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Article, pg 10 "Broad, connected knowledge of mathematics leads to more flexible choices"

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Article, pg 10 "Broad, connected knowledge of mathematics leads to more flexible choices"

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I agree with this because it does not lock the teacher into teaching math a specific way and allows the student to develop a way of solving the problem in a way that makes sense to them. Frank

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Pod Cast, 11:00 min, What is parent math night?

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Pod Cast, 11:00 min, What is parent math night?

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What is parent math night? How do you support a parent that struggles with math to feel comfortable that math night is not where the teacher will be judging their math ability? Frank

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Create and maintain a high quality curriculum that is aligned with the standards. Frank

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Pod Cast, 15:13 Parent question on "long way to get to the short way."

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Pod Cast, 15:13 Parent question on "long way to get to the short way."

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While it is true that these new math standards and algorithms are beneficial for students, there is a clear disconnect between the math that is being taught and the math that parents know. I think it is great that students are learning all these new methods, working up to mental math so early, and getting all these new and more efficient methods. My question is, is there a way to involve parents? How can we share these methods with parents so they can be yet another resource to help our students at home? I know these new methods were enlightening for me and my math skills but I doubt I would get the chance to see them as an adult were it not for being in this program. Natasha

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Podcast, 18:52 "Standards are not a curriculum, they are learning targets..."

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Podcast, 18:52 "Standards are not a curriculum, they are learning targets..."

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This is a great reminder for teachers that the standards exist to guide our teaching. The podcast goes on to emphasize that teachers have the freedom to use these standards however it is appropriate for their students. As teachers we aim to work on what is developmentally appropriate for our students and can even surpass what the standards say. Although the standards and the Core Curriculum seem daunting now, I can agree that they are a useful resource to guide my teaching. Natasha

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Article, pg 18 "The tendency to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy." 

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Article, pg 18 "The tendency to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy." 

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The quote was really important to me because it speaks to the changes I need to work on to be an effective and successful teacher in all areas but especially in mathematics. The practices I grew up learning may have soured my attitude toward math but that is not the experience I want to pass on to my students. I hope to encourage them, foster a curiosity for numbers and the use of math in their day to day lives. To accomplish these goals I hope to grow in my abilities and see mathematics as a doable skill rather than a daunting challenge. Natasha

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Article, pg. 2 "The "language" of mathematics is, in fact, used throughout life to communicate information and ideas in a manner that is both concise and universal."

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Article, pg. 2 "The "language" of mathematics is, in fact, used throughout life to communicate information and ideas in a manner that is both concise and universal."

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This quote really stood out to me and surprised me. We do not often think of math as a "language" or at least I do not, but after reflecting on it I realized how much sense it makes and how true this statement is. Math is certainly a part of our every day life and can be universally understood in a way that is exact, concise and definite. Ceili

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Article, pg. 4 "To achieve strategic competence, students should be able to form mental images of problems, detect mathematical relationships, and devise a solution method. This goes far beyond reaching a correct answer. Good problem solvers know more than one way to solve problems."

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Article, pg. 4 "To achieve strategic competence, students should be able to form mental images of problems, detect mathematical relationships, and devise a solution method. This goes far beyond reaching a correct answer. Good problem solvers know more than one way to solve problems."

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If and when I am teaching math I would very much like to remember this quote and make sure that my students know more than one way to solve problems.  Like our homework, it would be a great habit to find many ways to solve a problem when applicable.  It was interesting to me that US students tend to struggle with this concept. Ceili

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Podcast- Understanding the Concept not just the Algorithm, and "go slow to go fast." 

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Podcast- Understanding the Concept not just the Algorithm, and "go slow to go fast." 

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I found the podcast to be super interesting and engaging. Like Natasha "going slow to go fast" stood out to me and I suppose my question would be about when I really would know as a teacher that this is one of those moments when this needs to be applied. Also, the podcast mentioning that with the new way the standards have been formatted so that students are actually understanding concepts and how it can be damaging to do it out or order or in a different way- how do we make sure this doesn't happen as teachers?- Ceili

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How math is taught now it very different than when our parents and even ourselves were taught. The idea is to be able to carry over information from lesson to lesson, grade to grade, and so forth. Personally, I am still confused on some of the ways students are learning math, but they're getting the right answers and its carrying over when needed. -Kaylee Lemieux

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“There is a lot of choice in the common core standards.”

