester long concurrent enrollment college mathematics course into a full year. The first semester taught the content in a very traditional method, so the students have an idea of what the course is about. The second semester flipped the classroom allowing the students the time they need to learn how to think conceptually without having more content given to them. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 10 Flipped classrooms allow students to actively engage in the material (Bishop & Verleger, 2013). Flipped classrooms are defined to be the opposite of a traditional classroom. Students watch a video lecture online at home and complete some sort of learning activity on their own. In class the teacher acts more as a facilitator to lead a discussion about the material and then the students dive into problems to solve together. This allows the students time with the instructor to do more challenging problems and they can then collaborate with each other to develop their conceptual thinking (Bishop & Verleger, 2013). This success would also give the students confidence to build up their mathematics self-efficacy and concept. When this was done the students became successful in their required mathematics course for post-secondary education. Literature Review Before examining ways in which struggling students can be supported in becoming college ready, it is important to define and explain mathematics self-efficacy and mathematics self-concept, because it supports students in their mathematics courses. It is also important to explain why and how students develop gaps in their mathematics education and how these gaps will affect them in their future mathematics courses. This struggle will continue to follow them into their post-secondary education even if their post-secondary education starts as a concurrent enrollment course in the secondary setting. The research behind the flipped classroom is imperative to understand as well because it is critical in helping students attain success and learn how to think. Mathematics Self-Efficacy Mathematics self-efficacy is the ability to believe in one’s self to correctly complete a specific mathematical problem and/or task (Hackett & Betz, 1989). Hackett and Betz created this definition from Bandura’s (1977) theory of self-efficacy. Bandura defined self-efficacy to be a STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 11 person’s belief in their ability to successfully perform a given task or behavior. When one makes goals to accomplish a task and then successfully completes the task, they experience satisfaction which gives them desire to reach the satisfaction again (Bandura & Schunk, 1981). This will then give them an intrinsic interest in the task. The exact opposite can happen as well. When one does not successfully complete a goal, it creates a negative feeling which makes one not want to complete the task again (Bandura & Schunk, 1981). The cognitive process was studied to find that self-efficacy is directly related to behavior patterns (Bandura, 1977). When someone observes another’s behavior, that can start the cognitive process for a change in their own behavior if the one observing finds the behavior of the other stimulating. Students observe their teacher’s patterns and behaviors when learning. The student can strengthen the behavior learned by receiving feedback from the teacher and improving their performance on the skill or problem they are solving. The feedback can solidify the performance of the student and in return make the new behavior more permanent (Bandura, 1977). Behavior is driven by self-efficacy. Efficacy is the belief that your behavior will lead to certain outcomes. If the belief is strong enough, the behavior will be enacted. If it is not strong, the behavior will be avoided (Bandura, 1977): Not only can perceived self-efficacy have directive influence on choices of activities and settings, but, through expectations of eventual success, it can affect coping efforts once they are initiated. Efficacy expectations determine how much effort people will expend and how long they will persist in the face of obstacles and aversive experiences. The stronger the perceived self-efficacy, the more active the efforts. (p. 194) The effort put forth to do difficult tasks must be strong enough to be able to successfully complete such tasks. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 12 Further defining self-efficacy can be stated as a belief that one can do or perform a task well (Stajkovic & Luthans, 1998). This expansion on the research of Bandura discovered that when one thinks they are very efficient it will trigger enough determination to create effective results, while the ones with low self-efficacy will probably terminate their determination early and fail on the given task. Stajkovic and Luthan’s (1998) meta-analysis was specifically about how self-efficacy is directly related to work performance; when one begins their work with low confidence, their efforts to be successful in the coursework are most likely to fail. To be successful, “performers must have an accurate knowledge of the tasks they are trying to accomplish” (Stajkovic & Luthan, 1998, p. 241). To truly have a strong self-efficacy to successfully complete a complex task it requires “greater demands on required knowledge, cognitive ability, memory capacity, behavioral facility, information processing, persistence, and physical effort” (Stajkovic & Luthan, 1998, p. 241). Self-efficacy’s relation to work can easily be applied to a mathematics course (Hackett & Betz, 1989). Mathematics and self-efficacy were studied together, and the definition of self-efficacy held true with mathematical tasks, resulting in a definition of mathematics self-efficacy. The participants of this study were 153 women and 109 men in college. The study found that mathematics self-efficacy is what gave the participants the most confidence when presented with a mathematical task or problem (Hackett & Betz, 1989). When students do not do well in a mathematics course, they do not build the confidence to help them succeed in subsequent mathematics courses. Students develop a low mathematics self-efficacy which creates negative feelings, so they do not have interest in trying to do well in subsequent mathematics courses (Pajares & Miller, 1994). STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 13 Furthermore, Parajes and Miller (1994) considered a study by Bandura (1986) where he found that low mathematics self-efficacy can create mathematics anxiety. It was then studied whether mathematics anxiety had an effect on mathematics self-efficacy, and it did not. If a student was able to successfully complete a task or problem, their mathematics anxiety did not have an effect on their ability to perform due to their self-efficacy towards the task. Thus, as long as the student believes they can be successful, the anxiety will not change this belief. It is only when