Conferring is super important if you want to know your students as mathematicians! Find a way to do it! We do it in reading because we know it is important. It is just as important in math.
Dr. NickiRead Full Post | Make a Comment ( None so far )
Here are some great posters to present the mathematical practices to students. They are written in “I can” language and they have pictures and stages…before/during/after! We have to continue to think of ways to make the practices explicit to the students. I would do a great deal of this work in small, guided math groups. Students can talk about the things they do really well and the areas where they struggle.
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Here is a great word problem solving rubric! I would discuss this and make examples with the class so everyone understands all the elements. I would also make individual copies so students would have it as an “up and close” reference. They could keep it in their problem solving notebooks. I would go over their story problems in small guided math groups, guided by the rubric.
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Happy New Year!
Hello Everyone. Happy New Year! I wish you all an abundance of rich mathematical experiences this year. What are your math goals? What do you want to do as an educator? What do you want your students to be able to do? I am currently doing some research on student goal setting and how it looks across the grade levels. Please write in and tell me what you do in terms of setting math goals with your students.
One thing I have been doing is having students reflect on their math tests! This can be done individually, in small guided math groups or the whole class could be filling out the form at the same time. This has been so amazing. I have developed a few forms but the gist goes like this:
- Take a look at your math test. What’s the first thing you think? How did you do overall?
- What was easy?
- What was difficult?
- What do you still need help with?
- What is your plan to learn the concepts you need to work on?
Here are some sites I have found interesting in terms of students setting goals:
Student Goal Setting Templates:
2 of my favorites from the link above:
Another good template:
Have your students set math goals online:
Scroll Down to Goal Setting: I especially like the mini-goal template and the secrets of goal setting poster…
Cedar Rapids Schools students at work setting goals:
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We can use these 1″ plastic tiles in four colors to build models of math concepts, develop basic arithmetic skills and explore color and number patterns. Remember that in terms of a guided math lesson, you always want to think in terms of doing concrete activities, then pictorial activities and finally abstract activities. Spend time in small groups developing conceptual understanding as well as procedural fluency. We want our students to understand the math they are doing.
Here are some great general sites:
Exploring Prime and Composite Numbers
http://mapps.math.arizona.edu/sample_session.pdf (pages 15-24)
Addition and Subtraction of Integers
Also Google UEN lesson “Math 5 – Act. 29: Likely or Unlikely”
Google this UEN lesson as well- “How many ways can you represent a number”
Math Tile Video
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We have been talking about fostering adaptive reasoning among our students. Donovan and Bransford have defined it as the “Capacity for logical thought, reflection, explanation and justification” (p. 21). So this means students are thinking, reflecting, explaining and justifying themselves both publicly and privately. We build this by doing it as a whole group, as small groups, as partners and then as individuals. We must scaffold this type of thinking. The landmark report Adding It Up notes that even very young children from the ages of 4 and 5 can “demonstrate sophisticated reasoning abilities” if given the appropriate experiences (http://www.nap.edu/openbook.php?record_id=9822&page=129).
It goes on to note that “Research suggests that students are able to display reasoning ability when three conditions are met: They have a sufficient knowledge base, the task is understandable and motivating, and the context is familiar and comfortable” (http://www.nap.edu/openbook.php?record_id=9822&page=130).
Furthermore, it adds that one important “manifestation of adaptive reasoning is the ability to justify one’s work. ” But it clarifies that there is a difference between justify and prove noting that proofs are more complete whereas justifications are less formal. So, proofs would be where we would make the students write it down and explain it through a series of logical arguments whereas justifications would be more talking about it (http://www.nap.edu/openbook.php?record_id=9822&page=130). So for example, we might have students prove that a number is even or odd. We also might have them prove that 6 + 7 is a doubles +1 fact. We could have them prove that 1/4 is smaller than 2/3.
I challenge all of us to think about how we might start doing this in our elementary math classrooms. How might it look in your kindergarten classroom? How is that the same and/or different from how it would look in a 6th grade classroom? I think there are many possibilities.
Here is a great example of having students write a CONVINCE ME paper:
Remember IT’S ALL IN THE QUESTIONING….
