Handbook+Chapter+Overview+Videos

Handbook Chapter Summaries We will use this wiki page to post links to your video summaries. All videos should be uploaded to the [|CED Video Website]. Insert a hyperlink on the appropriate chapter title below to link to your uploaded video. __All videos must be posted by midnight September 7th.__

[|Screencast-o-matic] [|Sample screencast presentation]

Chapter 5: The Mathematical Education and Development of Teachers (Tamar)
 * //Great job Tamar! I am wondering if the author(s) discussed how to measure teacher quality and impact on student learning as it relates to professional development. Did they give a specific model or example of professional development that they think has worked? Did they talk at all about how to get teachers to reflect on a regular basis? Lastly, did they discuss on-line professional development? -Tyler//
 * //Tamar, that was a great presentation.Q3 in your Prezi discussed "principles used to guide PD design." Is this a list the author created from literature? Also, one of the characteristics they included was "continuity over time." Taking into consideration the busy schedule teachers have during the school year, did the author discuss how to manage this continuation over time without interfering with teachers' daily responsibilities? - Marggie//
 * Nice presentation. I really liked that you used a prezi inside of a powerpoint! In the future research section, you mentioned international opportunities. Was analysis of PD and how PD done part of this chapter or was the focus only on the US? Can you go into more detail about how international opportunities factor into the future research for PD? - Emily
 * Excellent organization of topics Tamar! I really liked the author’s view of professional development as a process and not an event. Does the author give any examples of differentiation within professional development so that all teachers can experience this evolution regardless of their previous experiences? - Blake
 * I found the list of questions to be thought provoking especially since I am currently involved as a higher ed consultant for a grant. For question 8, you mention mathematicians’ roles in teacher preparation. What exactly is suggested or studied? - Lara
 * Well done. The goals of PD mentioned by the author seemed to have left out the overarching goals, mision, and vision of the school context, did the authors discuss differences in perspectives and perceived needs of PD that come from an administrator's point of view as well? - James
 * You provided a very thorough summary. You mentioned that one goal of PD should be math content knowledge. I agree and wonder if you ran across any sources on studies done on the math content knowledge of elementary school teachers. Thanks and let me/us know. -Aaron
 * Well done. Do you feel the author believed that current PD for teachers is not effective in developing teacher effectiveness? Is it a ticket to be punched or relevant to teachers? – Doug
 * Good Job! I also liked the Prezi within the Power Point :-). Did the author mention or point out examples of effective PD? Or things that make PD ineffective? I wonder is it the PD that is wasteful/ineffective or is it the implementation of the knowledge or strategies obtained that is ineffective?-Tracy
 * This was a very comprehensive summary. Good job. I have several questions. The first question is how does the author define a "knowledgeable teacher"? Second, how does she propose or what research did she use to describe how PD should address equity? The third and last is which model did she use for "lesson study"? I'm looking forward to our discussion of these questions. -Nadia
 * I never thought about PD being as a process, not an event, this was a nice point for me. I have a couple of questions: what does the author say about teacher change with the use of the psychological and sociological frameworks? What do these recommend? I would also like to know more about evaluation of PD. I haven't experienced PD from the creator perspective so I was wondering how to efficiently evaluate PD. - Carrie
 * Great Job Tamar! It is interesting to define what it means to teacher development. Do you think the author seem teachers as active builder of PD or just partcipant of PD? (Zuhal)

Chapter 6: Understanding Teaching and Classroom Practice in Mathematics (Tracy) > > Chapter 7: Mathematics Teachers' Beliefs and Affect (Lara & Zuhal)
 * //I loved your Prezi Tracy! I think you said at the end that the authors didn't really give specific examples, but that was my question: Did they give ideas about how to successfully implement discourse, norms, and relationships in the math classroom? It seems like the main resistance I have heard from math teachers is they don't feel like they have time to spend on developing norms and building relationships in the classroom because they have too much content to teach...did the author(s) offer any ideas about how to help teachers get the benefits? -Tyler//
 * I really enjoyed your presentation, Tracy! Did the authors talk about how to encourage and remind students to be patient when learning mathematics and engaging in problem-solving? Also, with regard to "sociomathematical norms," did the authors address how setting those norms in elementary grades may differ from doing so in later grades? What specific equity issues did the authors address? And finally, can you elaborate on what the authors refer to as "interrogating meaning?" - Tamar
