Technology Reflection

Throughout this course, we have been shown and had to research our own ways to use many different forms of technology in the classroom. Using technology in today's classrooms is extremely important and it is important to stay up to date with how to use the different technologies. One thing that I really loved about this course is that we worked with the Smart Board a lot and in many different ways. This was especially important for me because I was not used to the Smart Board and had the opportunity to learn a lot of useful techniques that I can take to my future classroom. Having us as the students research Smart Board activities was also very helpful because we could learn from our colleagues as well as teach ourselves. Another activity that involved technology that I know was extremely beneficial was allowing us to research math apps and applets. So many of us brought wonderful ideas to the table and we were all able to explain how to use these in the classroom. I know that I would be able to use every one of these technologies in my future classroom. Overall, this class was extremely helpful in teaching many different technologies to take to the classroom and I believe this is so important for us as future teachers to continue working with.

Moving Beyond Brownies and Pizza

"A lack of fractional understanding is a well-documented obstacle to student achievement in upper elementary and middle school math" says the National Center for Educational Statistics. This article begins by pointing out their main focus as being about helping 4th graders to use number lines to develop a rich understanding of comparing fractions. The article then goes on to discuss that there are 3 main goals they are focusing on:

1. Build students' understanding of fractions as numbers with a definite magnitude
2. Increase students' understanding of measuring with fractions
3. Develop fraction number sense by avoiding early introduction of traditional fraction algorithms

Then, as they move onto trying to reach these 3 goals, they tell us that they will be focusing on 6 different types of lessons that identify ways that 2 fractions might be related to one another:

1. Both fractions are one unit fraction more than a half
2. Both fractions are one unit fraction less than a half
3. Both fractions are one unit fraction less than one
4. Both fractions can be used in the context of money
5. More of a bigger unit fraction or less of a smaller unit fraction
6. One fraction can be expressed in terms of another

There was then 2 different examples from students and their thought process about different perspectives of the same number line. Even though both students thought differently about the problem, it was clear that the number line was central to their thinking. The same process was shown for different students a few more times, as well. After the lessons, the teacher was able to see that all of the students in the class had made progress in relation to the original 3 goals. 

I had some extremely good thoughts about this article. I really liked the overall idea of getting the students to build an understanding of fractions as numbers with a definitive magnitude. Also, I think this teacher's example of her plan for the class was very well thought out and put into motion the best way it could have been. It also really got me thinking about the troubles students commonly have when being introduced to fractions. It's hard to realize that once some misconceptions or misunderstandings are made right off the bat, it is difficult to help the students get back on track and fully understand the concept they're working with. And this is common with any mathematical concept. This is the main reason I liked this article and it really brought that idea to life. 

Girls Build Excitement for Math from Scratch

This article begins by focusing on the idea of increasing "digital literacy and mathematical fluency" through a workshop dealing with computer coding. Computer coding helps people to advance mathematical understanding and spatial reasoning. Coding is significantly important with numbers showing that five of the top ten jobs in the United States are in information technology. However, they state that girl's attitudes towards math related careers diminished diminish at a far more substantial rate than boys, highlighting the need to focus on girls and STEM disciplines, and this led to the creating of the computer coding unit designed to girls in grades 6-8. The program that the girls use is called Scratch: "a graphical two-dimensional, drag-and-drop programming approach, with easy to understand graphical icons representing basic programming elements." They began using this program in the classroom by implementing lessons that may address how to create a new project, add and modify, move projects around the screen, etc. Scratch was also designed to help emphasize the role of mathematics and science in computing and technology. Three mathematical topics are focused on during the lessons: mathematical descriptions of position and movement, scaling and percentages, and mathematical abstraction of physics concepts. The article continues to talk about how Scratch could easily be implemented in your own classroom one to two hours a week. It talks about how math teachers could design a multidisciplinary coding unit with science, technology, and mathematics.

