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Teacher Training with Blackboard by Renan Sezer

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In the two teacher training courses offered at LaGuardia Community College for future elementary students blackboard component was added. In the first course the Blackboard component helped students investigate such topics as: career goals, education and board certification requirements, expected salary etc.

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In the second course web inquiry based learning component was added through Blackboard assignments in order to investigate the opposing views of what is generally known as “Math Wars”, i.e. teaching mathematics through reform curricula vs. a traditional approach.

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Blackboard assignments help students by: drawing shy students into class discussion starting an ongoing exchange of ideas exploring different view points and not being tied to one source of information increasing student authorship

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BlackBoard Assignment #1 Please answer each question individually. 1) How many years ago were you in elementary school? 2) Did you go to elementary school in the U.S. or in another country? 3) Think back to your elementary mathematics education and respond to the following questions: a) Was it a teacher-centered or student-centered classroom? b) What was the interaction between students during the mathematics classroom? c) What kind of activities were you assigned as mathematics homework (e.g. drill questions, word problems, writing assignments, exploration activities etc.)

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4) As a future elementary school teacher, you need to be able to explaining the reasoning behind basic mathematical operations and the steps required to do them. (For example you need to explain why when you multiply the denominator of a fraction by a number you multiply the numerator by the same number to keep the value the same. You must be able to explain why when adding and subtracting fractions you need to find common denominator and when you multiply and divide you do not. The reasons behind them are much more than saying “Because it is the rule.”) You will also need to be able to tackle a variety of word problems. With these in mind, write how confident you are in your mathematics knowledge? Do you have a solid mathematics back ground? Please be very honest.

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5) Based on your answer to question #4, what pedagogical styles of teaching would have prepared you better in terms of your mathematics knowledge? 6) If you had a child going to elementary school, what kind of things would you want him/her to learn and do in mathematics class?

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Sample Student Respond 1)It has been about eight years since I have been in elementary school. 2)I attended school in the U.S. 3) a) I recall each classroom experience was different. The dominate form of teaching in the classroom was teacher- centered. There was very little student to student interaction. A great deal of student-teacher interaction was practiced as well as long extensive notes to take which mostly made the classroom too silent for me personally. The teacher was always standing in front of the class or even sitting at the desk delivering the concept that was to be learned during a given time. I remember even one lesson was nothing but note taking without the teacher saying anything, only as a student was I told to review the notes for that evening as homework.

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3b) A typical mathematics session in my classroom was that all of the guided learning was directly drawn from the text book. Each chapter or lesson was approached step by step as it was given in the text book. These steps were often dictated by the teachers who would give examples and as a class we would answer them. After being introduced to the lesson, the students were then given problems to solve individually. Then the class would come together with the teacher and go over the problems. There was rarely any interaction among the students themselves. Group assignments weren’t really practiced except for science projects. 3c) The homework tasks that were assigned were always directly from the text. They mostly consisted of drill question and numerical problems. Word problems were seasonally assigned. They were assigned mostly when word problems were introduced as a lesson. I cannot recall exploration activities. My elementary school was not an expeditionary learning center. It was dictated text, lots of writing, and memory competition.

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4) First and foremost I am not comfortable in mathematics in my own knowledge at the top of my head. Often I have to refresh my memory, but I am looking forward to learning to a point where the information is already their and that I can retrieve it from memory. I doubt myself and my abilities when usually I am right or on the right track in solving a problem. I also have a bad habit of confusing certain laws and rules in math. My given mathematics background would be more solid if I had learned differently also upon my own efforts. 5) What would’ve helped me best is more interaction. I am a visual and expeditionary learner. Usually, anything with hardcore statistics and facts do not impact my learning ability as much as. It is through given examples and discussions that trigger understanding and what I learn to memory. More of this rather than dictation would have helped.

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6) If I had a child in elementary school, in contrast to my experience, I would want the child to learn basic mathematics. Without the basics it would be impossible to advance in higher levels of mathematics. As they learn in a mathematics class I would like my child to have the ability to practice the math in the classroom. In a classroom I’d want my child to be able to learn mathematics to a point of being able to calculate accurately. I’d want my child to obtain the concept and information where they can openly discuss it and the problem solving procedures. If the child can openly discuss mathematical concepts, the child is then capable of helping others who do not understand.