 * Tracy, good job!! According to your chapter the authors suggest teachers to establish norms for doing and learning mathematics. They suggested establishing general social norms before the sociomathematical norms. Being an ESL students I was wondering whether or not the authors mentioned how does the establishment of those social norms benefits those students whole first language is not English? - Marggie
 * Very nice work!! This was a great overview. Did they discuss motivation in this chapter? The chapter said that opportunities must be provided for student discourse and mathematical communication, but did the chapter talk about how do to this in the most productive way? I think many teachers agree that this should happen but are not sure how to make it happen. - Emily
 * Nice job and organization! You mentioned that dual focus is essenial element of classroom practices which includes what teachers' do and how it affects students.As follows, while examining features of classroom practices, you mentioned sentences started with: "Teacher should...." Is it one way relation or two way relation? So, students' practices may also affect what teachers' do in classroom practices, if so in what ways? Is there any studies mentioned about this issue in the chapter? (Zuhal)
 * Your Prezi was fun to watch! Is there any mention of students’ age and the ability to set classroom norms that differ from the traditional IRE? In my work with college students, I’ve noticed that it is difficult to set a norm of student discourse (not teacher discourse). Is it just too late for these students? - Lara
 * Great presentation! After doing my summary on the role of culture in teaching and learning mathematics, it was interesting to see the issue of culture come up in another chapter. Does the author give any specific suggestions for how to bridge the gap between home/community culture and classroom culture? - Blake
 * Nice presentation. What specifically did TIMMS find inconsistent between current practice and reform ideals for teaching Mathematics? -James
 * Tracy, you did an excellent job to synthesize the author's work while including your views on classroom practice. During our next class could you tell us more about the organization "Adding It Up" as I'm unfamiliar with their history, work, and recommendations. Thanks. -Aaron
 * Very nice job. Feature 3 – Do you feel that the author is correct concerning getting to know multiple aspects of each student’s learning capabilities or do you believe that the idea is great, but not feasible with the limited amount of time teachers have in the classroom? – Doug
 * I think that your chapter is essential to the learning and teaching of mathematics. In the chapter, the author addressed three features, discourse, norms and relationships as important components of effective teaching in the classroom. The third, fostering relationships so that teachers are aware of different cultures and students' home life seems to be an issue that a teacher who "cares" would be more drawn to. Is it possible that teachers can be made to "care" so that they may develop and foster relationships with their students outside of the "mathematics"?-Nadia
 * This is a very important chapter for teachers. I was wondering if you could give some more information on what the readings states on culture, my students are always asking me how to incorporate this, so I was wondering if you had some information I haven't heard about. In the video you spoke about interrogating meaning, used in science, what is this and can we apply this to math? - Carrie
 * //Good job! I'm curious to know more about the kinds of beliefs and behaviors that were studied besides general math anxiety, technology, and gender and how do teacher preparation programs impact those beliefs? -Tyler//
 * This was really great, Lara and Zuhal! What did Phillips say about challenges that arise in attempts to change/affect teachers' beliefs and affect for administrators, teacher leaders, and PD providers? - Tamar
 * Good presentation Lara and Zuhal!! One of the emerging areas of research you mentioned was that understanding children's mathematical thinking is key to change beliefs about instruction. Earlier in the presentation you mentioned that PD and teacher's reflection were critical in changing teacher's beliefs. To me this suggests that research about children's mathematical thinking should be included in PD if we want teachers to change their beliefs about instruction. Did the authors elaborated more in this area? - Marggie
 * I really liked that you gave for you reasons for choosing this chapter. Nice work!! You mention that the chapter talks about the beliefs held by teachers. Can you go into more detail about these studies and what they found? I would also be interested in the work done on why these beliefs are held. - Emily
 * Great organization! It was interesting that the author mentions inconsistencies between teachers’ beliefs and practices. Does the author address specific reasons why there are discrepancies between the two? - Blake
 * Did the author notice any significant differences in Math Affect or Anxiety as students progressed into higher grade-levels or harder math concepts? -James
