Detailed Feedback and Student Opinions

What impact does detailed feedback on a daily quiz have on student confidence, self-efficacy, and attitude toward mathematics?

I plan to give the students a one question "quiz" at the end of most every class (the only reason I am calling it a quiz is so they will take it seriously). The question will address the topic covered in class that day. This question will serve as formative assessment and as a medium for me to give each student detailed, individualized feedback that will be returned to them at the beginning of the next class. So not only do I know how they are (or not) understanding the material, so will they without having to wait for the next quiz or test when the pressure is higher. I plan to measure the students' opinions of their confidence, self-efficacy, and attitude toward math with focus groups (possibly a survey) at the beginning of a unit and focus groups after a unit test.

Instrumental Genesis

I am interested in researching how individual students go through the process of "instrumental genesis", which is the process of turning what is an otherwise arbitrary technological tool into an effective learning aid. A computer is just a computer until a student learns the skills to use the software installed on it as a device for learning. And this process dictates a lot of what the student is able to learn and understand from using that computer. However, apart from direct instruction, this process is largely individual, and so each student has a different perception of the computer, how to use it and how to benefit from it, which each student chooses to use it differently. I think that by developing multiple case studies of students of varying abilities and both genders, using observations and interviews, I'll be able to paint a picture of how different students individually feel about and utilize technology-based learning aids

Guided Discovery

How does guided discovery instruction impact students’ achievement in, and attitudes toward, math?

I want to develop a unit plan for the class I am student teaching that will allow the students to discover the content and form their own knowledge instead of the traditional method of direct instruction. I will guide the students by asking probing questions but rely on classroom discussion, brainstorming, and student discovery, with the appropriate use of technology, to teach the material. I will design a pre- and post-test to measure the students’ achievement. I am also interested in how this different approach affects their attitudes towards math. Do the students feel more empowered having discovered the material as a class instead of being “talked at” by a teacher? Do they prefer one instruction method over another? These attitudes will be measured by a Likert scale survey, as well as interviews and focus groups. I will also keep my own reflections and observations.

Using different models of assessment.

I plan to research the effect of using different models of assessment on the performance of students in a classroom with special attention to their learning styles. The different models of assessment I want to use include individual tests, group activities (could be projects, tests, quizzes, etc), and written assignments. My research is not limited to these models however, and I'm currently looking into the related research to find other ideas. The focus will be to see if certain students succeed at different models of assessment and whether their learning styles impact this difference. I am also interested in seeing if there are students who excel at all models of assessment and what their learning styles are (and if they learn well in multiple ways).

Prompted Math Journaling

Research Question: What impact does prompted math journaling have on student understanding of Algebra concepts? How do students feel about math journaling and what are the effects on their perceived math abilities?

I would like to investigate prompted math journaling, which will require students to summarize mathematical concepts in their own words. Requiring students to reflect on their learning and explain their reasoning will allow for assessment of their understanding. Research has shown that journaling is beneficial for students and increases the depth of their understanding and improves problem solving performance. I plan on using prompted math journaling to summarize a lesson or concept. It can be incorporated in homework assignments, tickets out the door, etc. I want to explore the impact of journaling on students’ math achievement and also interview students to better understand their feelings about math journaling. I am curious to see if students will like the exercise or if students who like numbers but not writing will be put off by it. I think it may help students who struggle with computations but understand concepts gain confidence in their math abilities. I also would like to see if it affects students’ attitudes towards math as a subject.

Becoming Mathematical Thinkers

What is the impact of teaching mathematics through problem solving on students’ ability to become mathematical thinkers?

I want to incorporate a problematic based method of teaching that allows students to become mathematical thinkers.  Mathematical thinkers have developed habits of mind that are their tools when attacking problems.  To make mathematics problematic to students, I would base my instruction around problems that may cause a slight struggle to the student but could be used to teach concepts and habits of mine. By introducing concepts this way, students will be able to take ownership of their learning and develop confidence in their skills.  My purpose is to measure how influential this style of teaching is on improving student’s habits of mind and their confidence when faced with problems. 

Self-Regulation

Research Question:

1) How does a student's ability to regulate his or herself in nightly homework affect the student's performance and comprehension in mathematics and what can be done to improve a student's ability to self-regulate?

Explanation:

Self-regulation is when a student thinks reflects on the way he/she learns, is motivated, and takes responsibility for his/her learning. I am particularly interested in how student's view the homework they receive. For example, some students need more homework problems than others to grasp a concept. Do student's know when they have done enough homework to have an understanding of what they have learned? There has been lots of research done on the relationship between self-regulation and school performance, so I would also like to see what kinds of activities improve students' abilities to self-regulate. These activities include individually logging grades and setting performance goals. I will try and measure how self-regulation affects performance, as well as seeing if an improved ability to self-regulate leads to improved performance.

Problem Statement

Does analyzing and addressing student misconceptions improve student achievement? I would attempt to answer this question by administering short quizzes daily, or at least after teaching a complete lesson, that test for understanding of the main concept(s) that I was trying to convey through my lesson. Then I would look at the student responses to these questions, only 3-5 questions per quiz, and try to understand where they went wrong in the problems (i.e. find the misconception). If a student got a question wrong, but I cannot understand where the misconception is, I will ask the student to explain their thought process in a talk-aloud format in order to see where their thought process strayed. Then I will address the misconceptions I find; either with the entire class, if the majority of the student shared the misconception, or with individual students, if only a couple of students make the same errors. I will use performance on summative assessments to see whether student achievement (conceptual understanding of content) improved after I had addressed the misconceptions I found.

Dr. Mac SPEAKS

I am looking forward to reading your definition of your research question.