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Another (Jin Wei’s) Response 1)I was in elementary school 50 years ago. 2) I went to elementary school in China. 3) a) It was a teacher-centered classroom. b) The students did their work independently. They couldn’t talk and discuss. c) All the activities of the students were under the teacher’s control. 4) I am a paraprofessional in PS226. I don’t want to be an elementary teacher in the future. I had been a high school English teacher for more than 20 years. Now I am studying in the college to learn the teaching method of maths because I am interested in maths and to earn 6 credits that the Department of Education requires. I think I have a solid maths back ground.

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5) PS226 is the public school for special education. Most of students are in Autism. Their speaking abilities are delayed. They can know some numerals and simple addition. It is difficult for them to work out the problems by using subtraction and division. Of courses I will do my best to help them to understand the basic concept of maths. 6) If I had a child going to elementary school I would want him/her to listen attentively in maths class and do his/her work by himself/herself. Only doing that he/she would master the basic theory of maths and have the solid maths back ground.

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A Response to Jin-Wei HI Jin-Wei you metioned that you would like your kids to work by themselves, i disagree because students need to work together. i believe that when students wotk together they learn and understand the lesson better. Students have the ability to explain their solutions to there class mates. Also you said you have a solid mathematics background, eventhough you were in elementary school 50 years ago. tell me how did you manage to still remember your basic math. probably your teacher had a eficient way of teaching her students.

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Blackboard Assignment #2 1) Review your response and those of your friends to question 6 in Blackboard assignment #1. (You do not need to write anything for this step. 2) Suppose you had a child in elementary school. Write a detailed letter to your child’s mathematics teacher telling him/her a) What your child should be learning in class b) What your child should be doing in mathematics class (For example should the class be mostly in lecture form or group discussion form? What percent of the class time should be spent in doing basic skills and what percent should be spent on problem solving and exploration activities?)

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c) Should your child be allowed to use technology in the classroom or doing homework? If so what kind of technology and when? d) What kind of homework do you think your child should be assigned (“Do not give too much homework” is not the answer I am looking for here. Some things you should reflect and write about are: whether the homework should be based on what is taught in class, should it have more drill or more word problems, could it have problems not done in class but given to them for exploration and challenge, should it involve projects where they are asked to investigate open- ended questions, should it have writing assignments in it?

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Ramy Guzman’s Response to 2 nd Assignment Dear Ms. Brown, My name is Ramy Guzman, mother of Melanie Guzman. I am concern about what Melanie will be learning in your class. I know that in order for her to understand and do well in math she needs to learn the basic skills. This is why I want you to please explain her each and every problem you assign, also show her various way of doing the problem and getting the right answer. I would like you to let her participate in class and also to give her challenging problems when you think she has learned the skills. This way Melanie can feel more confident when is given a problem. In my opinion you should give them a chance to explore what they have learn, after giving them the lecture you should assign them to small groups.

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Give them some problem and letting them use manipulative so they can see the difference in solving a problem with pencil and pen and using manipulative. They should spend an equal amount of time in basic skills and problem solving, exploration activities should be given every once in a while in order for you to know how much they know. Students shouldn’t be able to use technology during mathematics class, because math is a subject of thinking and finding solutions. In my opinion because of all the technology we have, students don’t have the chance of thinking.

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So I prefer my daughter to get less technology in the classroom and more problem solving, also at the end of class you should give them a couple of open minded questions this will give you a sense of what they learn and what they are confuse in. homework should be based on what was taught in class, but you can also give them one or two challenging problems which you will explain in the next class. By doing this you have a sense of which student are prepared for the next lesson and which students need more practice.. It should have some writing assignments this way students can explain there solutions. I am looking forward to hear from you I hope you take into consideration some of my advices and comments. If you have any questions please let me know. I want to be as much as possible involved in my daughters education all for Melanie’s best success. Sincerely, Ramy Guzman

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Response to Ramy’s Posting Dear Ramy, Your suggestions are vital to the basic math skills.However I think that although calculators should not be allowed the use of computers is vital.This is so because in today's society everything is being computerized.The child should gain hands on experience with the use of computers.If the child is able to use the computer and access information which is necessary to complete his assignments he would gain self confidence.This would help the child to be capable of using the computer for other assignments as well. I hope this response would help you to think thoroughly about the advantages and disadvantages of the use of computers.Being able to use the computer is very different from using the calculator.I totally disagree with the use of calculators when teaching basic math skills!