 * You two did a great job. I agree that beliefs and affect should be studied together. You stated that one research finding is, "Beliefs about gender greatly effect student performance and choice of profession." Can you give us an example of a recent study that deals with this statement. I ask as a former high school teacher of Calculus who saw many females outperform their male counterparts and had some classes in which the females outnumbered the males. -Aaron
 * Nice presentation. Do you have the impression that the author believes there has been changes in the classroom concerning gender or that there is still a vast difference in beliefs about gender and mathematics? Did you get the impression that the author felt the teacher beliefs in general were conscious or not? – Doug
 * Good Job ladies!! Can you all elaborate a little more on intended vs. enacted beliefs? Did the authors go into any detail on the specific teacher beliefs that "lie at the center" of reform curriculum?-Tracy
 * I liked the way that powerpoint was used in this presentation. It was mentioned that the authors did not have much research on affect and was wondering if a framework for this type of research was included in the article. Good job. -Nadia
 * Great job you two!! How would one measure belief and affect? Since the call for research on belief and affect, has any been conducted? I was interested to this, I wonder what research would look like that studies both. - Carrie

Chapter 10: Culture, Race, Power, and Mathematics Education (James & Nadia)
 * //Nice job! I'm curious to know how we can differentiate instruction effectively without treating students differently? For example, how do we address gaps that exist due to language skills? -tyler//
 * What a wonderful presentation, James and Nadia! Can you elaborate on what the authors mean by race, racism and power remaining "undertheorized?" Can you also describe how research was performed on culture? What instruments and methods were used? - Tamar
 * James and Nadia I loved the visual representation you used to show the organization of the chapter!! Could you elaborate more about "cultural-deficit thinking?" What did the authors mean by "utilize greater non-majority population?" Did they elaborate on why it was necessary to "utilize greater non-majority population?" - Marggie
 * Your animation was fantastic! I would like to hear more about your "ah ha" moment that segregation is worse. Does this mean that the US is more segregated today than in the 50's or the affects are more strongly felt or both?- Emily
 * This topic hits close to my heart and honestly I am disappointed. I feel like I know we’re increasing the gap and that there are so many problems that arise both culturally and within our classrooms. I was hoping for some “real” answers or solutions not just more areas to research to gain more information. Was there any mention of programs or schools that have been successful or ideas that will help us close the gap? I need hope! - Lara
 * Clear and nice organization! The chapter seems to address the problems and challenges, what are the possible solutions which teachers, educators, students and families need to hear about more? (Zuhal)
 * Great job James and Nadia and I especially like your function machine visual for the chapter organization. You mention a research goal of, "Discover the systems involved in mathematics achievement." One system I can think of is state mandated standardized testing. Could you provide additional examples? I also have a book on the Algebra Project that I'll bring to class. Thanks. -Aaron
 * You did an excellent job of summarizing all the key points here. There was obviously a huge overlap between this chapter and the following chapter on the role of culture in teaching and learning mathematics. One commonality that stood out was that of the disjunction of students’ understanding of mathematics concepts in-school and out-of-school. Did the author suggest ways to bridge this gap? - Blake
 * Nicely done. You stated the author accepted definitions. Do you think reasonable definitions without consensus would move the conversation and research forward without getting mired in debate is better than getting the consensus first, then move on? – Doug
 * I loved the chapter organization model!!! I am saddened that segregation is worse now. Do they say what they feel led to this happening? I also want to know if they suggest ways to bridge the gap? After listening to summaries of chapters 10 and 11, I know what culture is "defined" as, but I wonder how cultural competence is truly measured? -Tracy
 * Nice little animation you guys! I talk about this in EMS 204. My students are always asking me how we can teacher students in the way they need to be taught without making any students feel like they are being treated differently. Like when a student has something wrong, they always worry about going and helping them, even individual, without making them feel isolated. Does the author talk about this? I always have something to say for this but it isn't based on research, but experience, so I was wondering what your section said. Also, what is critical dialogue? I have something in mind but I wondered how they defined it and why minority students engaged more with this. - Carrie

Chapter 11: The Role of Culture in Teaching and Learning Mathematics (Blake) > Chapter 15: Early Algebra(Doug) > Chapter 17: Problem Solving and Modeling (Aaron)
 * //Very neat and clear presentation Blake! Did the authors discuss the role of curriculum at all in influencing mathematics culture in the classroom? - Tyler//