I was very surprised when I began reading this article that this is what it was about. Overall, though, I think this is a very interesting concept. It reminded me that in our high school we had a class that was similar to this, although they only considered it to be a "computers class." When I think back on it now, however, I remember how much math really went into the coding. You had to have a solid understanding of each mathematical concept before you could even begin to understand the program. This is somewhere that I could see trying to implement the Scratch program hitting a bump in the road. Even though this program is fairly interactive and usable, students would need to have a complete and thorough understanding of the concepts you would want them to use. I was extremely surprised that they wanted to implement this project in middle schools, because I just think they would have a very rough time being able to actually use this to its full potential. I like the idea and the goal they are working to accomplish and it is a great program, however I think something like this would be much more useful at the high school age once they have mastered these concepts and are closer to choosing their career path in college.  

Problem Project Reflection

This project was really something interesting. For starters, beginning this project took A LOT of time. It is extremely difficult to come up with an idea that students will be able to relate to and at the same time connect to the standards as it should. But we finally were able to come up with our great idea for a game day. We had found a similar idea to this on Pinterest and decided that it would be something really fun to play around with and extend it into a problem project for 4th grade students. Another thing that I thought was super fun about this project was working to tie in interdisciplinary connections. I love when projects or lessons can tie in multiple subjects, and we were excited about being able to include English and Visual Arts into ours.

Additionally, it was very interesting to listen to the other groups presentations and what they game up with for their grade bands. One thing that stuck with me after hearing the other groups' ideas was how as you get up into the higher grade levels, the more ill-structured you can make the whole project and you can give a little more creative freedom with the project still running smoothly. I feel as though groups dealing with younger ages felt the need to include a lot more information and instruction than the groups with older grades. Overall, I think our group as well as both of the other groups came up with some amazing ideas for such a difficult project.

NAEP Reflection

This project started out to be very challenging and really had us working hard and thinking about helping the students we were working with. It was interesting to see that even though we have worked with creating and reflecting different assessments throughout the education program, it is something different to really give the students feedback and think about how to create a follow-up lesson that will positively effect the entire class. I think that one thing we did very well while doing this project was choosing 3 students who had difficulties that were somewhat similar in their work. They weren't all exactly the same, but they were related enough on different difficulty levels that we were able to create a follow-up lesson that would help each one of these students' difficulties. 

It was also very interesting to listen to how other groups decided to go about this project and how they interpreted rubrics differently/what kinds of feedback they would give to their students. Although a lot of ideas others had were different than my own, I was able to take away a lot of good ideas and examples from them. All in all, I think a project like this is very beneficial for future educators and should be done more than once with different topics.

Number Operations: Multiplication and Division

The first thing I noticed about the beginning of this video is that the teacher did a very good job of introducing the lesson. She used a variety of techniques to get the students thinking about the idea of multiplication and division when she had them think about a well known quote, share ideas about what the quote meant, and then having them talk to a neighbor about what they already know about multiplication and division. She also went on to have students share their ideas about what they already know about multiplication and division with the entire class. This way students were able to see how others were thinking about problems that were actually the same, and could give students another way to go about solving problems in the future. Additionally, she went on to build on her beginning topic of "a picture is worth a thousand words" by showing the students how they can show their grouping with pictures.

As the teacher was going through the problems with students, I liked that she would take everyone's ideas and write them down on the board whether they were correct or incorrect so that she could work through the errors with the whole class. She continued with this concept through the division part and here is where you could really see how helpful talking to each other was for the students. It was interesting how much the students were sharing their ideas with each other and listening to their peers. This would be extremely helpful with some students who are struggling to put the idea into their own words because they can talk it out with a partner. As the teacher went back to her concept of drawing pictures to explain division, it definitely reminded me of strategies we learning in ETE 107 and showing how the groups are separated using a picture while we divide. This idea would really help students to make sense of what is being divided and into how many groups, etc.

I think one of the things I liked most about this video was how the teacher had the students build off the idea of comparing operations. As she compared operations throughout the entire lesson, she also continued to show the students all of the various strategies to solve the problems using mental math. This included using the pictures to show grouping. I think that this lesson was very well thought out and would help many students to deepen their understanding of multiplication and division, as well as helping them to be able to better explain their answers and thought processes for future problems.