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Blackboard Assignment #3 NCTM STANDARDS This assignment is related to the assigned reading of the following websites: NCTM: http://standards.nctm.org/document/appendix/numb.htm In the above document click on Principles or go to http://standards.nctm.org/document/chapter2/index.htm Then Standards: http://standards.nctm.org/document/chapter3/index.htm Then Pre K-2: http://standards.nctm.org/document/chapter4/numb.htm Then 3-5 (Overview of Standards 3-5): http://standards.nctm.org/document/chapter5/numb.htm W. G. Quirk’s website: http://www.wgquirk.com/TruthK12.html http://www.wgquirk.com/Genmath.html http://www.wgquirk.com/HMathStd.html http://www.wgquirk.com/chap3.html http://www.wgquirk.com/chap4.html http://standards.nctm.org/document/appendix/numb.htm http://standards.nctm.org/document/chapter2/index.htm http://standards.nctm.org/document/chapter3/index.htm http://standards.nctm.org/document/chapter4/numb.htm http://standards.nctm.org/document/chapter5/numb.htmhttp://www.wgquirk.com/TruthK12.htmlhttp://www.wgquirk.com/Genmath.htmlhttp://www.wgquirk.com/HMathStd.htmlhttp://www.wgquirk.com/chap3.htmlhttp://www.wgquirk.com/chap4.html

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1) Please use VERBS that indicate the kind of mathematical activity that takes place in a classroom that is described by NCTM Standards. Shortly describe the kind of activities that takes place in such a classroom. (You are NOT asked to list the Standards but synthesize your reading of the Standards and visualize a classroom based on NCTM Standards.) 2) Please use VERBS that indicate the kind of mathematical activity that takes place in a classroom that is described by W. G. Quirk. Shortly describe the kind of activities that takes place in such a classroom. (Try to visualize a classroom based on W. G. Quirk’s website.) 3) If you were an elementary school student, from which of the two classes would you have benefited more? Explain in detail why? (I do not want TWO WORD answers.) 4) a) What are some of the advantages of being in an NCTM friendly mathematics classroom? b) What are some of the advantages in being in a mathematics classroom described by W. G. Quirk?

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Diana’s Response to 3 rd Assignment 1) The kind of activity that takes places in a classroom that is described by NCTM standards substitute “math appreciation” content for traditional K-12 math content. NCTM believes that traditional K-12 math is too difficult for most children. Their version of “math reform” omits the essence of traditional K-12 math, including standard computational skills, symbolic manipulation skills, and mathematical reasoning skills. 2) The kind of activities that take place in the mathematics classroom as described by W.G. Quirk is more teacher centered than students. Students learn with the teacher instruction. W.G Quirk teachers are giving out their daily plan for the day.

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3) I f I was in elementary school I would like to take benefited the NCTM because it give me more benefits as student. It is more fun because I use visual and make me more confident with math because I use more creative ideas. The other method I don’t like because the teacher is the center of the class and it make me distrait and make me bored. 4) a) The advantage of being in an NCTM friendly mathematics classroom are teachers and students made a good relationship with students feel comfortable in ask question and receive well explanation for their teacher. Also students have the opportunity to interact with other classmates and learn with their ideas or mistakes. Teachers help students recognize that the challenge of genuine math are exciting and rewarding in ways that go well beyond the “math must be fun and easy b) The advantage of being in a Quirk guide mathematics classroom are that the teachers teach their specific topics in math. Teachers use the curriculum. It must be coherent, focus on important mathematics, and well articulated across the grades. Students are focus in what the teacher teach in classroom. Teachers don’t have time for students ask question.

