Methodology with Guided Discovery Learning

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

Participants: I will measure quantitative data from all or most of the students I teach. I will conduct interviews with selected students or volunteers.

Measures:
I will have a pretest and posttest of the material I will present through guided discovery. The students will take the pretest before the lesson, and the posttest may be included in the unit exam or quiz, or I may give out a specialized posttest separately.

I will conduct interviews and/or focus groups with selected students who provide a consent form. I will ask guided questions on their attitudes and feelings towards the lessons conducted by guided discovery.

I will keep diligent reflections of how the guided discovery lessons go, as well as any issues or anything that goes especially well. I may also ask my cooperating teacher to take observation notes.

Analysis:
Interviews will be tape-recorded and then coded for expressions showing their attitudes toward the different lesson-style.

The scores of the pretest and posttest will be compared, possibly with a t-test.

Effects of Detailed Feedback: Methodology

Research Question: What impact does detailed feedback on frequent quizzes have on student confidence, self-efficacy, and attitude toward mathematics?

Participants: All of the students in (most of) the classes I will be student teaching will be used. Volunteers (possibly selected students) will participate in focus groups.

Measures:
Artifacts: My comments on student quizzes
Pre- and Post-Treatment Survey: To measure confidence, self-efficacy, and attitude toward mathematics to be completed by every willing student at the beginning on my student teaching and again near the end. Questions will be answered on a Likert scale with the possibility of some open-ended questions.
Focus groups: Factors measured in the post-survey will be discussed in a group setting in order to provide deeper insights.

Analysis:
Pre- and Post-Treatment Survey data will be compared to see if there was a change in student confidence, self-efficacy, or attitude toward mathematics as a result of receiving or not receiving detailed feedback. I think giving the surveys to all (most) of my classes (even those that did not receive the treatment) will help reduce any extraneous factors that may affect student confidence, etc. over time.
Information gathered from the focus groups will be used to assess changes in student confidence, self-efficacy, and attitude toward mathematics.
I would also like to analyze my comments on student quizzes to see if the issues addressed stay the same or change over time which can help me determine if students are actually paying attention to my feedback and using it as a tool for learning.

Methodology

Research Question:

1. What is the effect of utilizing different types of assessment on the performance of students within the classroom?
2. Is the effect different for students with different learning styles?

Participants:

Two of the classes I will be student teaching.

Methodology:

There will be some qualitative data, but mostly quantitative.

Measures:

Observations: I will be observing student behavior during the different types of assessment to see if they are more engaged in some types than others. These observations will not be used as data but as a reference for me to look for students who need accommodation. For example, if certain students are not engaged in a group project, I would need to figure out some way to grade their performance on an individual basis or determine how to get them more involved with the group.

Interviews: I will use surveys to identify the learning styles of students in my classroom before I begin. I will also have questions at the end of each assignment simply asking “Did you enjoy this assignment?” and other open-ended questions about their feelings on the assignment.

Artifacts: The work of students will be collected and graded for performance. The work will include tests, quizzes, group quizzes, group projects, writing assignments, and maybe others if I think they will be helpful for the study.

How I will analyze data:

I am planning to look at the performance of each student on the different types of assessment that are used. I will then look at this analysis of performance with the learning styles that were identified before the study began to see if there is any difference between students. I will also consider the comments made by students at the end of each assignment but I am not sure how I will include this in my analysis.

Instrumental Genesis Methodology

Research Question:

How do individual students’ instrumental genesis influence their use of and perceptions of a specific technology-based learning aid (to be determined) in my mathematics classroom?

Participants:

All students in one of my classes in which a specific technological aid is heavily integrated will be observed and invited to focus groups. In particular, four students will be (purposively) selected by me and my cooperating teacher. These students will be individually interviewed and specifically observed, and case studies will be developed.