 * I really enjoyed your presentation, Blake. It was well-organized and informative. Can you elaborate on what the author means by "math [being] value-free and culture-free?" It seems that this chapter also struggles a bit to define "culture," as Chapter 10 did. - Tamar
 * Wow Blake, that was a paused, cleared presentation! Could you talk more about the role of culture? Specially, what are the practices of mathematicians according to the author? - Marggie
 * Fantastic! I feel that I really understand the outline and goal of your chapter. I was curious about ethomathematics. Can you give some examples?-Emily
 * Very nice and clear presentation! It is interesting to hear the existence of "borderland discourse" in your presentation, which I was thinking about this,without knowing the term, as I was working with international students in international private schools in US. I realized how their home culture affect the way they involved in mathematics activity. For instance, in clinical interview settings, when we asked them " would you like to continue?" their responses usually "Yes, until I finish it". So far, the international students that I worked with were more task oriented and tried to finish all the assigned task no Gmatter they feel. I am wondering that "in what grades does borderland discourse have more affect on students?" (Zuhal)
 * I would love to hear more about the influence of language, specifically mathematical terminology that has different meaning inside and outside of the classroom. I’m beginning to think a lot more about the role of language in the classroom and am hoping you can elaborate on what was mentioned in the chapter. - Lara
 * Blake will you please explain what a semiotic is and how that should be used to bridge the gap between out-of-school and in-school Mathematics. -James
 * Great presentation Blake. Like Emily, I'm interested in examples that fall within ethnomathematics as they would help me more fully understand the term and field of research. -Aaron
 * Very good job. Since the chapter was quite broad and qualitative in nature, do you feel it would be difficult to find and defend a strong correlation between culture and mathematics teaching and learning? – Doug
 * Good Job!! I have to "piggy back" a little here. Like James and Emily I want to know more about semiotic and ethnomathematics, respectively. After listening to summaries of chapters 10 and 11, I know what culture is "defined" as, but I wonder how cultural competence is truly measured? -Tracy
 * There are many overlapping themes between chapter 10 and 11 but I noticed that more focus was placed on culture and the discussion was more thorough. You mentioned that you liked their definition of mathematics because mathematics was almost described as a social science. Did the author only choose articles relating to mathematics education who viewed mathematics this way? I am not sure how widely accepted this definition will be to the general mathematics community. Is this view of mathematics necessary when discussing the role of culture and equity? Great Job!-Nadia
 * I also like that definition of mathematics! I might be alone in wondering this but what are semiotics? Also, I would like to know more of what the author said the difference between in and out of school mathematics. I know the obvious ones, where there any that struck you? - Carrie
 * //Good job Doug. I am curious about how the authors might have incorporated psychology research into this chapter. My understanding is that abstract reasoning skills don't develop until late adolescence, so how does that impact the implementation of early algebra? -Tyler//
 * //Doug, with the Math curriculum load in Elementary, considered by many, already overloaded, are the authors suggesting we still add more curriculum for Elementary teachers to cover or that the current standards be readdressed to force the teacher to teach the content in a different way? - James//
 * //Doug you were deliberate and thorough in your presentation. In one of your slides on critiques you wrote, "Definitions were used to maintain consistency, but still acceptable." Could you expound on what you mean during the q and a in our next class. Thanks and good job. -Aaron//
 * Clear and thorough summary and analysis of the chapter. Nice work! I am not familiar with what EA looks like in the classroom. Did the authors give examples of what a classroom would look like if it used EA? How is this different from what is currently done with the North Carolina Standards or Core Standards?- Emily
 * Very interesting topic and nice presentation, Doug! With regard to the "Traveler's Guide to EA", is that related to the content covered in EA or how and when EA is introduced and taught in school? Also, at about 3:20 into your presentation, in your organization critique, you write that "Definitions were used to maintain consistency, but still be acceptable." Can you clarify what you mean by that? And, finally, was there something in this chapter that you were looking for that wasn't there regarding EA? What was your motivation for choosing this chapter? - Tamar
 * I appreciated the lists of topics that can lead as transitions to algebra, but I’m still unsure exactly where and how the authors suggest this be done. Do the authors suggest specific ages or grade levels? I guess I’m wondering how early and what problems might look like. Thanks for a good summary of what seems to be a bountiful amount of information. - Lara