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The Dialogue That Follows Dear Diana, I have read your posting and it is very interesting however, I disagree with your reason for preferring the NCTM method. I don't think that math is based on creativity. I think that math is based on facts. Therefore we have to be taught the facts and concepts as they exist. We should not try to alter the main idea of math. Although there can be many fun problems there must be challenging problems based on the specific topic. Math lessons should not be based on how the students feel or what they think should be taught. Math lessons should be based on what is essential to build a good basic math foundation. Shelisa

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Diana, I disagree that math is in the NCTM class would be more creative. English class is meant to be made creative and not mathematics. I couldn't see how someone would get bored in the Quirk teached class. Mathematics is not meant to be fun after the 3rd grade in my opinion. Math is fun when you're just beginning it. Math is meant to be learned. If I had a more structed class maybe I would've learned math better. While I didn't find mathematics to be very interesting in elementary schoool I knew that is was something that had to be learned for my own future. Albina

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Albina You don't agree with me, I understand, but it is my opinion. Math is not my favority subject.I like the idea to learn with NTCM method because I like to learn with creativity. This method give children the oportunity to explore with visual and manipulatives things to made essay [easy] their knowledge in math. Diana

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Diana, My question is: whoever said mathematics was easy? I've never been told that math was easy. If I'm a woman in my 30's and I find math to be headache indusing [inducing], I'd hate to think how children feel about math today! Yes, you are entitled to your opinion. Thanks for letting me share mine. Albina

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Blackboard Assignment #4 By now you should have finished reading the websites listed below; if you have not please do so BEFORE you continue with Assignment #4. In the http://www.pdkintl.org/kappan/k0111rey.htm#1a website, there is a brief summary of the view point that supports the NCTM recommendations. There are many who oppose the NCTM recommendations (W.G. Quirk was just one of many.) Below you will find websites that express these opposing views. Some of these websites were developed by parents who are trying to get their voices heard. http://www.educationnews.org/nyc_math_warsnyc_honest_open_log.htm http://www.mathematicallycorrect.com/wsj.htm http://educationupdate.com/archives/2002/dec02/issue/spot_mathincit y.html http://www.educationnews.org/math_wars_new_yorkmath_forum_spo.ht mhttp://www.pdkintl.org/kappan/k0111rey.htm#1a http://www.educationnews.org/nyc_math_warsnyc_honest_open_log.htm http://www.mathematicallycorrect.com/wsj.htm http://educationupdate.com/archives/2002/dec02/issue/spot_mathincit y.html http://www.educationnews.org/math_wars_new_yorkmath_forum_spo.ht m

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1) Please go to Blackboard Assignment #2 and review what you and some of your classmates wanted your children to do in mathematics class from a “parent’s perspective” at the beginning of the term. (You do not need to write anything here but just reflect) 2) Having read the websites listed above, you should know more about parent’s perspectives as well as those that are pro-NCTM.

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In your group, half of you will take the position of parents who are against NCTM and half of you will take the position of teachers who are pro-NCTM. As a group you will discuss your different view points. The outcome of such a debate can be that either one group convinces the other or they as a whole reach a more balanced view on the issues. (During this debate take good notes on what points each side made and how an issue or issues resolved or not.) 3) I want you to make a powerpoint presentation – one per group- listing the original views of both sides and how those views got modified during the debate. What conclusions if any did you reach as a whole group? Please post your powerpoint presentation on the Blackboard.

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Points of the Debate Drill / Problem Solving Group work /Individual Work Does writing has a place in math classroom? Should use of technology be allowed especially a calculator

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Comparison of Debates Between Groups Group #2: Where your technology agreement is concerned, our group arrived at a similar conclusion with respect to the use of calculators. Our group thinks that they should be used only to solve long, difficult equations. When it came to the computers, the parents in our group were convinced by the teachers of the importance of computers. They agreed that the teachers could give assignments that involved the computers to access websites assigned by the teachers and supervised by the parents. When comparing your group discussion agreement and our conclusion the views vary somewhat. Your group agreed to have more group discussions. Our group decided that there needed to be a more balanced approach. Discussions would be part of the lesson, but shorter. Also, some would be lead by the teacher with the class kept as a whole.

