Taking it to the next level: Students using Inductive Reasoning

By: Jaclyn Murawska and Alan Zollman

This article started off with the difference between inductive and deductive reasoning. Inductive reasoning is when student understand some thing possible because they have seen it through multiple examples. Where deductive reasoning is using reasoning assuming it it true to arrive at a conclusion. The article then goes on to spend most of its time explain math inquiry, the different levels and each level's significance in importance. For example the 4 levels of inquiry from lower to higher are: 1. Confirmation, 2. Structured, 3. Guided and 4. Open. The article went on to give examples of each level of inquiry; it was dealing with a geoboard and line segments on the board to then develop their reasoning in of pythagorean theorm. They stated that in order for a teacher to be good at using inquiry in her classroom she needs to be really good at asking and developing questions. They talked about how this was a science approach to learning that is now being adapted and developed in the math words for teaching as well.

I am a huge advocate for inquiry math usage in the classroom, so I found this article to be really interesting and explanatory. It was cool to learn about the different levels of inquiry. I never really knew their was different levels, I just thought that inquiry was inquiry. I enjoyed that they provided and explaining of each level and also showed some student work throughout the article. The only part that I did find a little confusing was how they expected the students to make the connection to the rule of right triangles. Even after reading the article I tried to think about it more and I feel like I am still unsure as to how that would happen. Overall I found this article to be interesting and informative. I am excited to share what I learned with my group and also to use all the different levels of inquiry throughout my time teaching in the future.    

Video Blog Post II:

number operations: multiplication & division

Planning:

This video did not have the planning part like the other video had. Personally I liked the way the other video did that, I felt like that also helped me as a viewer to better understand what was going to be happening for the class time. However I really liked that she used the term active listening with the students. Really using that academic language with them is important.

Lesson:

I liked that she made sure she wrote what the students were saying to on the board, she was not just assuming. However I did not like that she asked a student to draw a picture and she would get back to it and then she never got back to it. To me that tells the student that she didn’t feel that she had time to hear about his thinking. Also I don’t think she provided enough wait time after her questions. I think she did a good job listening to the students but I also feel like she didn’t really stick with anything that they said. Every time a student made a suggestion she would go back to the boxes and writing the numbers in the boxes; which personally even I was confused and distracted by her doing that. I also did not like when she called a student to the board to write something and she erased what the student wrote and rewrote it. I could read what the student wrote, why did she erase it?

I also think she jumped the gun on their knowledge. She talking about multiplying and dividing single digit number and then she jumped to a two digit number by a single digit number. I don’t this the students were ready for that big of a jump so quickly.

Also I think that she should have made the lesson only about multiplication and do division a different day. There was just too much being spoken on. Also of the students were having a hard time figuring out the equal groups for multiplication what is there to say you should move on to division. They also never did any word problems with division so I just think it made a long lesson longer… Do division on a different day.

One of my favorite parts in of the whole lesson was when the student counted “20, 40, 60, 80” “6, 12, 18, 24” equals 104. While watching this I said “WOW” out loud. I was so blown away by that student’s thought process. To me I would have never thought to think about it that way. It was amazing to me that a fourth grader was able to use that skill and process the right answer. This was an ah-ha moment for me, really making it clear that all students really do process math skills differently and as teachers we need to work with them on that and not tell them their thinking is wrong.

The biggest thing that I did not like about the lesson was that she kept asking them how THEY would draw a picture. She spent so much time on that. And I am a firm believer that when you asked student to draw a picture you are going to get a variety of different kinds of pictures, but as long as it makes sense with the math problem it is not wrong. But it’s as if she wanted every student to draw the same picture when she should them the Charlie model. It was like she said “yeah your picture is nice, but this is what I want your picture to look like”; which I believe that this is really where she lost them. That picture just did not make sense to the students.

At the very end I did like that she explained the camera crew more to the students and told them thank you and also told them they would be rewarded for their good behavior.  

Faculty:

I felt like she did a good job addressing the positives of her lesson, but she never addressed the negatives of her lesson. I also really liked how the one teacher drew what she saw on the students’ papers. And she even kind of pointed out that the students really had no idea how to make sense of the Charlie model. Which I thought was really important because the main teacher thought that the Charlie model was awesome and so perfect, but if it doesn’t make sense to the students… It is not awesome. Also personally I found the Charlie model to be weird as well. That is not how I would have represented my picture for that question and also not how I would have wanted it to look after I saw that model as well.

Thoughts:

My overall thoughts have been address throughout the course of this blog post. 

NEAP Reflection

I actually really enjoyed the NEAP project. With being a math concentration I obviously enjoy math. I have taken my fair share of math courses, but this project was different than anything else I had done before. It was very interesting to look at the student's work and try to figure out their process skills form the notions they provided; just like teachers do on a regular biases. I was also cool to think about how your would assign the student with a grade, what parts are required and what parts acan be assumed knowledge?

Also for part two I really liked the part where we got to write the comments to a few selected students. I think that it really helped us to understand what makes a good comment that the student will actually be able to understand and be able to make improvements for next time. The one thing my group did comment on was that it would take a long time to hand write all the comment for a classroom, so maybe we would type them and staple them to each student's work.  

Overall I really enjoyed this project and I feel that me knowledge of teacher math and all other classroom related math procedures have improved.

