Sunday, March 14, 2010
Social Justice Mathematics Lesson Plan
https://docs.google.com/fileview?id=0B6dYRiMIXmpsMWFlZmMxNzMtNDYwOC00MDk5LTk3MTgtMzIyYTE3YTliZTMz&hl=en
Monday, March 8, 2010
Final Exam
1) Secondary Schooling in the 21st Century involves greater focus on relevant tasks and challenging curriculum. Classes will be organized around different career paths that students will choose. This will allow content to be taught in relation to practical application in those career paths which students have indicated interest in. These classes will incorporate real life experiences with the community, such as internship opportunities and professional guest speakers in the classroom. Curriculum will be more rigorous, pressing students to think critically and give reasons for their answers. They will be given challenging tasks that focus more on the process of solving the task than on the solution itself. Schooling in the 21 Century will also be more inquiry based, in which the teacher is not the disseminator of information, but rather the coach in guiding students’ thinking and discussion. This involves more activities in which the students explore and discover important concepts, rather than them simply being told them.
2) I will provide students with challenging tasks (such as POWs) that will require them to explore possible solutions to a problem without being told exactly how to do it. This will foster problem solving skills and allow the student to discover the need for certain questions to be answered. Students will be given opportunities to collaborate with their peers in order to gain insight into these challenging tasks. I do not believe that I will be able to incorporate these types of problems everyday in the classroom, or even every week, as they can be very time consuming. I can see myself practically including these types of exploratory and collaborative tasks at the beginning of each new unit. I may use these types of problems to introduce some of the key concepts that will be studied in the unit. I hope that by using these types of problems, students will value the concepts being studied further in the unit, as they will see a context for those concepts and a need for their development through the exploration of the POW.
3) During my first two years of teaching I want to incorporate more career oriented contexts for the mathematical concepts I will be teaching. I think it would be awesome to have guest speakers come in and share how math is used in their specific careers (especially careers that do not seem to involve math). I would like students to research the careers that they are interested in and give some kind of presentation on how mathematics is involved in these careers. I hope that continually relating the mathematical concepts in class to the real world, whether through careers or just daily life, would help students see mathematics as more than just “a subject that had to learn in school.” In my first year of teaching, I think I will focus on discovering some of these career applications myself and incorporating them into my lessons. I may also have students do the research project on careers they are interested in. In my second year of teaching, I may try to involve more guest speakers, possibly some of my students’ parents.
4) Later in my career I will try to incorporate more types of exploratory problems when introducing any new concept. Students will be constantly involved in collaborating about these exploratory problems. Later in my career I will also try to involve my students on in some community experience in which they see the applications of mathematics in different careers – maybe a field trip to a business where employees can explain how they use mathematics in their company.
5) These plans for action could fall under many categories. The challenging exploratory tasks could fall under “Creating New Curriculum Paths” as it proposes a more rigorous and discovery focused curriculum. The relevance to careers would also fall under this category as it gives a new direction or context in which all curriculum is to be studied. These plans for action also fall under “Powerful Teaching” since they involve making the curriculum more meaningful for students. They provide greater relevance to the content being studied and greater understanding for the need of these concepts. Students will also be allowed to explore new concepts through challenging problems (such as POWs) will give them opportunities to be more active and inquisitive learners.
2) I will provide students with challenging tasks (such as POWs) that will require them to explore possible solutions to a problem without being told exactly how to do it. This will foster problem solving skills and allow the student to discover the need for certain questions to be answered. Students will be given opportunities to collaborate with their peers in order to gain insight into these challenging tasks. I do not believe that I will be able to incorporate these types of problems everyday in the classroom, or even every week, as they can be very time consuming. I can see myself practically including these types of exploratory and collaborative tasks at the beginning of each new unit. I may use these types of problems to introduce some of the key concepts that will be studied in the unit. I hope that by using these types of problems, students will value the concepts being studied further in the unit, as they will see a context for those concepts and a need for their development through the exploration of the POW.
3) During my first two years of teaching I want to incorporate more career oriented contexts for the mathematical concepts I will be teaching. I think it would be awesome to have guest speakers come in and share how math is used in their specific careers (especially careers that do not seem to involve math). I would like students to research the careers that they are interested in and give some kind of presentation on how mathematics is involved in these careers. I hope that continually relating the mathematical concepts in class to the real world, whether through careers or just daily life, would help students see mathematics as more than just “a subject that had to learn in school.” In my first year of teaching, I think I will focus on discovering some of these career applications myself and incorporating them into my lessons. I may also have students do the research project on careers they are interested in. In my second year of teaching, I may try to involve more guest speakers, possibly some of my students’ parents.