Accountable Talk Icons
More Question Prompts for Problem Solving:
How Students Learn: History, Mathematics, and Science in the Classroom By National Research Council (U.S.). Committee on How People Learn, A Targeted Report for Teachers, Suzanne Donovan, John Bransford Edition: illustrated Published by National Academies Press, 2005 ISBN 0-309-08949-2, 978-0-309-08949-4
Adding It Up: http://www.nap.edu/catalog.php?record_id=9822#tocRead Full Post | Make a Comment ( 1 so far )
Here are some questions to get you jump started. Remember only introduce a few questions at a time. Picture icons are great and give non-readers more access to the poster.
The Language of Engagement
- I agree because . . .
- I disagree because . . .
- I don’t know….
- I don’t understand yet….
- I’m not sure….
- I’m still fuzzy …..
- I also noticed . . .
- Help me understand . . .
- Say more about what you mean . . .
- Can you show me/us how you did that?
- Why do you think that?
- Can you prove it?
- Can anyone add to that idea?
- Why is that true?
- How do you know that?
- I wonder . . .
- I got a different answer…
- I did it this way….
- I have a question about
- This was the tricky part
- Can you tell me more?
- Would you say that again?
- Can you give me an example?
Adaptive Reasoning is one of the key components of Mathematical Proficiency. Students with adaptive reasoning can think logically about the math and they can explain and justify what they are doing. The key to getting students to engage in mathematical discussions is to create a talk friendly environment. It is important that students feel that what they have to say will be considered worthy and important. They need to know that they will not be mocked, ridiculed or belittled.
We have to set talk as the norm in the classroom. The idea of using accountable talk in math class gives us a sturdy framework. Accountable talk in math class means that students talk about the math in a variety of ways. They learn to express their ideas as well as entertain the ideas of others; they learn to question themselves publicly as well as respectfully question the ideas of their classmates and teacher.
Here are some great resources to get you started. Cunnigham notes that “not all talk sustains learning. For classroom talk to promote learning it must be accountable to the learning community, to accurate and appropriate knowledge, and to rigorous thinking.” This is a key idea here. We want talk that promotes learning, that expands thinking, that contributes to the intellectual community.
Cunnigham has created a great graphic poster displaying various types of accountable talk- click the link at the bottom of the post – http://toolsfordifferentiation.pbworks.com/Accountable-Talk
Ramirez wrote a great teacher friendly article about getting students to be effective speakers in class when discussing the curriculum. See the article here and be sure to look at the chart she created with the specific skill sets http://www.teachersnetwork.org/tnli/research/achieve/Ramirez.pdf
Holyoke Public Schools created a very interesting curriculum map where they map out the accountable talk in a unit on fractions and decimals – see page 7 for a great list of teacher/student questions and see page 10 for an example of mapping the talk directly into lessons- http://www.hps.holyoke.ma.us/pdf/curriculum_math/grade4_fractioncardsanddecimalsquares.pdf
You absolutely must Google: Accountable Talk Toolkit and then open the toolkit (it comes up as an attached word document). It is phenomenal with very specific examples and ways to get started.
You also should Google: Lucy West – Robust conversations at every level. In this powerful powerpoint Lucy notes that students should be held accountable to the learning community, the content knowledge and mathematical reasoning. They should be encouraged and required to explain their thinking, based on the math topic at hand. They should talk like mathematicians and use math language in their explanations. Lucy quotes Tom Alec (The Tao of Democracy) – “Dialogue is the central aspect of co-intelligence. We can only generate higher levels of intelligence among us if we are doing some high quality talking with one another.”
To be continued….Read Full Post | Make a Comment ( 1 so far )
Today, I interviewed several upper elementary students about math. These were students who had failed the math test and were going to be going to summer school. I wanted to know what their perception of what happened was. Surprisingly, they all said they liked math and felt they had a handle on it. I thought, “Wow!” What does this mean? So, I told them that I would like to do a “math interview” with them, where we would discuss problems and how they solved them. They agreed and we were off!
Now there are several types of interviews, but I did a content interview. I wanted to know what they knew. This experience just reminds me again, that IT’S really important that we talk to students about math. Some things we will only ever know by having a conversation. We should be doing math conferences. We have to find time in our schedules. Even if we only do 1 or 2 a semester, it is probably more than we have been doing. Math conferences can make all the difference in a student’s progress. When student’s have the time to talk about math and their individual performance, they have the opportunity to set goals. When students set goals, they have the opportunity to meet them. So, look at the forms I’ve uploaded and use them! And let me know how they work, please:)Read Full Post | Make a Comment ( 2 so far )