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Your group had a “writing agreement”, where you decided to basically eliminate writing for math class. Our group addressed the parents concerns about too much writing with homework. We agreed that word problems and “think and write” questions would be part of everyday homework along with some drills. The think and write questions would be along the lines of asking the students to “write” out in words the steps they used to solve a particular problem. This encourages the student to learn the algorithms, but at the same time think for themselves and write. They can draw the algorithm from their understanding. Group I

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Blackboard Assignment #5 In your last Blackboard assignment (#4) you have wrote the view points you have reached after a debate on what is usually known as “Math Wars”. Below are some websites that reflect a more “balanced view” on the issue compared with the previous ones you have read through out the semester. Read these websites. http://gseweb.harvard.edu/~ncsall/fob/2000/saf ford.html http://www.education- world.com/a_curr/curr071.shtml http://gseweb.harvard.edu/~ncsall/fob/2000/saf ford.html http://www.education- world.com/a_curr/curr071.shtml

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The four websites below are the four pages of the same link and you can go to the next page simply by clicking “next”. http://www.ed.gov/admins/lead/math/ms/edlite- slide019.html http://www.ed.gov/admins/lead/math/ms/edlite- slide020.html http://www.ed.gov/admins/lead/math/ms/edlite- slide021.html http://www.ed.gov/admins/lead/math/ms/edlite- slide022.html 1) After reading the above websites, compare how they are similar and different than your final position as was outlined in Blackboard assignment #4. http://www.ed.gov/admins/lead/math/ms/edlite- slide019.html http://www.ed.gov/admins/lead/math/ms/edlite- slide020.html http://www.ed.gov/admins/lead/math/ms/edlite- slide021.html http://www.ed.gov/admins/lead/math/ms/edlite- slide022.html

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A Sample Answer After finishing debating on what is better for kids, we have many similarities and differences on whether the traditional or NCTM is better for the kids to learn. Some similarities were: Students understand and show more interest when taught with real life math problems. Students should learn how to use calculators in other to solve higher level math. We agree that students should understand the problem in other [order] to solve it. When students are involve in group discussion they tend to feel more comfortable. Also students show more enthusiastic in the lesson. Also students tend to understand better from their own peers than from teachers.

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Some differences were: During the debate we argued about what can be the best for the kids. As teachers we believe that the use of calculators at an early age should be limited. “but students still need to understand what is happening in those calculations” Because in order for a child to understand a problem one must first know how to do it with pen and pencil. Others believe that calculators shouldn’t be used at all. Some said that group discussions are good, this way all student contribute and it increase their proficiency. Others said that students get disturb when working in groups. Even though we had many differences we got to an agreement. If kids are taught with a combination of both the traditional and the NCTM, students will learn the math concept better. Students will have the ability to solve the problems more efficiently.

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Blackboard Assignment #6 Assume you are teaching in an elementary school that embraces the NCTM Standards. (You may want to refer to the following websites for the NCTM recommendations: http://standards.nctm.org/document/chapter3/numb.ht m, http://standards.nctm.org/document/chapter5/numb.ht m, http://standards.nctm.org/document/chapter5/alg.htm. ) However, some of the parents are concerned that their children are not spending enough time learning the basics. (You may want to refer to the following sites for parents’ concerns: http://www.educationnews.org/nyc_math_warsnyc_hones t_open_log.htm, http://www.mathematicallycorrect.com/wsj.htm.) http://standards.nctm.org/document/chapter3/numb.ht m http://standards.nctm.org/document/chapter5/numb.ht m http://standards.nctm.org/document/chapter5/alg.htm. http://www.educationnews.org/nyc_math_warsnyc_hones t_open_log.htm http://www.mathematicallycorrect.com/wsj.htm.

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1) You are asked to create 2 lesson plans (the items that need to be included in your lesson plan are listed at the end of this assignment for your reference) on the topic of “Adding Fractions with Different Denominators” that you would cover in two consecutive lessons. (Make sure that you are really doing only addition and not other related topics.) In preparing these lessons you want to take into account both the viewpoints of your school administration and those of the parents. Make sure you attach any hand-outs, homework sheets etc. you intend to give to your students. Your lesson plans should include ALL the drills/problems you intend to cover in class. Assume you have already covered the topic on “Adding Fractions with the Same Denominator” and other prerequisite topics which you should list in your lesson plan. 2) Write a description of how your approach addresses the standards and the parents’ concerns. Do NOT write what the NCTM recommendations are or what parents’ concerns are. What you need to do is item by item analyze your lesson plan (the motivational strategy used, each drill, each problem, the teaching strategy used, each item in the homework assigned) and discuss if it satisfies one view or another and if so why.

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LESSON PLAN: Grade Topic Aim Previous Knowledge Assumed Materials Needed Teaching Method Motivation Drills/Problems What Can Go Wrong? Homework

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