4) Later in my career I will try to incorporate more types of exploratory problems when introducing any new concept. Students will be constantly involved in collaborating about these exploratory problems. Later in my career I will also try to involve my students on in some community experience in which they see the applications of mathematics in different careers – maybe a field trip to a business where employees can explain how they use mathematics in their company.
5) These plans for action could fall under many categories. The challenging exploratory tasks could fall under “Creating New Curriculum Paths” as it proposes a more rigorous and discovery focused curriculum. The relevance to careers would also fall under this category as it gives a new direction or context in which all curriculum is to be studied. These plans for action also fall under “Powerful Teaching” since they involve making the curriculum more meaningful for students. They provide greater relevance to the content being studied and greater understanding for the need of these concepts. Students will also be allowed to explore new concepts through challenging problems (such as POWs) will give them opportunities to be more active and inquisitive learners.
Monday, March 1, 2010
Sunday, February 28, 2010
Reading Reflection 5 - "I'm thinking . . ."
Since we have free reign on how to present this week's response, I would like to write my thoughts as I read through Chapter 8, "Treating Expectations for Competence." If my thoughts seem disconnected, realize that I am writing them chronologically as they come to my mind when reading.
(p 117) The problem:
High status students are expected to do well on group assignments and may dominate the group while low status students are expected to do poorly on group assignments and may not participate.
(117) Two strategies:
1) "establishing cooperative norms such as 'everyone participates' and 'everyone helps'"
2) "giving every student a part or role to play"
(118) Design tasks where the low status students can be the experts and teach the high status students.
Question: How do you find a task that applies to the entire class in which the low status students are the experts? Perhaps just apply this principle one student at a time? (Not every task will be able to bring in all the low status students, but hopefully some of them?)
Task idea: In a task such as "Master Designer" (p. 168) choose the low status students to be the master designers in their groups. This makes them the one who knows all the answers and the rest of the group is asking them questions about how the final design of the shapes are supposed to look.
(120-122) Expectation training - this sounds like a good idea, training the low-status students so that they can be the "experts" in a group activity, but I am unsure how this is practically applied. What kind of situations would you be training these students for? As Cohen notes himself, this model is also a difficult one since it requires extra time put in for the teacher.
(122) Providing tasks that use multiple abilities increases the probability that each person will have a different skill to contribute. When introducing the task to the students, I think it is very valuable to stress to the students "None of us has all of these abilities. Each one of us has some of these abilities" (122). This gets the students thinking about what each person has to contribute and, like Maria shared on p. 122, the students might be surprised about what ability someone might bring to the group.
(128) We need to focus on intellectual abilities - working with others or working with one's hands are not seen at the same status of working with the intellect in our culture. When speaking of one's artistic abilities, one can focus on the intellectual ability to visualize something in a new way and represent it symbolically.
(128) I agree that it is important to remind students that they can develop new abilities and they are not simply abilities that people are born with. If this is not made clear, some students may hear the list of abilities you give for specific tasks and not find themselves capable of any of them. This could push them toward further non participation. Thus, we need to provide tasks that incorporate a wide variety of abilities, but emphasize the possibility of developing these abilities as well.
(131-133) We need to be looking for the specific ways that our low status students are succeeding and praise them for their successes. This is an excellent way to give confidence to low status students - and if we really believe that each student is valuable, then that means that each student has something unique about them that is worth getting to know. We need to be searching for that unique thing and make it known.
(p 117) The problem:
High status students are expected to do well on group assignments and may dominate the group while low status students are expected to do poorly on group assignments and may not participate.
(117) Two strategies:
1) "establishing cooperative norms such as 'everyone participates' and 'everyone helps'"
2) "giving every student a part or role to play"
(118) Design tasks where the low status students can be the experts and teach the high status students.
Question: How do you find a task that applies to the entire class in which the low status students are the experts? Perhaps just apply this principle one student at a time? (Not every task will be able to bring in all the low status students, but hopefully some of them?)
Task idea: In a task such as "Master Designer" (p. 168) choose the low status students to be the master designers in their groups. This makes them the one who knows all the answers and the rest of the group is asking them questions about how the final design of the shapes are supposed to look.
(120-122) Expectation training - this sounds like a good idea, training the low-status students so that they can be the "experts" in a group activity, but I am unsure how this is practically applied. What kind of situations would you be training these students for? As Cohen notes himself, this model is also a difficult one since it requires extra time put in for the teacher.