the student does not have this belief will the mathematics anxiety set it and start to take effect. Mathematics Self-Concept The relationship between self-efficacy and students studying mathematics was further studied and it was found that a student’s mathematics self-concept also had effect on a student’s mathematical ability (Pajares & Miller, 1994). Mathematics self-concept is how one views themselves in the field of mathematics. When comparing mathematics self-concept to mathematics self-efficacy, mathematics self-concept is how one would respond to the question, “Are you a good mathematics student?” Whereas mathematics self-efficacy is how one would respond to the question, “Can you solve this specific mathematics problem?” (Pajares & Miller, 1994). The development of mathematics self-concept can be related to Felson’s (1984) study of academic self-concept. This is one’s ability to perceive their own ability in a given subject matter. How one views themselves effects one’s performance in that subject matter (Felson, 1984). This perception was also affected by the anxiety that one may have towards the subject. As previously discussed, a low mathematics self-efficacy can create mathematics anxiety and this anxiety effects one’s mathematics self-concept. However, Bandura (1986) stressed that STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 14 although mathematics self-concept and mathematics self-efficacy are both predictors of how well one will do in mathematics, they are different phenomena. When studying 350 students preparing for college, Pajares and Miller (1994) found the strongest correlation between mathematics self-efficacy and performance. The students with a strong mathematics self-efficacy outperformed the students who had a low mathematics self-efficacy. Other aspects of the study showed that mathematics self-concept, anxiety, and gender, had some effect on the student’s ability to achieve, but it was not as significant as mathematics self-efficacy. It is important to note that the confidence that students receive when accomplishing mathematical tasks is truly what affects their ability to perform in a mathematics class. Whether the student has the thought that they may be no good at mathematics does not actually matter if within the class they can be successful; this thought of being no good at mathematics is the mathematics self-concept. However, mathematics self-efficacy represents the performance in the class, which is the reason if one has a low mathematics self-efficacy it can be detrimental for students who do not find success in their mathematics course. Even if a student has a low mathematics self-concept this will not have as large of an affect as the low mathematics self-efficacy. Explaining the Gaps Some students inevitably fall behind in their mathematics class. Parke and Keener (2011), studied students who stayed at the same high school for all four years. It was found that the students who stayed at the same high school performed much better in their mathematics courses versus the students who switched high schools. Hypothesized reasonings to why these students fall behind were numerous (Parke & Keener, 2011). One possible problem with students STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 15 switching is that they miss instruction time due to the fact that not all high schools have synchronized courses and lesson plans. Another possible reason these students were struggling is because they may be placed in a mathematics course that they are not ready for (Parke & Keener, 2011). In the results of the study it was found that once the students fall behind academically their attendance rate drops, which increased the student’s grades to drop even lower (Parke & Keener, 2011). Some high schools produced better mathematics students than others (Baird, 2011). In this study of why some students learn more mathematics in high school versus others it was also discovered that even some school districts produced better mathematics students than others. This study was about standardized end of level tests in Washington. Baird stated that it was hard to study the true cognitive ability from these scores alone. However, Hanushek and Kimko (2000) found that test scores were a good predictor of an individual’s productivity. In Baird’s (2011) study it was hypothesized why some schools produced higher scores than others and concluded that it could be attributed to school demographics, school-level resources, school/classroom size, teacher quality, and effective advising. Gaps in students’ understanding may be due to students not recognizing how the process of solving mathematics problems supports a larger concept (Tall & Razali, 1993). This study asked specific mathematics questions to first- and second-year students in college and tried to diagnose why some students struggled more than others. What was found was that some students could look at a problem and only see procedures and not a concept. For example, a struggling student would look at the expression 2𝑥 + 3 and would not see it as an object that can be manipulated. The struggling students could only focus on figuring out what 𝑥 is or were uneasy about dealing with it because they do not know what 𝑥 is. The struggling students lacked flexible STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 16 thinking and were most likely going to fail when given a mathematical task. Even though all students are taught the same procedure, there are some who do not get that procedure and are not able to turn it into a concept like it needs to be understood. The difficulties of these struggling students can be summarized into three reasons (Tall & Razali, 1993). First, students were “less likely to crystallize processes into manipulate concepts, thus imposing the greater burden of process coordination rather than concept manipulation” (p. 13). Second, students relied on only familiar processes making it so that they cannot manipulate concepts. Finally, since students relied on the processes they were “less likely to relate ideas in a meaningful way” (p. 13). The struggling students became confused because they could only think about individual procedures instead of concepts. This confusion led into low mathematics self-efficacy and mathematics self-concept as suggested by Pajares and Miller (1994). The gaps found in students mathematics education were that students are not learning the material well enough to show they understand the concepts (Long et al., 2009). In this study, students from Florida’s public high schools were studied as to why students entering college were underprepared for post-secondary general education courses. The students were most underprepared for their mathematics course. The results of the study found three main reasons students were underprepared. First, students were receiving passing grades without learning the material required for the course. Second, students learned the