 * Good job!! I am interested in what age group or grade EA would be implemented in. Did the authors mention how in depth the Algebra concepts be on this level?-Tracy
 * Great organization of topics! The authors clearly believe in an integrated approach to arithmetic and algebra at a young age. Did they address any concerns with the consequences of Early Algebra as it relates to students’ understanding of other mathematical skills? - Blake
 * Hi Doug!!! Our (Marggie and I) chapter also talked about process and object. I would like to know of this issue related to curriculum. What did the chapter say? I would like to know more about your concern about elementary teachers teaching algebra. - Carrie
 * What topics and when they should be added into the mathematics curriculum have always been debated. In the Common Core Standards, the elementary mathematics curriculum has been "thinned" out and it would be interesting to hear the views of those who promoted EA. As a result of the "thinning" of the elementary curriculum, there is a very ambitious number of topics to be covered? Do you believe the ideas of EA have been addressed in these standards?-Nadia
 * Great job! It is interesting to see the transtion topics to Algebra. How should this transition addressed? How are the responsible people? (Zuhal)
 * //Hey Aaron- Can you show us the Tokyo to Chicago problem in class on Monday? I would like to see the model that the authors recommend. Thanks! - Tyler//
 * Great presentation Aaron! Yes, can you share the Tokyo to Chicago problem with us? - Marggie
 * Can you elobarete on how metacognitve awareness affect students' problem solving ability? (Zuhal)
 * Aaron, Will you discuss what the authors felt were unimpressive about the research conducted utilizing the "old assumptions" for problem solving? - James
 * Good job. Did the authors show an inclination in differentiating between problems that they considered complex (involving several simple steps) versus complicated (difficult)? – Doug
 * Nice presentation! I like the quote about the "higher ordered thinking tracks" not providing any benefits. I am curious about how the new model approach differs from these "higher ordered thinking tracks"?- Emily
 * Really interesting presentation, Aaron. I liked how you made clear the "old" and "new" assumptions. Can you elaborate on the idea of "situated cognition" and why the authors feel research is needed on the subject? What do they think can be gained from such research? Can you also describe some of the research that has been done on problem-solving and modeling? What methods/structures/subjects were used? - Tamar
 * I bet this was an interesting chapter to read—nice synthesis. We all believe that we need better, more relevant modeling and problem solving in our classes, but how early? Is this chapter geared toward secondary and post-secondary instruction or does it begin with elementary school? - Lara
 * Good job!! You mentioned a few of the new research questions that the authors presented, what were some of the others? Were any examples other than the Tokyo to Chicago problem given in the text?-Tracy
 * You definitely have good taste in templates! You mentioned three concepts within higher order thinking: metacognition, habits of mind, and beliefs of disposition. Could you elaborate more about the author’s definitions for each of these? I am especially curious about habits of mind. - Blake
 * Like others have said I would like to see the Tokyo to Chicago problem.I would like to know more about your ah ha moment. Learning through modeling, students modeling or seeing models? I would also like to know more about problem solving strategies that are beneficial for students. - Carrie
 * This is always a topic of concern for mathematics educators. I was wondering if the authors provided research on exactly how technology has or can change problem solving. Did they provide any examples of how technology can be used to help students create models to solve problems? Did they include technology as a way of creating models?-Nadia

Chapter 22: Mathematics Thinking and Learning at Post-Secondary Level (Marggie & Carrie)
 * //Wow Carrie...were you a debate team??? You can talk FAST! :) Good job Marggie and Carrie...//
 * Very fast Carrie! I am an international student :) Just kidding.. It is interesting to see how teaching and learning was not integrated in early 90''s. What are the factors that contribute the integration of these two up to now? (Technology?, Interaction with Different Disciplines?, Conjectures about how we learn?) (Zuhal)
 * Marggie & Carrie, will you please elaborate on what is meant by "embodied cognition"? - James
 * You two included much in your presentation. Concerning the sociocultural approach to mathematics education, did you find a difference in the research between secondary and post-secondary education. For example, was the sociocultural approach first in secondary education research? Thanks. -Aaron
 * Nicely done. Did the authors feel or did you see a notable difference in the research abroad and the research in the United Stated? Were the goals similar and so on? – Doug
 * Nice prezi! I second Doug's question. You implied that the article had was heavily influenced by European sources; therefore, is the information presented applicable to the US as well?