(122) Providing tasks that use multiple abilities increases the probability that each person will have a different skill to contribute. When introducing the task to the students, I think it is very valuable to stress to the students "None of us has all of these abilities. Each one of us has some of these abilities" (122). This gets the students thinking about what each person has to contribute and, like Maria shared on p. 122, the students might be surprised about what ability someone might bring to the group.
(128) We need to focus on intellectual abilities - working with others or working with one's hands are not seen at the same status of working with the intellect in our culture. When speaking of one's artistic abilities, one can focus on the intellectual ability to visualize something in a new way and represent it symbolically.
(128) I agree that it is important to remind students that they can develop new abilities and they are not simply abilities that people are born with. If this is not made clear, some students may hear the list of abilities you give for specific tasks and not find themselves capable of any of them. This could push them toward further non participation. Thus, we need to provide tasks that incorporate a wide variety of abilities, but emphasize the possibility of developing these abilities as well.
(131-133) We need to be looking for the specific ways that our low status students are succeeding and praise them for their successes. This is an excellent way to give confidence to low status students - and if we really believe that each student is valuable, then that means that each student has something unique about them that is worth getting to know. We need to be searching for that unique thing and make it known.
Monday, February 22, 2010
Reading Reflection 4 - Groupwork Ch. 4-5
Chapter 4 of Cohen's Designing Groupwork discusses the need for "Teaching Specific Cooperative Behaviors" (p.44-52) dependent on the type of groupwork one has in mind for students to participate in. Cohen gives the example of the different student behaviors required for learning stations (different tasks in the room for students to work with their group members to complete) and for small discussion groups. Some of the student behaviors for learning stations include "helping students do things for themselves" and "explaining by telling how and why." For small discussion groups, student behaviors include "allowing everyone to contribute" and "finding out if group is ready to make decision." Teachers need to train their students in these behaviors specific to the groupwork they will have them participating in.
I think that it is important for the teacher to discuss with the class the connections between the training processes and the groupwork used to teach content. This will help students see the training exercises as more meaningful and will remind them of the principles of the training as they do groupwork to learn content. I also think that there are so many different principles for making groupwork successful, that it can be helpful to focus in on just one or two things that you want your students to remember for the specific groupwork activities you will have them participate in.
Cohen also discussed the skills students need in order to participate in high-level discourse. Students may be engaged in high level thinking during group work, but they may only verbalize the conclusions to their thinking. Students do not naturally discuss the logic which led them to their conclusions unless instructed to do so. Being able to articulate one's thinking process is important for communicating scientific ideas, analyzing social problems, and explaining the logic behind mathematical deductions. The skillbuilder "Rainbow Logic" (Appendix A, p.172-175) helps students develop the ability to communicate their thought processes.
It is important for us as teachers to help our students develop this skill of explaining one's thinking, as it will aid us in assessing our students understanding of specific content. If a student can explain their thinking, we can more accurately pinpoint the heart of a student's confusion or understanding. Training students to explain their thinking also helps them think more carefully, paying attention to why they think what they do.
Any of the skillbuilding exercises that one uses to train their students for groupwork need to meet the five social learning principles that Cohen discusses. These are:
1) New behaviors must be labeled and discussed.
2) Students must learn to recognize when new behaviors occur.
3) Students must be able to use labels and discuss behavior in an objective way.
4) Students must have a chance to practice new behaviors.
5) New behaviors should be reinforced when they occur.
-Cohen, p.48
Teachers also need to reinforce and teach students certain skills during the groupwork activities. Teachers can listen in on groups as they work and ask questions to challenge students to give reasons for their ideas. Teachers can also take notes on good examples of behavior that he/she observes and bad behavior. After the groupwork, the teacher can share his/her notes and lead the class in a discussion about how the good behavior led to successful work and how the bad behavior could have been dealt with differently by the group members.
I think that this reinforcement of groupwork skills is critical, as it will help students to be more mindful of the training that they initially received. One training activity is not going to be enough to change a students' habits in relating to others. If the teacher continually draws attention to these skills, and the students become convinced of their effectiveness in groupwork, the skills may eventually become norms.
I think that it is important for the teacher to discuss with the class the connections between the training processes and the groupwork used to teach content. This will help students see the training exercises as more meaningful and will remind them of the principles of the training as they do groupwork to learn content. I also think that there are so many different principles for making groupwork successful, that it can be helpful to focus in on just one or two things that you want your students to remember for the specific groupwork activities you will have them participate in.