material to pass the course, but were not retaining it once they moved on. Third, students simply did not learn the material, but were then given a passing grade so they could move on and graduate high school (Long et al., 2009). STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 17 Course Repetition If students are not ready for the next mathematics course, they should retake the course until they are ready for the next course. This used to be the normal pathway for a student who failed a course (Shepard & Smith, 1990). However, a research synthesis on grade retention was done and found that repeating students are more likely to drop out of high school. Students who have to then repeat two full grade levels have almost a 100% chance of dropping out of high school. When students are forced to repeat courses there is a negative connotation that comes with it. Instead of feeling happy for the time to relearn the material most students feel embarrassed and sad that they failed, and they have to retake the course (Shepard & Smith, 1990). Instead of repeating, the students who struggle should receive remedial help to pass the courses they are underprepared for so they can earn the necessary credits to graduate high school (Shepard & Smith, 1990). The remedial programs are often run before and after school concurrently with the courses they are taking, but sometimes during the summer. Sometimes schools offer a class dedicated for the student to do remedial work and credit recovery (Shepard & Smith, 1990). The help that secondary schools give to these struggling students is tremendous. Conversely, students may finish all the necessary courses to graduate high school to be able to move onto a secondary education; but, about thirty percent of the United States freshman are not prepared for college level mathematics (Long et al., 2009). Postsecondary Remedial Coursework These underprepared freshmen enter college and need help. Some colleges are prepared for the freshman who are not ready and upon entering college these students may be put in remedial courses (Weisburst, Daugherty, Miller, Martorell, & Cossairt, 2017). However, this STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 18 study done in Texas about postsecondary remedial course work showed there are negative connotations associated with putting students through remedial courses. The course work seemed to create barriers for students and increased time and money spent towards graduation. Many students in these programs were discouraged because they were deemed not college ready (Weisburst et al., 2017). Although the study showed negative results to the remedial course work, the college students did see the value in the study skills they learned to help them be successful in their other coursework (Weisburst et al., 2017). A similar study about students repeating courses and sometimes even full years as an undergraduate found that students benefited from repeating courses or their entire first year to develop new study habits and time maturing into a serious student (Tafreschi &Thiemann, 2015). The study compared high school grade retention to post-secondary grade retention and found it was different because post-secondary education is completely voluntary. Although there were benefits to repeating courses as a freshman or sophomore, undergraduate retained students (whether voluntary or forced) were more likely to drop out (Tafreschi & Thiemann, 2015). The study found two reasons students were more likely to drop out. First, the failed students never entered into their major coursework. Second, it put students a year behind on graduating and thus a year behind on entering into the labor market. The study also found that “Stigmatisms by fellow students or instructors, and the costs related to re-adjustments to new peers are likely to influence the drop-out decision, too” (p. 20). The students who had to repeat courses were found that it effected their major choice, study pace, and grade point averages (Tafreshic & Thiemann, 2015). When a student needs remedial post-secondary education, this does not mean they will not become just as successful as the student who does not need remedial help. However, the STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 19 remedial students will end up paying more for their education and the university will have to pay more for the remedial student too (Long et al., 2009). An estimated $118.3 million dollars were spent on remedial coursework for college students in Florida 2003-2004. These estimated costs were split between the state and the students who were underprepared. All of these costs were devoted to coursework that was not for the students’ intended major. This is a lot of money to be spent on education that was supposed to be done through public education. It was also studied that the cost of paying tuition over and over again for remedial course work increased dropout rates throughout universities (Long et al., 2009). Potential Solution To fix this problem of low confident and underprepared students going into the general education mathematics course for post-secondary education is not like prescribing medication to a sick patient (Tall & Razali, 1993). The results of this study suggested to provide students with a course that can give them the confidence they need to understand the mathematics procedures and turn them into mathematical concepts (Tall & Razali, 1993). This course will then give the students time to focus on what they already know so they can develop the deeper conceptual thinking without confusing their brain with new concepts. This will eliminate the gaps that the student has and then allows them to gain the mathematics self-efficacy they need to be successful and pass the course. Within this course students should learn problem-solving strategies rather than learning mathematical content and procedures (Tall & Razali, 1993). The study strongly implied that this problem-solving course cannot be done at the same time as starting a new mathematical course. This course can be done in the secondary setting with a concurrent enrollment course. Normally, the general education mathematics course taught at the university is only a semester STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 20 long. If the course was taught for a full year in the secondary setting Tall and Razli’s (1993) ideas could be implemented; and with effective teaching strategies students can be provided with the conceptual learning they need. The general education mathematics course is not new material, it is a combination of the mathematics content the student learned throughout their secondary education. When extended to a full year the course can first be taught in a traditional method where students take notes in class, and complete homework at home. The first semester is a practice run for the class. The students will complete the entire course in the first semester in a guided