Measures:

Observations – The classroom in general and the four selected students specifically will be observed using and demonstrating (i.e. presenting) use of the technology aid. Particular attention will be paid to their work methods (i.e. see Guin and Trouche 2002 for different profiles), as well as any direct evidence of student perceptions (such as comments on usefulness, exacerbation, etc.)

Interviews – The four case study students will be interviewed individually. In the interviews, the students will be asked about their perceptions of the technology aid and it’s utility. The students will also be given a novel problem, and asked to use familiar techniques with the technological aid in an unknown situation. This will help further identify and address the individual aspects of the student’s instrumental genesis.

Artifacts – The work that each of the four students provides in the interview will be included in a portfolio of various works collected throughout the study from these four. These works will be selected on the basis of demonstrating idiosyncratic characteristics of the individual student’s understanding or use of the technology aid, both positive and negative (in order to develop as full of a picture as possible)

Focus groups – The students in the class will be invited to one (or multiple) focus groups. In these, the focus will be on the students’ perceptions about the technology aid, with leading questions used to keep the students discussing the aid more qualitatively, how they “feel” about the aid and using it in the class.

Analysis:

Based on the data collected on the class as a whole, the class observations and focus group meeting(s), the first goal will be to develop a framework for analyzing the factors that contribute to individual student’s perceptions of and uses of the technology aid and instrumental genesis. Then, using the data on the four individual students, four case studies will be developed. The four case students will be selected to hopefully display a wide variety in individual instrumental genesis. They will use the student work artifacts, especially what is collected during individual interviews, to highlight the specific aspects of their instrumentation and instrumentalization.

Methodology

Research Question: Does analyzing and addressing student misconceptions improve student achievement?

Participants: All of the students in one of my student teaching preps.

Measures:

Artifacts – short 1-2 question daily (or every other day) quizzes that test procedural and conceptual understanding of the previous day’s (or couple of days’) material; unit tests that test procedural and conceptual understanding of the completed unit; lesson plans where misconceptions found in quizzes are specifically addressed

Interview – interviews with students where I have them do mathematical tasks relating to recently covered material orally, explaining their thought processes

Observation –log/note-taking of the methods and thought processes I use when analyzing the quizzes for misconceptions, log/note-taking of the methods and thought processes I use when analyzing the oral interviews for misconceptions

Analysis: My study will include both qualitative and quantitative research. I will compare the scores of the quizzes to the scores of the unit tests to determine if there was improvement in student achievement after I re-taught based on misconceptions that I identified and analyzed from the student quizzes and interviews. I will categorize common misconceptions based on my observations in my log of my analytic process. Then I will attempt to see if there was a change from the types of misconceptions that most frequently appeared in the quizzes and oral interviews to the types of misconception that most frequently appeared in the unit tests. Finally, using interviews and quizzes addressing the same material, I will compare the misconceptions I identified and analyzed using the oral interviews to the misconceptions I identified and analyzed using the short quizzes.

Habits of Mind - Methods

What impact does incorporating habits of mind instruction in a high school mathematics class have on students’ improvement of mathematical thinking and problem solving self-efficacy?

Participants:

                Students in the class I will teach my Unit Plan.

Measures:

Pre- and Post Self-Efficacy survey – I will create a survey to measure how confident they are in their problem solving.  The survey will probably be a Likert Scale. I will include general questions and give specific examples of math problems.  They will then be asked to select different level of confidence they have towards those problems.

Pre- and Posttest – This will depend on the content I am teaching.  I will create a pre- test that test their problem solving skills based on the concepts already learned during the year.  I will then create a posttest with similar problems along with additional problems from the unit I taught.

Student Journal Reflections – I will ask students to write reflections about what they learned about themselves in solving mathematics problems.  This will be used to measure confidence as well as their problem solving improvement.

Focus Group – I will hold a focus group at the end of the unit to assess the attitudes students have towards problem solving. (I may hold one at the beginning as well)

Analysis:

This study will include qualitative and quantitative research.  I will compare the pre- and post Self-efficacy surveys to see if their confidence in problem solving improved.  I will also compare the pre- and posttest to see if their mathematical thinking abilities have improved. I will use the Student Journal Reflections to evaluate their confidence and ability improvements.  The focus group will be used to assess their confidence and evaluate the students’ feelings towards problem solving.

