{"content":{"sharePage":{"page":0,"digests":[{"id":"36498162","dateCreated":"1301002923","smartDate":"Mar 24, 2011","userCreated":{"username":"crystalgremillion","url":"https:\/\/www.wikispaces.com\/user\/view\/crystalgremillion","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"},"monitored":false,"locked":false,"links":{"self":"https:\/\/klam-emeralds.wikispaces.com\/share\/view\/36498162"},"dateDigested":1532763053,"startDate":null,"sharedType":"discussion","title":"Stroup","description":"What could (and should) be the relationship between learning "the basics" and big ideas like calculus? How does this stance differ from how traditional curricula are organized? What are your opinions about these ideas?","replyPages":[{"page":0,"digests":[{"id":"36639366","body":"One problem with calculus versus many lower level math classes is that it is difficult to apply its concepts to places other than a pencil and paper. Concepts taught in calculus can be gradually taught as more advanced applications of the "basics." If students are "simultaneously introduced to big ideas" while learning the basics, they can (and statistics lead toward) a higher understanding of fundamental concepts that are thought to be prerequisites to advanced math courses.
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\nThe norm for our education system's teaching of calculus is very late in secondary education. It is expected that a student is not ready for calculus until they have mastered the basics. Personally, I feel that concepts taught exclusively in calculus and other advanced math courses could be taught to younger students. At the very least, it can better prepare them for calculus as well as give them a deeper understanding of the basics. Many people will tell you that the hard part of calculus often isn't the calculus, rather the algebra. If students become experts of the basics before they enter calculus, their progress will be accelerated because there are much fewer misconceptions and gray areas in their fundamental mathematical understandings.","dateCreated":"1301285648","smartDate":"Mar 27, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"36640442","body":"The relationship between learning the basics and big ideas should be intertwined. While students are taught the basics, peices of big ideas like calculus should also be brought in and introduced as the "elaboration" of the basic ideas. That way calculus is not a foreign idea to students and they get to learn some of it while learning basic concepts. This stance differs from traditional curricula in that traditional curricula calls for teaching the basics first and then teaching big ideas later. The problem with the traditional system is that because of the heavy focus on basics, many students never get to the big ideas.","dateCreated":"1301288864","smartDate":"Mar 27, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36641408","body":"Big ideas like calculus should be an extension to the basics. Unlike the current curricula the most effective way to learn the big ideas is to teach students these ideas while teaching the basics so the basics remain fresh in the memory. Rather than treating both of them in two different level.
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\nI agree to this idea because often times calculus in the current curricula comes after a long list of prerequisites this results in students forgetting the basics learnt in the beginning of the process. Therefore basics that is considered as a foundation is not stable.","dateCreated":"1301291667","smartDate":"Mar 27, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36702452","body":"The relationship between these big, all encompassing ideas and the small concepts that are the building blocks to them should be very close. The bid ideas and the basics should be taught right alongside each other. In this article, it shows us evidence that by exploring the big picture, we will then start to uncover the underlying principles. This method of exploration and self-discovery will help student to truly understand the basics.
\nThis is much a different stance then the one that is used in schools right now because it has been such a strong belief forever that you can't understand the big idea unless you build up to it, or separate it from the little things. There is also the idea that students can't be taught something like calculus at such a young age. Because of this, schools teach the principles and then teach the big idea. Sometimes students don't even get to that big idea, which hinders them because they weren't ever able to connect the things they learned to something meaningful.