way so they can feel successful and start to gain mathematics self-efficacy. The second semester the students will then be taught the same content, but in a flipped classroom setting to allow the students to further develop their mathematics self-efficacy and conceptually understand the material rather than only procedurally. Flipped classrooms. Flipped classrooms are a great way for students to gain confidence and learn more conceptually (Bishop & Verleger, 2013). The flipped classroom is where a video lecture replaces an in-person lecture to be watch outside of the classroom and the classroom becomes the place for practice through group-based problem-solving activities. Through the comprehensive research of the flipped classroom it was found that video lectures moderately exceeded in-person lectures. Although some students prefer in-person lectures, it was more important for students to have an interactive classroom where activities are held instead of lectures (Bishop & Verleger, 2013). The flipped classroom, if done correctly, can expand the curriculum because of the practice time in class and the group learning (Bishop & Verleger, 2013). The most important components that make it so the flipped classroom produces the learning outcomes desired are STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 21 human interaction (in-class activities) and online technologies at work (outside the classroom). Even though there are still some controversies that this is a better way to learn, the opinions of the students in the classroom studies had overall positive comments and the students liked the change in learning (Bishop & Verleger, 2013). In one of the flipped classrooms studied versus a traditional classroom it was found that there was an increase of 21% more correctly answered exam questions in the flipped classroom setting versus the traditional classroom (Bishop & Verleger, 2013). This potential solution could give the students the learning time they need to gain confidence and fill in the gaps they are missing so they can pass their general education mathematics course. Another study from Miami University also supports that students can learn more in the flipped classroom setting (Lage, Platt, & Treglia, 2000). This study referred to the flipped classroom as the inverted classroom, it had the same criteria that was previously described in the comprehensive study by Bishop and Verleger (2013). In the results on the Miami University study many students commented on how much more they learned in this class versus other classes they had taken. Many of the students commented that they enjoyed the demonstrations in class and that it helped them more fully understand the concepts, which then helped them be successful on the exams (Lage et al., 2000). Flipped classrooms connect more to today’s students (Bergman & Sams, 2012). Today’s students are growing up with a constant connection to the internet that has a host of many digital resources. When watching the online lectures, students appreciated the ability to pause and rewind if needed. Many students come to school with their electronic devices that connect them to these resources (Bergman & Sams, 2012). The flipped classroom allows the students to engage further with these tools and this helps them connect better with the content. Because of STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 22 this constant connection, the flipped classroom helps students work ahead if they are ready. This allows the instructor to spend more time with the students who need to go slower (Bergman & Sams, 2012). Since the majority of class time is devoted to group-based work, the struggling students can receive more one-on-one help from the instructor. It also allows the instructor to know their students better because they get to spend more one-on-one time with them. This helps the instructor know how to better help the struggling students so that they do not get left behind (Bergman & Sams, 2012). Application of the flipped classroom. Although this project does not intend to study the learning outcomes of the students in the mathematics course itself after receiving the flipped classroom learning method; it will try to design the most effective way to present the curriculum. This curriculum will be designed to give the students more confidence and thus increasing their mathematics self-efficacy. This will allow the students to spend more time conceptualizing ideas and not just memorizing procedures, thus filling in the gaps that they are missing. The students in this course will then be more prepared for college as they will have completed the general education mathematics course requirements for their undergraduate degree. Summary Mathematics self-efficacy is a vital part of student success in mathematics courses. Mathematics self-concept is also important, but not as important as the student feeling they have the confidence to correctly complete a given mathematic task in their mathematics course (Pajares & Miller, 1994). Not only does confidence play a role in student success, but how the student thinks about the mathematical concepts affects how well they will do in their mathematics course. Often students will have gaps in the mathematics education due to many reasons such as, switching schools during their secondary education (Parke & Keener, 2011), not STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 23 learning and/or retaining the material taught in their mathematics course (Baird, 2011), or just simply being given a passing grade in a mathematics course when it should not have been given (Long et al., 2009). Tall and Razli (1993) found that many of these gaps are due to how students were thinking. The struggling students could not think conceptually, and this was their downfall. The students who have low mathematics self-efficacy and gaps in their mathematical education create a problem for the post-secondary education institutions (Long et al., 2009). The secondary schools can get students to graduate high school (Shepard & Smith 1990), but once they are there the remedial programs some colleges have in place are not successful (Weisburst et al., 2017). The potential solution is to allow the students to take their general education mathematics course in the secondary setting as a concurrent enrollment course. Instead of teaching for only one semester, extend the course into two semesters so that the students have an opportunity to build their mathematics self-efficacy and fill their gaps. The course would do this by flipping the classroom the second semester which allows for student success and deeper cognitive learning (Bishop & Verleger 2013). STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 24 PURPOSE For the struggling students to become successful in their concurrent enrollment mathematics course they need to build their mathematics self-efficacy (Pajares & Miller, 1994), and change the way they think about