Math Applets

Applet #1: Alien Angles

Math Playground
URL: http://www.mathplayground.com/alienangles.html

Angle Aliens supports Grade 4 Common Core Math Standards in Measurement and Data.

"Friendly aliens are traveling to a new space colony on Planet Geometry. Unfortunately, some aliens have lost their way. You have been placed in charge of the rescue mission. It is your responsibility to set the correct angle on the rescue launcher. The computer will generate the launch angle. To be successful, you must estimate the angle on the rescue launcher within 5 degrees. There are 10 aliens to find in all. Good luck with your mission."

This would be a great applet for 3-5 graders studying angles in Geometry whether it is just now being introduced, or whether it is used for a review game. First of all, I believe students would respond well to this applet because of the nature of the game being about aliens and a rescue mission. This will help to keep the students' interest while they are practicing their Geometry skills. As far as their Geometry skills go, students will be able to begin to recognize what certain angle measurements look like in terms of drawings or figures. For example, a student will begin to see that a 90 degree angle takes an "L" shape, or that 180 degrees lies flat. This will also help build their estimation skills when working with angles, as they are asked to provide an estimate of a certain angle by drawing the lines themselves just from remembering what that angle may look like. I would definitely use this applets in the classroom with beginning and more advanced Geometry students.

Applet #2: Platform Scale Subtraction

Visual Fractions
URL: http://www.visualfractions.com/scale/platformscale3.htm

Platform Scale Subtraction supports Grade 5 Common Core Standards in Measurement and Data.

In this applet, you are given a virtual "scale" on the screen and are shown 5 "Gregs" (simply the name of the character that each student is weighing. The instructions are as followed: 

"Press the <Start> button when the program begins. Five Gregs will appear and one of the Gregs will drop down to be weighed. You can weigh Greg by moving the larger and smaller weights to the right or left on the graduated bar. 

The bottom (larger) weight shows units and the top(smaller) weight shows hundredths of a gram. Move the weights until the bar is level. 

The red pointer on the right should be on the center mark when you arrive at Greg's weight.

When you arrive at Greg's weight a plunger will gently push him to the right. You will be prompted to type the difference between the remaining gregs and the Greg you weighed. Type the difference into the edit box and press the <Submit> button. If the amount you submitted is correct, another Greg will land onto the scale. Continue until all Gregs are weighed.

After five Gregs are weighed, you will have a chance to weigh more Gregs by pressing the <Start> button or you can press the <rReport> button to report the time it took to weigh five Gregs.
The program will keep track of the total Gregs you have weighed and the time you took to weigh them.

A challenge - See if you can find the differences mentally."

This applet would be very useful in class to bring a visual representation for the students to see as you are discussing weight/weight changes and measurement. With this applet, students are able to actually see the scale, play around with different measurements, and put their knowledge to the test as they manually set the scale to difference weights and subtract them from the original. I really liked how this applet was set up when I first discovered it because of how many different skills it allows the students to work on at one time. However, one of my complaints about this site is that I can see it being somewhat tricky for young students to navigate or make use of the game. It would take some time introducing this applet to the students, and it may also take time for them to get used to this idea and be able to use it on their own. I would recommend using this activity on the Smart Board and as a whole class activity to make the most of your time and for students to reap the full benefit of this applet.

App #1: Splash Math

iTunes Store
URL: https://itunes.apple.com/us/app/3rd-grade-splash-math-games./id449564960?mt=8 

Math Splash supports Grade 3 Common Core Math Standards.

Splash Math is an app for 3rd grade classrooms that includes a variety of fun and interactive math problems aligned to Common Core Standards. "The app reinforces math concepts with self-paced and adaptive practice anytime, anywhere (works on iPhone, iPad, laptops, and desktops)."