 * Great presentation, and artful way of getting everything in by the 7-minute mark! :) How new is the research on neuroscience and how mathematical knowledge is obtained--Do the authors comment on this? How has it influenced research on post-secondary mathematics education? - Tamar
 * As your only other fellow student from last semester’s Advanced Mathematical Thinking course I’m wondering why we didn’t read this chapter…any thoughts other than the fact that we read a lot of the articles mentioned or perhaps because we didn’t focus on technology or statistics? Overall, it was fun to be familiar with so many of the terms and authors you mention. - Lara
 * Very clear and concise presentation! You mentioned the sources being primarily from Europe with only a few from the United States. I was curious about the author’s thoughts about the effect of various international curriculums on post-secondary mathematics education. For example, different states within the United States have different mathematics curriculum so different countries definitely have different mathematics curriculum. What is the impact when Universities around the world have to decide on a mathematics curriculum for their college or university? - Blake
 * Good job on the Prezi Marggie!!! - Carrie :)
 * With the inclusion of many AP courses in high school and the deficit of mathematics ability of incoming freshmen, I wonder if the authors could use research from both levels to understand post-secondary mathematics education. What level of mathematics at the post-secondary is the focus of this article?-Nadia

Chapter 27: Research on Technology in Mathematics Education: The Perspective of Constructs (Tyler & Emily)
 * //Wow Tyler and Emily...you rock! ;) - Tyler//
 * Clear presentation! Well organized! What does "use of technology as an amplifier" and "use of technology as a reorganizer" means? - Marggie
 * Tyler & Emily, nice use of the Prezi. The authors seem to be advocating for updating the curriculum to take advantage of newer and available technological tools in the classroom. Do they address the equitable concerns that such a shift may cause as some schools,LEAs, and families may not have adequate access to these resources and thus would be at a disadvantage? -James
 * Great job on explaining the evolution of technology and mathematics education. Could you explain what 'representation as artifact vs representation as instrument' means during our next class meeting. Thanks. -Aaron
 * Very good job. Do you feel there is a difference in the use of tech and the ease of use as a crutch versus a tool to enhance learning? Example: GSP requires understanding geometry to truly enhance the learning in the classroom while the graphing calculator is frequently used as a crutch by students who do not necessarily understand the mathematics. – Doug
 * Beautiful job, Tyler and Emily! Your presentation is really well-organized, well-paced and easy to follow. I also appreciated your inclusion of the terms "pedagogical fidelity" and "instrumental genesis." They were new to me. Can you elaborate on some of the structures and methods of the research done on assessing how technology enhances learning? - Tamar
 * Nice presentation ladies! You mention the authors wondering if a trajectory exists between representation as artifact to representation as instrument. I find this thought fascinating especially since we know Jere is so involved in developing learning trajectories. Have others talked about or studied a learning (or other type) trajectory for technology cognitive tools? - Lara
 * Nice job Tyler & Emily! I would like to know more about your cool rectangular based pyramid. How do the authors connect these? What are the implications of the connections? - Carrie
 * Great use of graphics to explain the outline of the chapter! Technology is definitely at the forefront of many things that we do in education across all subject areas. I was curious if the authors address the challenges surrounding future research in this area due to the pace at which technology is changing and time it takes to get things published. - Blake
 * Good job!! I loved your use of the little pyramids. I am sure that most teachers agree that technology has an important place in the classroom, however many are unsure of how to infuse it into their lessons. Did the authors provide ways to infuse technology in the classroom? What impact do you think a teachers resistance to technology has on Mathematics Education?-Tracy
 * Nice job on experimenting with Prezi. It would have been easier to follow your comprehensive summary if the maps were larger or if was individually magnified. I wonder if the authors addressed how a teacher's expertise or lack thereof impacts students' ability to learn the technology and the mathematics associated with it.-Nadia
 * Good prezi! It is interesting to see the definition of cognitive tools. How can technology become a cognitive tool? What are the trajectories on the way of cognitive tools? How can learner enter cognitive terrain with the help of technology? or Technology become the environment for it. (Zuhal)