\nAs far as my opinions, I believe that if the research in the article is correct, then this is a great way to teach. I remember having the feeling about some math classes that i was doing the math for nothing, and i think that is what a lot of students think. This idea for teaching will allow students to understand why they are doing what their doing and also help them retain the basics.","dateCreated":"1301361193","smartDate":"Mar 28, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36788114","body":"Casey,
\nI like what you said about it being hard to apply the concepts of calculus to paper. I remember thinking that as I was reading the article. I believe that this can be done though, but it has to be done in the right way. Calculus skills requires a lot of out of the box thinking that could definitely benefit from a little bit of background knowledge and practice in the basics.","dateCreated":"1301458599","smartDate":"Mar 29, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36797220","body":"Amanda,
\nI agree with you to making connection while learning is important because it helps them remember better. Calculus otherwise would be a foreign subject like Hala said.","dateCreated":"1301485766","smartDate":"Mar 30, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36800720","body":"Hala,
\nI really like what you are saying about how students focus too much on the basics and forget about the big picture. Even in my calculus class now, I just memorize the formulas and have no clue of the meaning of what I'm supposed to find.","dateCreated":"1301490519","smartDate":"Mar 30, 2011","userCreated":{"username":"TuyenN","url":"https:\/\/www.wikispaces.com\/user\/view\/TuyenN","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36818390","body":"Tuyen,
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\nI agree that teaching more intense concepts alongside the basics could prove to be more beneficial to students in the end. However, I feel that it should be done very delicately because there is a lot of room for misconceptions and confusion when teaching advanced concepts.","dateCreated":"1301504598","smartDate":"Mar 30, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"36853980","body":"Ebby
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\nI agree with what u said about big ideas should be extention of basics in stead of two completely different things. That way the student can understand application of big ideas and basics to real world problems.","dateCreated":"1301535236","smartDate":"Mar 30, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}}],"more":0}]},{"id":"36498126","dateCreated":"1301002895","smartDate":"Mar 24, 2011","userCreated":{"username":"crystalgremillion","url":"https:\/\/www.wikispaces.com\/user\/view\/crystalgremillion","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"},"monitored":false,"locked":false,"links":{"self":"https:\/\/klam-emeralds.wikispaces.com\/share\/view\/36498126"},"dateDigested":1532763055,"startDate":null,"sharedType":"discussion","title":"Bransford et al.","description":"According to Chapter 7, the interplay between which 2 variables is a critical role in effective math and science instruction? Elaborate with evidence. Also, describe a teaching method from this chapter that you found particularly interesting and explain why you think it is considered \u201ceffective."","replyPages":[{"page":0,"digests":[{"id":"36637464","body":"The most effective teacher in math or science has a high content knowledge and pedagogical knowledge. The best teacher isn't necessarily the most knowledgeable. It is important that a teacher be able to express methods and concepts in a way students can comprehend. Referring to figure 7.1, students who were asked to perform a conceptual analysis of several physics problems using hierarchal principles and procedures demonstrated an approximate 10-15% higher correct answer rate than students who were taught using traditional methods.
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\nThe teaching method of this chapter that I found particularly interesting was the bridging method. After the critical interview studies, I found that it is important to address misconceptions when teaching, rather than evaluating. With bridging, the addressing of misconceptions is the initial stage of teaching. After the initial stage, if performed effectively, only progress can occur. There will be much less time wasted addressing misconceptions when relevant material has already been taught (and likely misconstrued if assimilated with misconceptions).","dateCreated":"1301281787","smartDate":"Mar 27, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"36639298","body":"The most effective teacher is one that has a full understanding of a subject matter and the conceptual boundaries that hinder student understanding of that subject matter. A teacher can not be effective with just content knowledge, he\/she also needs to have experience with the conceptual boundaries. My high school chemistry teacher was highly knowledgeable in chemistry but couldn't convey the knowledge to us because she didn't have the understanding of conceptual boundaries that we as students were struggling with. She would always explain something and then say "but you already knew that" and we would be at complete loss. She either did not see the conceptual boundaries that were hindering our understanding or she refused to address them. As a result, we highly struggled in the class and survived on rote-memorization.
