#number talks

[prenumbers]

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[autisticeducator]

Math: Mental vs Common Core Written

I'm not a fan of the way Common Core math has been implemented. See, here is my problem. It makes math way too complicated, especially for the early childhood and childhood grades. My autistic brain loves math. It is a bunch of pictures and patterns that my brain can easily interpret. Other autistics (many but not all) are also gifted in math. I have a deep understanding for math. I will admit being high functioning autistic without a learning disability is likely why I understand Common Core math. That understanding is why I hate Common Core math. Back in the mid and late 90s, we had one way of doing subtraction (at least on paper), what is now called vertical method or the standard algorithm. Now kids are taught to subtract in multiple ways. This would be fine if kids got to pick their favorite method and stick with that but they are tested on all the methods so they must remember how to do all the methods, including the standard algorithm. Common Core also doesn't actually deal with the issue of the inability of many to do mental math. This is not taught in many schools and it has to actually be taught if you expect most kids to do mental math effectively. The Number Talks program, when implemented correctly and done on a regular basis (aka every day) can actually teach kids how to do mental math. The Number Talks program, when done correctly, encourages kids to discover the intended strategy on their own first before the teacher actually teaches into the strategy. This method of teaching mental math has strategies that are similar to the methods taught in Common Core but, at least in my opinion, make more sense when done mentally rather than on paper. I would advocate using number talks because it can be good for all students. But for the autistic students, number talks provide these key benefits: 1: If it is done on a regular basis, say first thing in the morning or right before the math lesson, it provides a regular routine for the autistic students to grasp onto. 2: It is a short 5-15 minute exercise focused on mentally solving one type of math problem, which can help limit frustration from trying to remember too many things at once. You don't want to overload autistic students. 3: It promotes and encourages students to solve the problem in their own ways. 4: The hand signals allow the autistic students to participate and demonstrate that they have solved the problem and if they agree with another student's answer if they aren't interested in being called on themselves. Personally, I would rather have number talks be more heavily promoted for use in schools as it teaches students a valuable skill that can be used at any time: no pencil and paper or calculator required.

[aearwaker-blog-blog]

Video 3.6 (Doubling and Halving) Video Response

This video was about doubling and halving in multiplication. I found this video very interesting because I didn’t know what doubling and halving was. So, not only did I learn a good way to do multiplication, but I also got to observe the teacher’s actions and how the students thought about the problem in their heads.

What I found interesting was how many of the different kids visualized the problem differently. Some saw it with the original problem (4 x 7) and others saw it when it was doubled and halved (2 x 14). Also, some saw it vertically and others saw it horizontally. I liked it when the teacher connected the two different diagrams by showing that they both had the answer 28. Then she had the kids show how they would change the 4 x 7 diagram to make it 2 x 14. By having the kids connect the two diagrams, she helped set them up for the next question that she asked. She asked the children what the diagrams have to do with multiplication. This was a very key question in her lesson. Not only is she finding out what the children understand about multiplication, she is assessing how well she her lesson is going and she is helping the students make important connections between the procedures and multiplication. Making these connections will help the students with their number sense and later on in life.

If my teachers in elementary school had helped me make these connections between the method and my number sense then I would have known what doubling and halving was when it was mentioned in class. It would have also helped the other students in our class since they didn’t seem to know when this method should be used either. Overall, I thought this was a decent video because the students were doing almost all of the work instead of the teacher. 

[aearwaker-blog-blog]

5.6 Video Response

    During the number talk, the teacher did a really good job asking and not telling. In this video, when one student got the wrong answer the teacher did not disregard his answer but allowed the students work it out by themselves. The teacher could have just told the student who got 426 that he was wrong and told the class what he did wrong. Instead she asked the students what they thought he did wrong and why. One of the students explained by 426 could not be the correct answer. I found this a good way for the student to understand better. In the first class of EDE 339, Dr. Tapper mentioned that what the students have to say to one another is more meaningful than what the teacher has to say. This moment allowed one the students to explain his thinking, not only did this help the one student who did not get the right answer, but it also helped the student explaining understand the problem more. Being able to explain the math shows comprehension. Also, when the student was explaining, the teacher repeated that the student was saying in a more organized manner. This helped clarify what the student was trying to say for the other students.