mathematical concepts (Tall & Razli, 1993). The purpose of this project was to design curriculum that will give the students greater self-efficacy and develop conceptual understanding through teaching in a flipped classroom setting (Bishop & Verleger, 2013). The objective of this project was to develop a flipped classroom curriculum for the general education mathematics course: Mathematics 1030: Contemporary Mathematics. The project showed the structure of the semester course extended into the full year. This portion allows the student time with the material to really learn it conceptually and not just procedurally as suggested by Tall and Razali (1993). This will also allow the students to gain success through the course so they can build the mathematics self-efficacy they need to be successful throughout the course (Pajares & Miller, 1994). The project goes into specific detail about the flipped classroom portion and gives an actual sample of one of the sections taught for the concurrent enrollment course. The flipped classroom portion really supports both ideas presented by Pajares and Miller (1994) and Tall and Razali (1993). This is why the project was focused on this specific portion in the curriculum, to show case the manor the flipped classroom supports these successful learning patterns (Bishop & Verleger, 2013). STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 25 METHOD It is imperative that students be successful in their general education mathematics course for post-secondary education. Many students can take their general education mathematics course while they are still in high school as a concurrent enrollment course. For the students to do well, mathematics self-efficacy is a vital part of student success in a mathematics course. This gives them the confidence that they can be successful in the tasks required for the course. Even if they do not perceive themselves as a good math student, they can still be successful if their mathematics self-efficacy is built within the course (Pajares & Miller, 1994). In addition to confidence, how the student thinks mathematically will affect how well they do. The student needs to be able to think conceptually about the mathematics not only procedurally. When students can only think procedurally it hinders their abilities (Tall & Razali, 1993). Many students will have gaps by the time they reach this general education mathematics course. These gaps are due to not actually learning the material from previous courses and still receiving a passing grade (Long et al., 2009). Also, it could be that they learned the material but they did not retain it (Baird, 2011), or they missed material completely due to illness, vacation or switching schools during their secondary education (Parke & Keener, 2011). These struggling students can cause problems for post-secondary education institutions (Long et al., 2009). This is why allowing the students to take their general education mathematics course as a concurrent enrollment course in high school is a great solution. The high schools have the ability to adjust the general education mathematics course to benefit the student. High schools are great places for remedial programs and supporting struggling students (Shepard & Smith, 1990). Some universities do have some remedial programs in place, but are not as successful (Weistburst et al., 2017). If the high school can adjust the general education STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 26 mathematics course into an entire year this would allow the students time to gain the confidence needed and actually learn the material they need to pass the course. This can be done by teaching it traditionally for the first semester and then inverting the classroom the second semester giving the students time to deepen their procedural thoughts to conceptual thinking (Bishop & Verleger, 2013). Context This project takes the undergraduate course Mathematics 1030: Contemporary Mathematics taught in the concurrent enrollment setting and extends it into a full year. This course is specifically offered through Weber State University, however many other colleges offer a similar course. It should be noted that this course is not accepted for every major at Weber State University, however 65% of Weber States’ undergraduates only needed this course to fulfill their quantitative literacy requirement to graduate in 2017 (Weber State University, 2017). Normally, this course is taught at the University, but it recently became available as a Concurrent Enrollment course at the high school level. This course is also only designed as a semester long course. However, when the course is taught yearlong it allows the time to implement some of the ideas that Tall and Razali (1993) suggested. During the fall semester the content was be presented in a very traditional format, notes, quizzes, and practice problems. During the spring semester the content was presented in a flipped classroom format. However, it should be noted that most of the content is not new to the students. The content has very similar topics they have seen in their previous high school mathematics courses. Thus, this allowed them time with the material to start to change the procedures that they know into conceptual ideas. Setting STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 27 The curriculum designed for this project was for students in the concurrent enrollment course in the high school setting. Senior students will only be allowed to take this course. The high school demographics of the school where this was implemented are as follows. The high school serves grades 10-12. The school has a little more than 1600 students enrolled, each grade has around 500-600 students. The male to female ratio is about equal, with slightly more males. The ethnicity is predominantly Caucasian, with less than 300 students having a different ethnicity. The next highest ethnicity are Hispanics, around 130 students can be identified as this ethnicity. The school also reports the special education students make up about 9% of the population. Seventy-three percent of students scored above an 18 on the ACT, with an average score of 21 (Utah State Board of Education, 2019). Additionally, the mathematics average score was a 21, which is the required score to enroll in Mathematics 1030 (Weber State University, 2019). The concurrent enrollment credit is from Weber State University, because of this Mathematics 1030 must follow set constraints implemented by Weber State University. Weber State University credit started in the spring semester for the course, and thus the first semester was elective mathematics credit towards the student graduation. In the spring semester Weber State sets the dates of the midterm and the final. They also write the midterm and the final. Weber State does not require a certain pace, but because of the content covered on the midterm and final all high schools that teach this course have to teach enough of the content before the specified date of the midterm and final. Weber State also provided the content the course covered in the book, Mathematics All Around, Pirnot, 6th edition (Pirnot, 2018). From this book Weber State also provided suggested homework problems that the students should complete to better prepare for the midterm and final. