Math Ed 377 Mathematics Teaching and the Classroom
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Math Ed 378 Practicum in Mathematics Education
Activity Descriptions
Lesson Plans: You will spend much of your time for this class writing and revising lesson plans (approximately one every two weeks). Two times throughout the semester you will actually teach this lesson to your classmates. There are thus two different, but related assignments regarding writing lesson plans:
Prepared Lesson Plans: (45 points each) On cycles when you are not assigned to teach a lesson, you will still be assigned to prepare a lesson (lesson plan template). Your lesson plan is due on the day that one of your peers teaches that lesson. You will find it very interesting and informative to watch someone else teach a lesson on a topic for which you too prepared a lesson.
Grading rubric:
8  The fundamental mathematics concepts are appropriate to the lesson and unit and the concept descriptions are well articulated and mathematically correct
3  The description of requisite mathematics is relevant and well connected
3  There are relevant connections to the Common Core or other relevant literature
3  Tools for enhancing discourse or described, including a brief rationale for why such tools (and possibly not others) were chosen
3  Abbreviated unit sequence (previous, current, subsequent) is well thought out reasonably justified
10  The phases of the lesson are detailed, with an organization and flow consistent with developing the fundamental mathematics concepts through reasoning and sensemaking activities
10  Anticipated student thinking is described with forethought and detail
5  Responses to student thinking is mathematically oriented, insightful and detailed
Taught Lesson Plans: (95 points each) For each lesson that you will actually be teaching (once again, only twice during the semester), you will first prepare a draft lesson (lesson plan template), then make an appointment to come in to discuss that draft with me (this must be done no later than 24 hours before you teach). The final draft of your lesson plan is to be completed on the day you teach the lesson but will be submitted with your reflection no later than 1 week after the lesson is taught. You will have 30 minutes to teach your lesson and then 15 minutes to receive feedback from me and from your peers. Your lesson and the discussion that follows will be digitally recorded on a miniDVD and you will be given the miniDVD to take home with you. Your assignment is to watch this miniDVD, analyze the lesson based on your own experieence and the feedback you recieved in class, and synthesize these reflections into a reflection paper.
There are far too many aspects of teaching for you to address them all in your reflection. For these reflection papers your assignment is to compare and contrast students’ mathematical thinking and the aspects of the lesson that either facilitated or hindered that thinking. Focus more on the students and on the structure of the lesson than on yourself as the teacher. As the audience for this paper (your peers and I) will have participated in the lesson with you, you will not need to spend time recounting or summarizing the content of the lessons, although brief descriptions will likely be necessary in order to provide context for your discussion. Also, although you will certainly notice them, avoid discussing idiosyncracies such as saying "like" or playing with your hands. Stay focused on the aspects of the lessons that either facilitated or hindered mathematical learning. This analysis should lead naturally to a discussion of how the lesson could be improved.
Because this paper is reporting on reflections on your own teaching, writing in first person is appropriate. This is not a journal entry, however, or an email to a friend. This is a report of a teaching analysis. Your paper should be wellorganized, with an introduction, a thesis, wellconstructed paragraphs, and a conclusion. Your paper should be 35 pages in length, doublespaced, with standard (1 inch) margins and in 12point font. Use headings sparingly if at all. This paper is due one week from the day you teach your lesson. You will also submit your lesson plan at this time. You may want to include some hand written notes on the lesson plan indicating how you might handle things differently if you were to teach the lesson again.
Grading rubric:
8  The fundamental mathematics concepts are appropriate to the lesson and unit and the concept descriptions are well articulated and mathematically correct
3  The description of requisite mathematics is relevant and well connected
3  There are relevant connections to the Common Core or other relevant literature
3  Tools for enhancing discourse or described, including a brief rationale for why such tools (and possibly not others) were chosen
3  Abbreviated unit sequence (previous, current, subsequent) is well thought out reasonably justified
10  The phases of the lesson are detailed, with an organization and flow consistent with developing the fundamental mathematics concepts through reasoning and sensemaking activities
10  Anticipated student thinking is described with forethought and detail
5  Responses to student thinking is mathematically oriented, insightful and detailed
15  Met with Dr. Peterson and made appropriate revisions based on this discussion
35  35 page reflection paper demonstrates thoughtful reflection, analyzes the lesson using evidence from viewing the lesson, and is clearly articulated
Classroom Observations: (20 points each) You will be observing mathematics classrooms in local middle schools, junior high schools, and high schools 6 times throughout the semester. (The first three observations will be in the same classroom, the last three in a different classroom.) You have been assigned a research lesson group and you will carry out these observations together with that group. For each of these observations you will be asked to look for and document specific aspects of mathematics teaching and learning. You will then synthesize your notes into a 24 page paper.