Methodology

Research Question: How does a student's ability to regulate nightly homework affect performance and comprehension in mathematics? What can be done to improve a student's ability to self-regulate?

Participants: All of my students in the classes I will be student teaching. I am going to select four students from each class based on a stratified sample. I will divide the class into A students, B students, C students and D/F students and then randomly choose a student from each group.

Methodology: Both Quantitative and Qualitative measures will be used.

Observation: I would like to video/audio tape as many lessons as possible. I plan on videotaping one lesson a week and audio taping one or two more a week. For the lessons I do not video/audio tape, I will take note of any significant occurrences that may not have happened on a previous video/audio taping day. These recordings and notes will be coded for various types of student participation (on/off task, voluntary/non-voluntary).

Interview: I will use pre- and post-class surveys using a Likert scale (I feel like this is going to be a common theme), pre- and post- class one-on-one interviews with selected students. I will attempt to get a third party to conduct the interviews so that the students’ responses are not influenced by the fact that I am interviewing them. Interviews and surveys will focus around the students’ self-regulatory abilities as well as their attitudes towards my methods of improving these abilities.

Artifacts: I will collect homework periodically (once/twice a week). Photocopies of these homework assignments will be used and coded based on completeness, effort and correctness. I will also be using the students’ quarter test results.

Analysis: All of the data I collect will be used in some sort of comparison to the students’ self-regulation. The pre-class survey will include a section designed to measure self-regulation. The results of this initial survey will be compared qualitatively to the various observations, interviews and artifacts listed above. The pre-class survey will also be quantitatively analyzed with regards to the post-test survey and the quarter test results. The post-test survey will also be analyzed with regards to the quarter test results.

Methods- 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?

Participants: Algebra I or Algebra II students- the entire class and a small group of 5-7 students who will be formally interviewed

Methodology: Mixed methods – both qualitative and quantitative research

Measures: - Artifacts: Writing samples in the form of tickets out the door, warm-ups, homeworks, and test/quiz questions
- Interview: pre-test and post-test survey using a Likert-type scale to assess students’ attitudes about their math abilities, survey using a Likert-type scale to assess students’ attitudes towards math journaling, formal one on one tape recorded interviews with 5-7 students to assess their feelings towards math journaling and how it has affected their confidence in their math abilities

- Observations: Note taking during and after writing activities

How I will analyze data: Calculate the mean, average, and standard deviation for all surveys – this information will reveal how the students feel about math journaling and gauge their confidence levels in their math skills. I will organize writing samples by each student and evaluate the content of conceptual math understanding on each assignment. Each assignment will be graded, so I can use Excel or another statistical software tool to find the rate of improvement for each student, the class as a whole, etc. I will use this information to see if students improve their math understanding and reasoning skills with increased practice in math journaling. I will also transcribe the tape recorded formal interviews and highlight key excerpts and keep these transcripts in my research notebook. My notes will also be highlighted for key ideas and observations. All of this data will be brought together to convey as completely as possible the answer to my research question.

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. 

Topic 1. Your Topic.

We will begin by reflecting on a topic. It will be several weeks before you make a final decision about your topic, and it is time to think about it and get feedback from your peers and me. I am interested to know what you are thinking at this point. Please post a paragraph or two (click on comment below) by August 20. Comments on other posts are welcome.

Welcome New Math Ed Researchers

Welcome New Math Ed Researchers

This blog is our space to reflect on the research process and to share thoughts for the research project. It will be read by our Action Research class. I hope that you will use it as an opportunity to reflect on your understandings, and to learn from each other. Feel free to share questions and ideas. Comments on other posts are always welcome. I insist that we function as a supportive and cooperative group. Be constructive and be respectful.