Last spring semester began a new venture in mathematics teaching and learning. Colleges and universities went virtual with their instruction and testing. Faculty with online courses experience had an easier transition while other instructors with no experience had more difficulty transitioning to virtual learning. This fall is a mix of classroom and virtual learning situations. The previous blog by April Strom did a great job of addressing instructor strategies for online/remote/virtual teaching. Now we need to take the next step in teaching and learning by focusing on helping students become improved classroom and virtual learners. Zientek, Ozel, Fong, Griffin (2013) indicated that affective and other characteristics such as self-efficacy, cognitive strategies, motivation and self- regulated learning can predict up to 41 percent of the variance of math grades. Zientek, Fong and Phelps (2017) indicated that four sources of non- cognitive variables like math self-efficacy explain 35.8% of learning variance. Coleman, Skidmore and Martirosyan (2017) in their review of literature on online developmental math indicated that self-directed learning is one of the key variables to student success. With this new world of virtual learning it is just as important to teach students how to become improved learners. We need a team approach for mathematics learning where the instructor and student work together to improve learning. One strategy is helping students improve self-directed learning which requires ownership of both students and faculty.
Student self-directed learning has been around for a while. The concept came from online instruction research. Self-directed learning is defined as the “process in which individuals take the initiative, with or without the help of others, in diagnosing their learning needs, formulating goals, identifying human and material resources, choosing and implementing appropriate learning strategies, and evaluating learning outcomes” (Knowles (1989). This concept can be directly applied to any type of mathematics learning design including virtual instruction. There are usually considered three interconnected dimensions of self-directed learning which are self-management, self-monitoring and motivation (Garrison,1997). However other authors indicate metacognitive learning and applying learning skills is part of self-directed learning. Also, self-regulated learning can be considered a subcategory of self-directed learning. Self-regulated learning is a combination of cognitive, metacognitive, behavioral motivational, emotional and affective learning (Panadero, 2017). Students who improve self-directed learning and apply self-regulated learning strategies improved math success. So, how can we help students improve these two areas. IMPACT has some suggestions.
In Chapter Four of the IMPACT document the focus is on student and faculty ownership to improve learning. The three components of student ownership are discovery, responsibilities and continue Learning. Whether prompted by the student or instructor the most important responsibility is self-assessment by reflecting on the quality of their work based on stated criteria (syllabus), judging their current grade/learning skills, and making appropriate revisions. However, most students are not taught this formative type of self-assessment concerning their thinking, working ,learning, study skills and test-taking skills. They do understand their summative type of assessments – test grades. Faculty need to foster student ownership, empower students to take ownership and promote self-regulated learning. Faculty also need to, ”Keep abreast with current research on learning and teaching and incorporate finding in the course.” (p 38). Faculty can “Offer workshops for students that include (but not limited to) mathematics study skills, anxiety reduction and technology usage.” (p. 39). So, the responsibility is both on the student and faculty to promote self-directed learning. However, most students lack skills to develop their own self-directed learning behaviors. They want to improve their learning and grades however they need faculty training. So how can they do that?
Students know how to evaluate summative types of self-assessment; however, they have difficulty with formative self-assessments. Consider Jim’s scenario:
Jim gets a “D” on his first College Algebra test and tells himself to study more. Then he fails the next test and comes to see me.
“Jim. How are you doing?”
“I got a ‘D” on my first test, so I studied more for the second test.”
“How did you do?”
“I failed it.”
“ I know. How did you figure out how much you needed to study for the tests?”
“I don’t know. I didn’t study much more because I got all the homework right.”
“How did you know when you had studied enough?”
Jim stared at the fishing pictures behind me, “Dunno. What do you mean?”
“How did you study? For example, did you have a plan for preparing for this past test--- review homework problems, lecture notes, and practice problems?”
“I didn’t do much because I understood almost everything during class, and my homework was 100 percent. I did not have any homework to review. My notes were a mess. They didn’t help much. In fact, they kind of messed me up.”
“I just need help with the problems I got wrong on the test.”
I smiled at him while placing his notes back in front of him. “I know, but in the long run you need to improve your notes and take homework notes . You are right. Your notes are confusing. That’s okay though because we can fix that.”
Jim looked up at me and stopped frowning. “Okay. I’ll try. It can’t get much worse, and I have to pass this class. I know I have to do something.”
“OK. I will first show you how to take lecture and homework notes. Then we can review your missed test problems.” Then I will have you take a survey to improve your other study skills”
“Great, you have given me some hope”
So, what is the student’s real problem? First, he has no idea how many hours he studied for the first test, so what is more study time for the next test? Second, he does not have good study and test preparation skills. I have worked with thousands of students like Jim. They want to improve their grades; however, they don’t know how. They are not taught how to stop, identify what they are doing as far as studying, assess what they are doing, and make necessary changes to study behaviors and motivation.