Rich Task Reflection

Although I was unable to be there on the day that my group taught the lesson I felt that it was still necessary to write a blog post on my reflection.

We had lesson in mind but when it came the to start typing the lesson one of the other girls showed us the barbie lesson idea and we all loved it. I really enjoyed finding that lesson, we all agreed that it would be much more fun for everyone in the class than the other lesson we had in mind.

I typed most of the lesson plan because I knew I would not be there the day to teach the actual. It was really cool to think about the inquiry with the math lesson we had created. I really liked that the lesson used a common child's toy and applied math to it. I think this is something that every student could relate to and could also enjoy.  

Applets and Apps

Applet:http://illuminations.nctm.org/DeepSeaDuel/

Deep Sea Duel

This applet allows for students to pick what level of difficulty they wish to practice during the game. They are then given a screen with a “goal” number and bubbles with numbers inside each of them. They will then be asked to build the “goal” number in a 3 number combination. This allows students to understand parts of a whole and positive and negative values.

I like this applet because it allows for the students to visually see the math steps they are computing in their heads. I also allows for students to better practice their knowledge on decimal, positive and negative numbers.

Applet: Kahoot

https://play.kahoot.it/#/?quizId=9f8af42b-d67d-40f3-988a-ef61fceb2529

Kahoot is a website where teacher can create their own interactive games for their students or they can browse the library of games and use a premade game. The Kahoot can have as many questions as you please. It also allows you to decide how much time it will allow for the students to pick an answer. As the creator you are able to decide if you want to make it a points game or not. With Kahoot you are also able to insert pictures and videos and create questions off of that as well. Kahoot also tracks the students’ right and wrong results and will make a stats chart for you at the end of you request such.

I really like Kahoot because I believe that it allows the teacher to have full control over the material that her students are benefiting from. I love that you are able to personalize every aspect of the game creation. This game could be used in lue of a test for your students, by it tracking the right and wrong answers you would be able to place an accurate grade to each one of your students.

App: Explain Everything http://explaineverything.com/

This is an app that provides you with a blank page and tools to create a situation on that page. It allows you to place animations, add text and add voice recordings. In a math setting the teacher could as the student to show her what they learned about functions and expressions by creating an Explain Everything.

I like this app because it allows students to demonstrate their learning at a higher-level because by asking them to explain what they know or have learned is at one of the highest level on the Blooms taxonomy Pyramid. This can also be in lue of a test. The teacher will be able to go back and watch the student’s explain everything and she can assess the student's knowledge based off of that.

Thinking through a Lesson: Successfully Implementing High-Level Tasks

This article addressed the idea and concept of Thinking Through a Lesson Protocol (TTLP). This is a concept that is used to help teachers create higher-level thinking situations for their students. Teacher want to create higher level thinking situations for their students however this can cause some teachers to be more nervous about the situation because it means that they will have to set back from the direct instructional method of teaching. This article addressed the different parts that a teacher should think about before, during and after implementing a lesson. TTLP is a way for teachers to think about possible situations that could occur with their students during the lesson. This is a way for teacher to feel more confident when working with higher-level tasks with/for their students. TTLP also allows for teachers to better understand the possibility of different method of actions that different students could possibly take. As a teacher it is important to understand that different does not mean wrong.

I really liked this article because it helped me better understand how to make sure I am helping my student achieve higher-level thinking skills. I liked how one of the personal testimonies stated how she does not write down answer to each of the questions but just simply thinks about it so that she feels better prepared or is able to better understand a student’s possible thinking process on the problem. I also really liked this article because I think that TTLP mirror the mathematical process. Math is completed in steps or parts and developing a proper math higher-level thinking lesson should also be thought-out and completed in parts. This also helps us to make sense of each part to better make sense of the whole. I look forward to using this method in some of my math lesson to come in the future.       

A Model for Understanding Understanding in Mathematics

This article was about the use of "moves" or in other words steps to help students understand their processing skills. This article addressed how teachers can phrase certain questions to better understand their students' current understanding of the topic. The article provided many different detailed examples of how certain "move" questions would look and to what goal they are aiming for. The article addressed different levels of moves and different focus points; for example, examples of the concept and understanding what the generalization and why that generalization is accurate. They also discus moves that will help students understand the process to the problem and why that process is correct for the situation at hand. The last moves the article addresses is the understanding of the outcomes and why the outcome makes sense and is accurate to the findings of the problem. The article explains how moves help teachers from questions of understanding for their students in both a lesson setting and a testing setting. Research shows that the moves do not need to be done in a specific order; however they should follow a logical order and be at the student's level of cognitive development with the situation at hand.

I really liked this article. With being a math concentration I have taken my fair share of math courses here at Bradley; however we have never really discussed how to teach our students or measure their level of understanding. I really found these moves to be very informative. They better showed me how to phrase questions to understand my students' understanding of the topic at hand. I think that these moves should be placed at the end of a teacher's lesson plan. I think it would be a good idea for her to come up with a few possible moves that the students could benefit from. She could come up with a list of moves in the order in which she would as them and if she had a student with a math learning disability she should compile a different set of moves developed around that student's cognitive ability level. I am excited to keep this information with me and to use these moves in my classroom in the future.