    The white board filled with different strategies helps show that not just one way works best when it comes to solving math problems. The first strategy was taking of chunks, then there was a number line and lastly there was students counting up. In the last class, Dr. Tapper had said that addition is easier for our brains. The students who added up to 100 from 674 had a much simpler time working with the large subtraction problem. 

[aearwaker-blog-blog]

Video 3.1 Response

    I liked how the teacher had the students use their thumbs to show that they were done. This is a good way to show the students are done, while being quiet for the other students that are still figuring out the problem. I also liked how the teacher asked for multiple strategies used by the students. This shows that there isn’t just one way to do math. Students were using strategies that are in our textbook such as doubles/ near doubles.

    She broke all down the problem with the problem with the different strategies; this helps the student comprehend what they are doing instead of just using a procedure. In one of the strategies, a student added their 30’s and then the 7 and 8 then had to add the answers together. When the student said that they knew that 6 +1 was 7, the teacher quickly asked if the numbers were really 6 and 1. This gave the student a chance to correct herself and said that she knew that 60 +10 was 70. This helps reinforce place value and shows comprehension.

    When the teacher had 3 strategies on the board, she asked about the sharing strategy to make friendly numbers. This was a good way for the teacher to remind the students of another strategy that could be used. While the teacher had one student share his thinking about making both the numbers 40’s, she neglected to ask for more strategies to “share” numbers. Why did she ask a question then not go in to detail about it or not ask another student’s strategy for sharing the numbers. The problem 38+ 37 could have been 40 + 35, but this way of thinking was not put up on the board even after the teacher asked about sharing to make friendlier numbers. 

[aearwaker-blog-blog]

Video 2.1 Response

The first thing that I noticed was that the teacher had the students in one section of the classroom. This strategy was mentioned in the book. “Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions.”  Another thing was that the teacher asked for multiple strategies while recording them on the whiteboard. The dots she used to help the students focus on the numbers was also important. Having something physical makes it much easier to workout math problems, such as the unifix cubes we had in class our first day. The students could go up to the board to help explain their strategy. After the teacher had a bunch of strategies on the board, she lead a discussion about specific strategies that they had learned in class. These connections between the strategies such as 10’s and doubles helped the students understand how to apply the things they learned to different problems.

Besides the math strategies, the students had also used had signals for “me too.” This was a good way for the students to indicate that they got the same answer or not. It allows the teacher to see instead of trying to hear which students are struggling and which are not. It also keeps the classroom noise at a reasonable level. 

[urlpdf-blog]

Guest Blog: Number Talks in a 3rd Grade Classroom

Magen Schott, 3rd grade teacher at Knowles Elementary, is our guest blogger this week! She has been using number talks with her students, so we asked her if she would share her thoughts on the topic. Thank you Magen, for sharing your learning and inspiring others through your experiences. "Since beginning Number Talks in my classroom, my kids are able to have great conversations about their mental computations. It's easy to have a conversation in Language Arts class about the main idea of the book, the author's purpose, etc.  Before reading Number Talks, we never had REAL conversations in Math about numbers.  It has been amazing to listen to my kids discuss numbers in this way.  Students have learned to reason with numbers, and their mental math ability has greatly increased.  Our classroom is a "safe" place for the kids to be wrong, and they are open to admitting their mistakes.  They all learn from each other, and most have begun to try out and adopt different strategies that others are using.  I feel that they think about numbers differently now-- that numbers can be taken apart and combined with other numbers to make new numbers.  They have great conversations about manipulating numbers to make the problem easier and organizing numbers into groups of thousands, hundreds, tens and ones." Below is a impromptu video recorded during a recent school improvement visit.  Watch Magen's class in action!

Comment below how you use number talks in your classroom...