This program is currently being used by more than 10 million teachers and students, and many teachers have given this app great reviews such as this one:

"I’m very impressed with the thoroughness of content in Splash Math. I really like the workbook concept and it works well here. This is most definitely a well thought out, well designed, educational and entertaining Math app."

Splash Math has various key features such as:

• self-paced math programs
• explanations for wrong answers
• scratchpad for rough work
• virtual rewards and games
• monitors progress with a real-time progress dashboard
• progress synced across multiple iPhones, iPads, laptops, and desktops
• HD graphics and sound effects 

Likewise, Splash Math covers the various topics needed to align with the Common Core Standards:

"1. Place Value - Ones; Tens; Hundreds; Thousands; Ten thousands; Expanded and word forms
2. Number Sense - Compare; Order and round numbers 
3. Addition – Two and three digit addition and regrouping
4. Subtraction – One, Two and Three digit subtraction and regrouping; Subtract Across zeroes
5. Four Digit Addition – Two and three digit addition and regrouping with four digits
6. Four Digit Subtraction – Two and Three digit subtraction and regrouping with four digits; Subtract Across zeroes
7. Multiplication Facts - Properties of multiplication; Multiply by 0 to 10 
8. Division Facts- Properties of division; Divide by 2 to 10 
9. Fractions – Identify fractions, Model fractions; Equivalent fractions; Compare fractions
10. Time - Read and set time; Elapsed time 
11. Measurements and Data - Measuring length; Units of length, Capacity, Weight; Data on Line plots and Bar graphs; Perimeter; Area
12. Geometry - Triangles; Quadrilaterals
13. Decimals - Tenths; Hundredths 
14. Multiplication - Multiply multiples of 10; Estimate products; Multiply 2, 3 digit numbers 
15. Division - Divide multiples of 10, 100; Estimate quotients; 2/3 digit quotients 
16. Money - Add and Subtract money; Multiply and Divide money"

All in all, I think this is a WONDERFUL app for the classroom. First of all, this app is eye appealing, fun, and interactive for all students. It allows students to be entertained while working through the math skills necessary for their grade level. I also love that this app is self-paced and students can work to the best of their ability without being rushed. This app also gives great explanations for wrong answers so that students can reflect on the feedback. Another huge plus for this app is how it allows students to sync and track their progress through various devices. This is a great way for students to keep practicing at home from where they left off in class. This also could be a helpful benefit for teachers as they could give a fun homework assignment of completing some Splash Math activities at home. Lastly, this app is wonderful just due to the sheer amount of informations and topics that it covers.  

A Model for Understanding Understanding in Mathematics

When I first began reading this article, it interested me right away because of its topic of “understanding understanding.” This is something that we talk a lot about in all of our classes as we progress through the education program, and something that I think a lot about in the actual classroom. A concept that was new to me in this article was talking about teachers using different “moves” while teaching, and how those moves can vary when teaching concepts and ideas. Another thing that I liked in the article was how it helped get this point across by giving examples of what kinds of questions a teacher will ask her students to check for understanding. In the closing of the article, they pose the questions: “Can effective instructional sequences be described in terms of moves? Do moves help structure knowledge in ways most readily grasped by the learner?” That is something that I would even like to research more on my own.

Rich Task Reflection

I learned a lot working with my group for this project. One of the things we really focused our attention on at first was getting to know what exactly should constitute a "rich task." Once we were sure we've wrapped our head around the idea, we shared ideas that we could use for teaching our lesson. Something that I was surprised to learn was that once we had selected a lesson, how difficult it would be to adapt the lesson to fit our class's needs. It is something valuable to remember, though, especially when thinking about how lessons and projects will need to be adapted through the various classes.

It was also very interesting watching other groups do their lessons and also very helpful. There were a lot of tips that I was able to take from how the other lessons were presented, how they decided to assess students, and what kind of reflection questions were asked after the lesson was completed. I thought it was interesting that both of the other groups decided to use a worksheet to follow along with their lessons, however, they used the worksheets in a way that was actually helpful to the students and not just as a time filler.