This quote stood out to me because when I first heard it, I was questioning it, but then when Audra elaborated, it made a lot sense to me so I agree with that statement. Even in the first few weeks of class, Audra has had us do the handshake and high-five problems in multiple different ways. I believe this is a good example of what she meant when she was talking about it in the podcast, because with common core, students need to apply multiple methods of solving problems for the material to stick.

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How can we better close the gap between how parents were taught and how we want our students taught? As someone who is learning the "correct way" to teach math, I can attest that its hard to teach an old dog new tricks. -Kaylee Lemieux

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“What happened to the traditional algorithm?”
This question that Alicia asked is also one that I had for a while. I was very intimidated and hesitant about the new ways of teaching math at first. However, after I broke down my guard and allowed myself the opportunity to be willing to learn, the newer methods that are now implemented make a lot of sense. One of my issues in school with math was that we would learn a topic, get tested on it, and move on—it could have been months, years, or until the next standardized test that I would visit that topic again.

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Creating a high quality curriculum benefits everyone involved. Students, teachers, and parents. -Kaylee Lemieux

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How to get parents involved if they do not have the time or are not involved in their child's school life? Sometimes it sounds impossible for some parents to budge. I know offering things like math night, meetings, etc. may work but most of the time that only works for the parents who are willing. Wondering if you had any suggestions? -Meaghan

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“Having a productive disposition or being engaged in mathematics relates to making sense of math. It implies both believing that math does make sense and having the desire to make sense of it.”
Making math make sense and applying it in real life for your students makes a huge difference in how they feel about the subject!
Alexa

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Most adults do not enjoy math because of the way they were taught. The podcast explains how there is not love for math because the understanding is not there. I believe this is so true for kids and adults because math is fun to solve until we stop being able to solve it. -Meaghan

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I really agree with how we now teach students basics like commutative or distributed property before we teach them the traditional algorithms. Honestly, now that I am teaching math in elementary school, math is actually making much more sense to me. However, I do understand how this could be frustrating or difficult for parents. - Halsey Gargano

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Generating love for math usually didn't happen in the past, so that is the goal now. Do we have any research behind the way or the feelings people have towards these new math strategies? - Halsey Gargano

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"U.S. students have great difficulty with multi-step problems and often falter when a different phrase or word is used than they have learned or when a problem is put in an unfamiliar setting." Breaking those problems down and slowly teaching students will help them hopefully grasp these problems. Also putting math problems into real world situations is important to help students visualize when they will use these tools. -Meaghan

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ARTICLE: "Interesting and challenging problems are ways to get students engaged. It is also important to give them a sense that they are learning new things and making progress... It fosters the... idea that attention and hard work pay off" (5).

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ARTICLE: "Interesting and challenging problems are ways to get students engaged. It is also important to give them a sense that they are learning new things and making progress... It fosters the... idea that attention and hard work pay off" (5).

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I will be sure to keep this in mind when I am a teacher and try my best to keep my students interested. I want to be sure that my students are aware of their abilities to make progress and learn. I know that students can become very frustrated with themselves with math, and want to give up. I want to be sure to keep my students engaged and help them gain self confidence in themselves. -Kayla

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ARTICLE: "Ma’s study also made clear that broad, connected knowledge of mathematics leads teachers to more flexible choices than limited, compartmentalized knowledge. The Chinese teachers noted that “although a standard algorithm may be used in all cases, it may not be the best method for every case" (10).

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ARTICLE: "Ma’s study also made clear that broad, connected knowledge of mathematics leads teachers to more flexible choices than limited, compartmentalized knowledge. The Chinese teachers noted that “although a standard algorithm may be used in all cases, it may not be the best method for every case" (10).

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I definitely agree with this statement. Teachers need to be able to approach different math problems with different methods because what may work well for you may be gibberish to another. When I was in 4th grade I remember struggling with learning multiplication. The teacher taught the class by using traditional multiplication. It just was not clicking for me. She then came up to me and showed me how to multiply by using lattice multiplication and then it all made sense to me. To this very day, the way I multiply is by using the lattice method and traditional multiplication is too disorganized and unclear for me to process. - Kayla

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The article states that mathematical proficiency has five components: (1) conceptual understanding, (2) procedural fluency, (3) strategic competence, (4) adaptive reasoning and (5)productive disposition. My question would be is one component more important than another? Or are they all equally important and just work together?- Kayla

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The article states that mathematical proficiency has five components: (1) conceptual understanding, (2) procedural fluency, (3) strategic competence, (4) adaptive reasoning and (5)productive disposition. My question would be is one component more important than another? Or are they all equally important and just work together?- Kayla