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 28 Scope of Project This project focused on the flipped classroom portion in the spring semester. Specifically, the last chapter covered in the content, Chapter 14: Statistics, which covers organizing and visualizing data, measures of central tendency, measures of dispersion, and the normal distribution. The curriculum design of the flipped classroom was to focus on the student solidifying concepts and gaining confidence to build a strong mathematics self-efficacy, so that they could successfully pass this course. Although the course content contained six chapters from the book, this project took the last chapter studied and showed the curriculum in a sample. Procedure The course began in the fall semester and all the content was covered in the fall semester. The material was taught in a traditional format, which is very similar to how the students’ other math classes were taught to them previously at this school. Each day a new section was covered beginning with a quiz on the previous section. The new section was taught through notes that the students filled in while the teacher filled them in on the iPad, which was connected to the projector so the students could see. Each “notes” section was recorded so that the students could view it again at home or if they were absent, they could view it as well. After each “notes”, an online homework was assigned. The online homework was through the online program that is attached to the book, MathXL for School. The homework problems assigned were the suggested homework problems provided by Weber State University. At the end of each chapter, students were given a chapter review, which prepared them to take a chapter test. Each chapter test contained problems that were similar to the problems that would show up on the midterm and final. The midterm and the final in the fall semester was written by the teacher and was similar to the midterm and final written by Weber State in the spring semester. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 29 In the spring semester, students learned all of the content over again, starting at the very beginning. However, the content was taught through a flipped classroom. Before each class period the students watched a short 10 to 15-minute video refreshing their memory of the section they learned in the fall. They then completed a five-question lesson check quiz to check for understanding on the content. Once the students arrived to class the teacher began a discussion on the section the students learned about the night before. After which the teacher then initiated a class activity that helped the students understand the section more conceptually and increase their confidence as they worked together to solve the intended task. The remaining portion of the class was reserved for the students to do the homework assigned from the book. The teacher then had the opportunity to help students one-on-one with homework problems. This helped the students’ mathematics self-efficacy increase as well as their conceptual understanding. Once per chapter the students completed a quiz before the class activity begins. After each chapter a review was given and a chapter test. These quizzes and tests were similar to the ones they took in the fall but were slightly different and harder to better prepare the students for the actual midterm and final. As the curriculum was taught, notes were kept on how well the curriculum was received by the students. This was helpful for the evaluation and review of the curriculum written for the course. The project was not about how well the students did, because the project is purely curriculum, but it is interesting to know how smoothly the curriculum went as it was given to the students. Curriculum The curriculum can be viewed through Canvas Commons. Login into your Canvas account or make a free Canvas account at https://canvas.instructure.com/login/canvas. Go to the STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 30 commons link on the left-hand side of the screen once you are logged in (see Figure 1). Search for: QUANTITATIVE REASONING 1030 CE (see Figure 2). The entire spring semester course will be available to view; however, this project will only be evaluated on chapter 14 (see Figure 3). Note: The quiz, class activities, and test are located in the files (see Figure 4). They are not posted in the module because they are not for students to view online. Figure 1. Screen shot of Commons link STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 31 Figure 2. Screen shot of search bar Figure 3. Screen shot of Chapter 14 Module STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 32 Figure 4. Screen shot of Files link Evaluation The content was evaluated by instructors who teach this course at Weber State University. The instructors provided feedback on the lesson videos, lesson checks, and class activities. They used their expertise to decide if the curriculum would provide the students with confidence building activities as well as conceptually building activities. They also reviewed the quizzes and tests to ensure the tasks asked would properly prepare students for the final. They felt that all of this has been completed, and the curriculum was considered successfully completed for this project. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 33 DISCUSSION Students often struggle in their general education college mathematics course (Long et al., 2009). The reasons they struggle could be the lack of mathematics self-efficacy (Pajares & Miller, 1994), or it could be that they have many gaps in their mathematics education and do not have the conceptual knowledge needed to pass the mathematics course (Tall & Razli, 1993). To help these students this project designed curriculum for a concurrent enrollment mathematics course that would satisfy their general education mathematics requirement for their college education. The curriculum was written for Mathematics 1030: Contemporary Mathematics, a course offered by Weber State University. The concurrent enrollment course was originally designed to be completed in one semester, however the curriculum for this project was extended to a full year. The first semester of the course was taught traditionally, and the second semester was taught in a flipped classroom format giving the student opportunity to gain the mathematics self-efficacy they need to conceptually understand the material (Bishop & Verleger, 2013). The curriculum was designed for the mathematics course taught at high school that had an