So, what should we do? Teach self-directed learning behaviors. These behaviors can include ownership, self-regulated learning, math self-efficacy, self-assessment, self-management, motivation, self-monitoring, emotional/affective learning, study skills and formative and summative assessments.
We do not need to teach all these skills, however the more skills we teach the more students will become successful. It is also important to realize that talking about these skills one time does not create lasting results. We must remind the students periodically in a casual way. For instance, at the end of a class, if you noticed students were not writing down important information, you ask, “How are your notes?” Remind them that good notes save time when reviewing for the test. Also ask them about their progress to their course goal grade. Now you are coach and instructor. A good coach will help students during practice (classroom) and teach them how to practice outside of class. We need to become great coaches by teaching students self-directed learning behaviors through as many of the mentioned behavioral strategies.
Below are resources for teaching self-directed learning:
Ownership: Taking Responsibility and Showing Initiative: Students and faculty must share the empowerment of taking responsibility for learning. It is a team approach. Read or reread Chapter Four of the IMPACT document.
Self-regulated Learning: Instructors can develop different models to improve student self- regulated learning. They can focus on improving student cognitive strategies, volition, and self-efficacy. There are six models. Review Panadero (2017).
Mathematics Self-Efficacy: Instructors need to implement more mathematics self-efficacy instruction strategies to improve instruction and motivation. The four areas of self-efficacy are: enactive mastery experience, vicarious experiences, verbal persuasion, and physiological and affective states. One strategy is to “catch” them doing something right and praise them for it. Review Zientek, Fong and Phelps (2017).
Summative and Formative Assessment: Both students and faculty need to expand these assessments. Students and faculty understand summative however, students need to be taught formative self-assessments for evaluating their learning. Faculty need to expand formative assessment. Review: Summative vs Formative article.
Self-assessment of Math Study Skills and Motivation: Students must assess their math study skills to adjust their self-directed learning. To apply self-directed learning behaviors students first need to know their math study skills learning behaviors and know how to improve their learning behaviors. Also, most math study skills evaluation scores are low which is great motivational news because that implies math study skills are a major part of their learning problem. Not their math intellectual ability. Use the free Math Study Skills Evaluation with username “msse” and password “seventh”.
Self–management of Study Time: Student time management along with grade goal setting are the two major aspects of self-directed learning. Students need to know how much time they are studying and their grade goal. Then they can adjust the amount of study hours to obtain their wanted grade. Instructors need to teach students how to complete a time management schedule to be turned in as a homework assignment. Use the Winning at Math Electronic Time Management time management schedule.
Self-monitoring of Math and Test anxiety: Today anxiety is one of the key interfering factors of self- directed learning and self-assessment. As anxiety increases students’ procrastinate on doing their homework and assessing their performance. Maloney and Beilock (2012) in their short article discussed, understanding, antecedents and how math anxiety affects affective factors and indicates that just doing more math problems is not the solution. Instructors need to teach students anxiety reduction techniques to help them improve their learning and demonstration of knowledge.
Self-directed Learning from Test Assessments: Self-directed learning requires a feed-back loop on taking tests and then assessing the results to change learning, study, and test-taking behaviors. Faculty must give students the chance to assess their tests even in the virtual environment. Use the Six Types of Test Taking Errors.
Emotional and Affective Learning from Math Study Skills and Metacognition: Self- directed learning not only requires students to monitor their learning, they need skills to change their motivation, learning, studying and test-taking behaviors. However, just like with John they have not been taught those skills. It is the instructor’s responsibility to teach these skills especially in the virtual learning environment where more focus is on self-directed learning. Some of these study skills are note-taking, reading, online homework, learning preferences, mindfulness, tutor learning, test preparation, test anxiety reduction, test-taking and metacognitive learning strategies. Winning at Math (Nolting, 2020) is the reference.
In our new virtual world, we cannot just instruct students. We need to coach them to becoming self-directed learners. Just saying to students that they need to become self-directed learners through self-management, self-monitoring and motivation is like the coach telling the player to get better without teaching them how. Both lose the game or in our case fail. To improve learning and grades we need a team approach. As mentioned in the last AMATYC, NOSS and National Math Summit Planning Committee Webinars, “The status quo is unacceptable.”
This semester instructors can start teaching students these self-directed learning behaviors. This will help some students however it is very unlikely to improve your overall class pass rate. So, his semester instructors also need to develop an overall plan to systematically implement these self-directed learning strategies into the classroom or co-requisite labs. Research has shown that by implementing self-directed learning with math study skills, anxiety reduction and test-taking skills improves math success. Let us become “math heroes'' to our struggling students!
Knowles, M.S. (1989). The making of an adult educator: an autobiographical journey (1st ed.). San Francisco, Calif.: Jossey-Bass
Nolting, P.D. (2020). Winning at Math: Your Guide to Learning Mathematics Through Successful Study Skills (7th ed.). Bradenton, FL: Academic Success Press, Inc