Grading rubric:
20  24 page paper meets the specific observation expectations in a thoughtful, wellarticulated manner
Teacher 
School 
1st Period 
Research Lesson 1 
Research Lesson 2 
Porter Nielsen 
Mapleton Jr. High School 
7:55  8:45 
Group 1 
Group 3 
Kyle Peterson 
Pleasant Grove High School 
7:45  9:03 
Group 3 
Group 4 
Trina Ward 
Spanish Fork High 
7:55  9:18 
Group 4 
Group 1 
Loraine Hanson 
American Leadership Academy 
8:45  9:50 
Group 5 

Thomas Marker 
Maple Mountain High School 
7:55  9:17 

Group 2 
Gayle Ware 
Mt. Nebo Jr. High 
8:00  8:45 
Group 2 
Group 5 
Research Lessons: (105 points) Twice during the semester you will create research lessons as part of a lesson study group. In each case you have been assigned to one of 5 Research Lesson groups, and each group has been assigned to work with a particular cooperating teacher (the same classroom in which you will do your classroom observations). You will meet with this group as you plan, teach, revise and teach again a mathematics lesson. (It is called a research lesson because of this iterative, intensive process.) The overall process should proceed as follows:
 Meet briefly with the cooperating teacher when you conduct Observation 1 (or 3). Discuss with them the mathematical goals they would like you to accomplish when you teach a lesson in their classroom on Wednesday, Oct. 13 (or Nov. 23).
 Meet regularly with your group to plan your lesson. Use the standard lesson plan template.
 Take some time when you conduct Observation 2 (or 4) to discuss your research lesson with the cooperating teacher and get their feedback.
Meet with Dr. Peterson as a group to discuss your plans and to get feedback (must be done no later than 1 week before you teach the lesson to your peers).
 Teach your research lesson to the class during the time appointed. Arbitrarily choose one member of your group to teach the lesson and make this choice no earlier than the day before you teach. The lesson you teach to your peers will most likely be shorter than the lesson you teach in the schools so select only a portion of your final lesson to teach to your peers.
 Make revisions to your lesson based on your experience teaching it to your peers and based on their feedback.
 Teach your research lesson in your teacher's classroom. (Plan to arrive 30 minutes before class starts on these days.) Once again arbitrarily choose one member of your group to teach the lesson and make this choice no earlier than the day before you teach.
 Individually write a 35 page reflection paper discussing the evolution of your lesson and what you learned from the research lesson process. The following questions will be useful in drafting your report:
 How did your overall lesson goals and big mathematical idea evolve over the course of your research? To what do you attribute these changes?
 How did your tasks and questions evolve over the course of the lesson preparation? To what do you attribute these changes?
 Based on your experience teaching your lesson to your peers, how well did you anticipate student thinking and responses? Were there some responses that you did not anticipate?
 How did your reflections on teaching your lesson to your peers influence future drafts of your lesson plan?
 Based on your experience teaching your lesson in your teacher's classroom, how well did you anticipate student thinking and responses? In what ways were you able to integrate those responses into the lesson as it was being taught?
 If you were to teach this lesson again, what would you do differently?
 Finally, send me a brief email in which you evaluate (on a scale of 010) the cooperation and work ethic of each member of your group, including yourself.
Grading rubric:
8  The fundamental mathematics concepts are appropriate to the lesson and unit and the concept descriptions are well articulated and mathematically correct
3  The description of requisite mathematics is relevant and well connected
3  There are relevant connections to the Common Core or other relevant literature
3  Tools for enhancing discourse or described, including a brief rationale for why such tools (and possibly not others) were chosen
3  Abbreviated unit sequence (previous, current, subsequent) is well thought out reasonably justified
10  The phases of the lesson are detailed, with an organization and flow consistent with developing the fundamental mathematics concepts through reasoning and sensemaking activities
10  Anticipated student thinking is described with forethought and detail
5  Responses to student thinking is mathematically oriented, insightful and detailed
15  Met with Dr. Peterson and made appropriate revisions based on this discussion
10  Average of your peer evaluations of your cooperation and work ethic in the group
35  35 page reflection paper demonstrates thoughtful reflection, analyzes the lesson using evidence from viewing the lesson, and is clearly articulated
Final Exam: (50 points) We will have a final exam (comprehensive, essay based) during our scheduled final time on December 15 from 7am to 10am.