Cohen also discussed the skills students need in order to participate in high-level discourse. Students may be engaged in high level thinking during group work, but they may only verbalize the conclusions to their thinking. Students do not naturally discuss the logic which led them to their conclusions unless instructed to do so. Being able to articulate one's thinking process is important for communicating scientific ideas, analyzing social problems, and explaining the logic behind mathematical deductions. The skillbuilder "Rainbow Logic" (Appendix A, p.172-175) helps students develop the ability to communicate their thought processes.
It is important for us as teachers to help our students develop this skill of explaining one's thinking, as it will aid us in assessing our students understanding of specific content. If a student can explain their thinking, we can more accurately pinpoint the heart of a student's confusion or understanding. Training students to explain their thinking also helps them think more carefully, paying attention to why they think what they do.
Any of the skillbuilding exercises that one uses to train their students for groupwork need to meet the five social learning principles that Cohen discusses. These are:
1) New behaviors must be labeled and discussed.
2) Students must learn to recognize when new behaviors occur.
3) Students must be able to use labels and discuss behavior in an objective way.
4) Students must have a chance to practice new behaviors.
5) New behaviors should be reinforced when they occur.
-Cohen, p.48
Teachers also need to reinforce and teach students certain skills during the groupwork activities. Teachers can listen in on groups as they work and ask questions to challenge students to give reasons for their ideas. Teachers can also take notes on good examples of behavior that he/she observes and bad behavior. After the groupwork, the teacher can share his/her notes and lead the class in a discussion about how the good behavior led to successful work and how the bad behavior could have been dealt with differently by the group members.
I think that this reinforcement of groupwork skills is critical, as it will help students to be more mindful of the training that they initially received. One training activity is not going to be enough to change a students' habits in relating to others. If the teacher continually draws attention to these skills, and the students become convinced of their effectiveness in groupwork, the skills may eventually become norms.
Sunday, February 14, 2010
Reading Reflection 3 - Groupwork Ch. 1-3
Chapter 1
Groupwork is introduced as an opportunity to "talk, explain, and argue" about concepts and ideas (1). Groupwork allows students to delegate authority on their own which makes them responsible for their specific part of the work. Members within a group need each other in order to complete the task. Students who usually "check-out" during class tend to be more engaged in learning through groupwork.
The most beneficial groupwork I have participated in is when students are sharing their opinions or experiences regarding a specific idea. I think that groupwork that takes advantage of the differing perspectives of students is the most beneficial.
Chapter 2
Students within each group can offer different skills which can help the group as a whole. Groupwork is especially helpful in understanding abstract concepts and problems that do not have a clear answer. Discussion within groups promotes higher order thinking through frequent "oral summarizing, explaining, and elaborating what one knows" (15). Groupwork also helps engage the "checked-out" student and helps build healthy relationships between students of different backgrounds.
I have found that groupwork on the POWs in EDSS543 have been especially interesting in providing insight into multiple ways to solve a problem. Hearing one person's thoughts inspires other people to take those thoughts further, whereas by oneself, an individual may not have made the original "thought leap" to further the exploration.
Chapter 3
A common problem in groupwork is when a student's status (expert, academic, peer, societal) that has nothing to do with the task at hand "becomes the basis for dominance in the group" (38). Groupwork provides the opportunity for individuals to overcome individual prejudices, but if the teacher does not train the students and facilitate this groupwork, it could also enhance these prejudices.
I am curious how to deal with these status issues as a teacher - I guess I will have to keep reading :) I have been in groups before where there is one person who always talks and sometimes they present to the class the "group" perspective - which really was mainly their own. I have been on the end of trying to give input to the group in the midst of this dominant personality, and it is often dismissed. This has pushed me to less participation in the group since I don't want to put energy into the fight to get my opinion heard.
Groupwork is introduced as an opportunity to "talk, explain, and argue" about concepts and ideas (1). Groupwork allows students to delegate authority on their own which makes them responsible for their specific part of the work. Members within a group need each other in order to complete the task. Students who usually "check-out" during class tend to be more engaged in learning through groupwork.
The most beneficial groupwork I have participated in is when students are sharing their opinions or experiences regarding a specific idea. I think that groupwork that takes advantage of the differing perspectives of students is the most beneficial.
Chapter 2
Students within each group can offer different skills which can help the group as a whole. Groupwork is especially helpful in understanding abstract concepts and problems that do not have a clear answer. Discussion within groups promotes higher order thinking through frequent "oral summarizing, explaining, and elaborating what one knows" (15). Groupwork also helps engage the "checked-out" student and helps build healthy relationships between students of different backgrounds.
I have found that groupwork on the POWs in EDSS543 have been especially interesting in providing insight into multiple ways to solve a problem. Hearing one person's thoughts inspires other people to take those thoughts further, whereas by oneself, an individual may not have made the original "thought leap" to further the exploration.