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\nA teaching method I really thought was effective was the qualitative strategies by students. The example where students have to explain what they would do to solve the problem and why it would work. It is effective in my view because it lets the teacher take a peek into the student's mind and see their understanding and misconceptions. It works kind of like a mix between formative assessment and clinical interview.","dateCreated":"1301285497","smartDate":"Mar 27, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36651634","body":"The interplay between the teacher's content knowledge and pedagogical knowledge is a critical role in effective math and science instruction. A good teacher does not only possess knowledge in the concepts but are also flexible to teach in different ways so that all the students can understand the concepts. Teachers that just teach in one way for all the concepts mat not reach out to some students. For example when a concept is introduced and some students have not understood the concept. In such cases the teachers conceptual know;edge is not enough to make the student understand but rather the teacher needs to use his or her pedagogical knowledge and come up with a more effective methods of teaching to make all her students understand the topics.
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\nThe most effective teaching method that i found was interactive lecture. In interactive lecture, different situations are thrown the students, and they are expected to come up with an hypothesis. I think this is effective because it creates an disequilibrium within the students that helps the student to adapt the new concept. This also helps the student to clear any misconceptions.","dateCreated":"1301316952","smartDate":"Mar 28, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36746460","body":"The interplay between the disciplinary knowledge an pedagogical knowledge need to be used in order to teach the information, as well as know how to use that information to create an environment that helps students understand the material. Teachers, good or bad, have content knowledge about the subject they are teaching, but don't necessarily have a structure as to how to teach the subject efficiently. So, because if this you need to be able to weave these two types together to make actual learning take place.
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\nOne method that I thought was interesting, because it was linked to a method that we already learned about in class, was the Cheche Konnen approach. This was kind of related to Vygotsky and the social learning method. This approach has student ask questions, theorize about the questions and then they are given time to argue their side with students in the class. This helps the students to justify their thoughts. When you have to justify yourself to someone else, that means you really need to understand the concept you're arguing and have to know the details of the concept. I also find this method of argumentation interesting because I know from experience and reading that verbalizing your thoughts can help you clarify them.","dateCreated":"1301420277","smartDate":"Mar 29, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36787354","body":"Ebby baby, I totally agree with you when you talk about the interactive lecture creating an environment of disequilibrium. This is one of the many important ways that teachers can get students to reverse their their thinking permanently.","dateCreated":"1301457931","smartDate":"Mar 29, 2011","userCreated":{"username":"admiller2","url":"https:\/\/www.wikispaces.com\/user\/view\/admiller2","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36797546","body":"Casey, I also think that misconceptions must be cleared while teaching because it is easier to make corrections while learning than after learning.
\nHala and Amanda, I also think that allowing the students to justify their thoughts will help them to bring out any misconceptions and is helpful for the teachers because they become aware of the misconception in the class and can clarify them as the learning occurs.","dateCreated":"1301486601","smartDate":"Mar 30, 2011","userCreated":{"username":"Ebbybaby","url":"https:\/\/www.wikispaces.com\/user\/view\/Ebbybaby","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}},{"id":"36822554","body":"Ebby, I really like how you brought up disequilibrium when talking about interactive lectures. I feel that a large amount of pedagogical knowledge is extremely useful in this type of class setting because the teacher can clear up misconceptions while making each lesson better with regards to previous data such as passing rates etc.","dateCreated":"1301507905","smartDate":"Mar 30, 2011","userCreated":{"username":"Caseyb.crittenden","url":"https:\/\/www.wikispaces.com\/user\/view\/Caseyb.crittenden","imageUrl":"https:\/\/www.wikispaces.com\/user\/pic\/1296425910\/Caseyb.crittenden-lg.jpg"}},{"id":"36853706","body":"Ebby, I really like how you connected interactive lectures with disequilibrium. It is so true, I hadnt even thought of that","dateCreated":"1301534993","smartDate":"Mar 30, 2011","userCreated":{"username":"HalaSiddiqui","url":"https:\/\/www.wikispaces.com\/user\/view\/HalaSiddiqui","imageUrl":"https:\/\/ssl.wikicdn.com\/i\/user_none_lg.jpg"}}],"more":0}]}],"more":false},"comments":[]},"http":{"code":200,"status":"OK"},"redirectUrl":null,"javascript":null,"notices":{"warning":[],"error":[],"info":[],"success":[]}}