average mathematics ACT testing score of a 21, which is the minimum requirement to get into the concurrent enrollment course Mathematics 1030 (Utah State Board of Education, 2019). The school is also predominantly Caucasian, and all the students must be seniors to be enrolled in the course. Also, this course does not satisfy the mathematics requirement for college graduation for all majors, however, it did satisfy 65% of Weber’s graduating class in 2017 (Weber State University, 2017). Although curriculum has been written for the entire year, the evaluation of this curriculum is only on the flipped classroom portion and only the section that covers descriptive STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 34 statistics was looked at. During the process of writing the curriculum there were successes and struggles. Once the curriculum was written and used in the classroom notes were kept of the successes and struggles found implementing the curriculum. The following paragraphs will discuss these successes and struggles; they will also mention limitations of this curriculum project and suggest recommendations for future uses of the curriculum. Successes Canvas was used as the platform to host the videos and quizzes and it was a good platform to use. The layout was simple and easy for the curriculum to be implemented; it was also easy for the students to use. Canvas was easy to navigate and convenient to use because the school district where the curriculum was implemented wants all classrooms to use Canvas so students have access to the curriculum 24/7. The videos for the students to view were made on an iPad using the application, Explain Everything. This application was also very convenient and easy to use. It has many backgrounds, and color writing options. There is also a way to import graphics and pictures so they can be used in the video. While writing the curriculum the videos were reviewed by the Weber State University experts before they were posted for the students to see and changes were made to make them more concise and clear. Each video was made to be about ten minutes long, however some ended up to be about fifteen minutes in length. This length was decided because students prefer shorter videos, fifteen to thirty minutes is the ideal length (Maher, Lipford, & Singh, 2013). The book used by Weber State had many questions that were easy to implement as the quiz questions for the students to complete after they watched the video. Canvas has the option to allow students to take the quiz more than once if they so desire. This was helpful so that the student would know they did not get the question right, but were able to try again right away, STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 35 thus building up their confidence. The quizzes were all multiple choice. Multiple choice quizzes have pros and cons. The con is that students could retake the quiz again and again and just eliminate answers as they go, and never learning the material. The pro is that the students can figure out the right answer by taking the quiz again and then they can hopefully use the right answer to figure out how to do the problem. Once the students were in class and participating in the class activity, they seemed to enjoy themselves more. The activity got them talking aloud about the topic. It made them discuss what ideas and thoughts were going on in their brain and share that with other students. It seemed that students were able to conceptually understand more because of these activities. Students also really enjoyed working on their homework in class! They loved being able to ask as many questions as they could so that they actually understood the problems. This portion was one of their favorites about the flipped classroom. It seemed to help boost their mathematics self-efficacy that they could complete all of the homework problems correctly. Students would often comment, “I am so happy I do not have homework tonight.” Or, “It is so convenient that you [the teacher] are right here to ask questions to.” It was also common to hear the comment, “I actually did and understood all of my homework.” Students were also asked if they felt that their mathematics self-efficacy improved and if their mathematics self-concept had improved. One response said, “I feel like I am better at doing my homework and knowing how to do certain math problems, but I would still say that I am not a very good math student.” This is interesting because that coincides with the research of mathematics self-efficacy and self-concept (Pajares & Miller, 1994). Students can do well if they have a strong self-efficacy, not necessary a strong self-concept. Another student commented, “After taking this course I feel way more confident going into college.” STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 36 One hundred percent of the students in the classroom who used this curriculum passed the class with a C or better. A C grade is the minimum requirement for students to receive for the class in order for it to count as their mathematics requirement to graduate college. Eighty-nine percent of the students received a B or better and 11% received a C. Although the effect of the curriculum on the students was not being reviewed for this project, it is important to note that all students were successful using this curriculum. Struggles and Recommendations Although all students were successful, there were a few problems with the curriculum that needs some work. Not all of the students watched the videos at home and completed the quiz before class. There were several that would only work in class and would do nothing outside of class except for study for exams. This made it hard to have classroom discussions. Some students would not know what everyone else was talking about, so they did not participate in the discussion. To fix this problem, it might help if students were assigned to lead the classroom discussions. That way they would be forced to watch the video and complete the quiz so that they could lead a discussion on it. The discussion would be a part of the student’s grade, so the student had more pressure to do it. Hopefully this will allow the students to take more ownership on watching the videos and participating classroom discussions. The class activities were fun, however some of the students did not want to participate because they were still working on their homework. They also felt that the class activities were problems that they did not need to know and wanted them more related to the homework problems. This was adjusted in the curriculum and the section that was being reviewed had class activities designed to be done before the homework. The class activity was changed to be a task that was more homework driven. It would be recommended that this order stay, and the class STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 37 activity have more focus on problems that the students will see