Chapter 3
A common problem in groupwork is when a student's status (expert, academic, peer, societal) that has nothing to do with the task at hand "becomes the basis for dominance in the group" (38). Groupwork provides the opportunity for individuals to overcome individual prejudices, but if the teacher does not train the students and facilitate this groupwork, it could also enhance these prejudices.
I am curious how to deal with these status issues as a teacher - I guess I will have to keep reading :) I have been in groups before where there is one person who always talks and sometimes they present to the class the "group" perspective - which really was mainly their own. I have been on the end of trying to give input to the group in the midst of this dominant personality, and it is often dismissed. This has pushed me to less participation in the group since I don't want to put energy into the fight to get my opinion heard.
Monday, February 8, 2010
Innovative School: Roosevelt Middle School
http://www.rooseveltmiddle.org/
http://www.ibo.org/ (Inernational Baccaluaureate Program)
http://www.ibo.org/ (Inernational Baccaluaureate Program)
Saturday, February 6, 2010
Reading Reflection 1 - Rethinking High School
The repeated focus on authentic and challenging learning experiences resonated with me as I read the first chapter of "Rethinking High School," by Daniels, Bizar, and Zemelman. The chapter cited that the national curriculum standards call for "real, rich, complex ideas and materials" and oppose lessons that "water down, control, or oversimplify content" (14). They also say that "students learn best when faced with genuine challenges, choices, and responsibility in their own learning" and "the most powerful learning comes when children develop true understanding of concepts trough higher-order thinking" (14). I think too many classrooms these days are losing students' interest because students are not challenged to think for themselves. Students are simply fed tons of information and expected to regurgitate it back out - how boring! It seems that many teachers fall into this pattern of just spoon-feeding information to their students because they do not think that their students can handle it any other way. Teachers are also stressed to get through a certain amount of material for testing sake and feel that they do not have time to wait for their students to think. Some of my most enjoyable times of learning come when I am faced with a problem that is not immediately solvable. I have to play with the idea and explore possibilities using the resources available to me. I apply what I already know (with some guidance and discussion with those around me) in order to solve the new problem. I was encouraged to read in Chapter 1 that studies show that students who are challenged with this more authentic type of learning have performed significantly higher on standardized tests than students in traditional classrooms.
The only measure of reform mentioned in Chapter 1 that I think we need to qualify is the student-centered focus of investigating students' own questions over "arbitrarily and distantly selected content." I agree with this at the heart, that we should relate the material we teach to students' lives and interests. I think this can be taken too far, however, when teachers do not come with a specific curriculum in mind and let students run the discussions of the class whether they relate to the content area or not. I have heard of a class such as this where the teacher began the class with "So, what should we talk about today?" and the class continued in conversations of all kinds, not focusing in any specific direction or even relating to the content area of the class. I think we need to remember that students still need guidance and instruction in the classroom - they don't know everything and we do have something to teach them.
One reform that I would like to focus on more is how to create a "small" feel in high schools and community in the classroom. I would like each student to feel known and included in my classroom. I think much of this can be obtained through group work, so I am interested in learning how to use group work effectively in the classroom. I think sometimes group work is used in classrooms (even in this credential program) just so that we can say we use "group work." The nature of the group assignment given is not very conducive to group work, however, and this can make the assignment less effective. I am interested in learning when group work really is more beneficial than working independently, and how to implement it effectively.
The only measure of reform mentioned in Chapter 1 that I think we need to qualify is the student-centered focus of investigating students' own questions over "arbitrarily and distantly selected content." I agree with this at the heart, that we should relate the material we teach to students' lives and interests. I think this can be taken too far, however, when teachers do not come with a specific curriculum in mind and let students run the discussions of the class whether they relate to the content area or not. I have heard of a class such as this where the teacher began the class with "So, what should we talk about today?" and the class continued in conversations of all kinds, not focusing in any specific direction or even relating to the content area of the class. I think we need to remember that students still need guidance and instruction in the classroom - they don't know everything and we do have something to teach them.
One reform that I would like to focus on more is how to create a "small" feel in high schools and community in the classroom. I would like each student to feel known and included in my classroom. I think much of this can be obtained through group work, so I am interested in learning how to use group work effectively in the classroom. I think sometimes group work is used in classrooms (even in this credential program) just so that we can say we use "group work." The nature of the group assignment given is not very conducive to group work, however, and this can make the assignment less effective. I am interested in learning when group work really is more beneficial than working independently, and how to implement it effectively.
Monday, January 25, 2010
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