on their homework. However, some of the class activities will need to be more conceptual than the homework problems. Thus, in the future there will more class activities that are conceptual and the students will take more ownership to do them because they will be more a part of their grade. While writing the curriculum the videos were hard to keep under ten minutes. Many of the videos were pushed to be around fifteen minutes just because of how much content needed to be it into it. Remaking the videos was somewhat of a long process but working on them each year to improve them would be recommended. The quizzes also need to be adjusted to be better. Sometimes the quizzes would be way to easy and sometimes they would be way to hard. The book had good problems to use, but many of the problems do not check for quick understanding. Also, it would be good for the quizzes to not be multiple choice, however this would require using another program other than Canvas, because Canvas’s multiple-choice quizzes are not great to use. In the future this will be worked on, so that students have to take more ownership in learning the material to complete the quiz and not just guessing on a multiple-choice question. Limitations Since this was only a curriculum project it was difficult to say whether or not the students did fill in the missing gaps in their mathematic education. Or if their mathematics self-efficacy really improved. The students for whom this curriculum was written voiced that they did feel their mathematics self-efficacy improved and they felt that they conceptually understood the concepts better than they had in the past. It was clear from the comments that they had made they truly felt better about themselves after taking the course. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 38 Curriculum is also tricky because it needs constant adjustments to the needs of the students in the class and sometimes the curriculum requirements change. Weber State University is changing the book that is being used for this class in two years, and thus the videos, quizzes, class activities and homework problems will all need to be adjusted to fit the new curriculum. STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 39 REFERENCES Baird, K. (2011). Assessing Why Some Students Learn Math in High School: How Useful Are Student-Level Test Results? Educational Policy, 25(5), 784-809. doi: 10.1177/0895904810386595 Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191-215. doi: 10.1037/0033-295X.84.2.191 Bandura, A., & Schunk, D. H. (1981). Cultivating competence, self-efficacy, and intrinsic interest through proximal self-motivation. Journal of Personality and Social Psychology, 41(3), 586. Retrieved from https://www.uky.edu/~eushe2/Bandura/Bandura1981JPSP.pdf Bandura, A. (1986). Social foundations of thought and action. Englewood Cliffs, NJ: Prentice Hall. Bergman, J. & Sams, A. (2012). Why you should flip your classroom. In J. V. Bolkan, L. Gansal, T. Wells, & K. Landon (Eds.) Flip your classroom: Reach every student in every class every day (pp. 19-34). Eugen, Oregon & Washington, DC: ISTE & Alexandria, Virginia: ASCD. Bishop, J. L., & Verleger, M. A. (2013, June). The flipped classroom: A survey of the research. Proceedings of the ASEE national conference, 30(9), 1-18. Felson, R. B. (1984). The effect of self-appraisals of ability on academic performance. Journal of Personality and Social Psychology, 47(5), 944. doi: 10.1037/0022-3514.47.5.944 Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for research in Mathematics Education, 20(3), 261- 273. doi: 10.2307/749515 STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 40 Hanushek, E., & Kimko, D. (2000). Schooling, labor-force quality, and the growth of nations. American Economic Review, 90(5), 1184-1208. Lage, M. J., Platt, G. J., & Treglia, M. (2000). Inverting the classroom: A gateway to creating an inclusive learning environment. The Journal of Economic Education, 31(1), 30-43. doi: 10.1080/00220480009596759 Long, M. C., Iatarola, P., & Conger, D. (2009). Explaining gaps in readiness for college-level mathematics: The role of high school courses. Education Finance and Policy, 4(1), 1-33. doi: 10.1162/edfp.2009.4.1.1 Maher, M., Lipford, H., & Singh, V. (2013). Flipped classroom strategies using online videos. The Journal of Information Systems Education, 23(1), 7-11. Retrieved from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.682.1134&rep=rep1&type=pdf Pajares, F., & Miller, M. D. (1994). The role of self-efficacy and self-concept beliefs in mathematical problem-solving: A path analysis. Journal of Educational Psychology, 86(2), 193-203. doi: 10.1037/0022-0663.86.2.193 Parke, C. S., & Keener, D. (2011). Cohort versus non-cohort high school students' math performance: Achievement test scores and coursework. Educational Research Quarterly, 35(2), 3. Retrieved from https://search.proquest.com/openview/11c4016b0055458c5bc1af90dafa16f9/1?pq-origsite= gscholar&cbl=48020 Pirnot, T. L. (2018). Mathematics All Around 6th Edition. Kutztown University of Pennsylvania: Pearson Shepard, L. A., & Smith, M. L. (1990). Synthesis of research on grade retention. Educational Leadership, 47(8), 84-88. Retrieved from STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 41 https://www.researchgate.net/profile/Mary_Smith100/publication/234709494_Synthesis_ of_Research_on_Grade_Retention/links/56d06c2808ae4d8d64a38c0e.pdf Stajkovic, A. D., & Luthans, F. (1998). Self-efficacy and work-related performance: A meta-analysis. Psychological Bulletin, 124(2), 240. Retrieved from https://www.researchgate.net/ Tall, D., & Razali, M. R. (1993). Diagnosing students’ difficulties in learning mathematics. International Journal of Mathematical Education in Science and Technology, 24(2), 209- 222. doi: 10.1080/0020739930240206. Tafreschi, D., & Thiemann P. (2015). Doing it twice, getting it right? The effects of grade retention and course repetition in high education. USC Dornsife Institute for New Economic Thinking, 55, 198-219. Retrieved from https://dornsife.usc.edu/assets/sites/818/docs/SSRN-id2561048.pdf Utah State Board of Education, (2019). Data and Statistics. Retrieved from https://www.schools.utah.gov/data Weber State University. (2019, Spring). Math 1030 Contemporary Mathematics [Course syllabus]. Available from Weber State University website: https://continue.weber.edu/.../Syllabi/CE%20MATH%201030%20Syllabus.docx Weber State University Continuing Education Concurrent Enrollment Mathematics. (2017). Why take concurrent enrollment mathematics? [Poster]. Weber State University: Author Weisburst, E., Daugherty, L., Miller, T., Martorell, P., & Cossairt, J. (2017). Innovative pathways through developmental education and postsecondary success: An examination of developmental mathematics interventions across Texas. The Journal of Higher Education, 88(2), 183-209. doi: 10.1080/00221546.2016.1243956 STRUGGLING STUDENTS AND CONCURRENT ENROLLMENT 42