Yesterday, I mentioned looking at vector addition apps to use with my college prep class to help them as they learn the material. The only free one I found, BabuVectorsHD had no instructions and was not intuitive. I figured out how to draw an arrow but I could not figure out how to get the arrow exactly as I needed it so the directional section of the vector would be right.

What you see if all that you get. I found it difficult to actually draw the vectors with the correct length and angle. This makes it too hard for my students who are learning vectors to use.

I did a bit of looking and there are very few apps that actually deal with vector math instruction but I did find a couple of ones that show vector addition and subtraction and one for vector products. I also found a combined algebra II/vector Algebra app that looks interesting and is only $1.99.

I think I am going to bite the bullet and buy three or four paid apps to see which one will meet the needs of my students. I might need more than one depending on how they present the material to the students. It seems as if there are so many apps for lower math classes but as you go higher in mathematics, there are fewer apps available. Hopefully I will be able to report back on the apps come next week.

## Friday, January 30, 2015

## Thursday, January 29, 2015

### Videos and Vectors

I just started my college prep math class on vectors. I had them read the book and then I talked about it and found a nice video on adding vectors graphically to show them. After the video, I sat with students to help them begin but they had trouble so today, I worked again and after three problems, I put the video on again and had the students watch it again. This time, I stopped the video at each step and we discussed how it related to what we were doing. This is working really well. Furthermore, I was asked to start the class again with the same video before they attempt additional problems.

In the past I would have shown one video and moved on but I think when it is a topic that is so different from any other mathematics they've had before, they need the reteaching and scaffolding and by reshowing the video numerous times. This seems to be working best with them.

I found an app that supposedly shows vector addition but it had no instructions and is not intuitive to use. Furthermore, it kept closing on me so that made it harder to use. I am going to continue to explore it and report back on it later.

In the past I would have shown one video and moved on but I think when it is a topic that is so different from any other mathematics they've had before, they need the reteaching and scaffolding and by reshowing the video numerous times. This seems to be working best with them.

I found an app that supposedly shows vector addition but it had no instructions and is not intuitive to use. Furthermore, it kept closing on me so that made it harder to use. I am going to continue to explore it and report back on it later.

## Tuesday, January 27, 2015

### Technology and evaluations

Up until today, I did not realize how heavily into technology we now are. I had my preconference and the principal asked for an indepth lesson plan with objective, etc. He is the first principal to ask for one so one of the other teachers sent me a copy of her lesson plan via e-mail so I could use it for my lesson plan. After I turned in the hard copy, he asked me for an electronic copy for him because the hard copy would be part of my file. In side the lesson I have the students using the iPads to read QR codes with the warm-ups, they will be able to search for a leap second (yes it does exist.) as part of the warm-up. They will be using the ipads to write down information before putting it on their papers so they are correct and I will have the guided practice on my smart board. Although I do not use an app for behavior, I know many other teachers who do record behavior.

When I started teaching, we still had to request the films from the media center and have a projector to show the film on during class. Usually, we had a student who knew what to do if the film studdered. Now I just do a search on the web and show the video the same day or the next day. I can find worksheets, explanations, step by step instructions and so many more resources than I ever had but it also means they expect me to use the technology in my day to day teaching. So I have to make sure that whatever technology I choose to use is enhancing the learning experience and not there because I have to use technology.

I am on the committee whose job it is to rewrite the evaluation and I think we need to stick a component in that is strictly designed to look at the integration of technology even if it is just using a smartboard.

When I started teaching, we still had to request the films from the media center and have a projector to show the film on during class. Usually, we had a student who knew what to do if the film studdered. Now I just do a search on the web and show the video the same day or the next day. I can find worksheets, explanations, step by step instructions and so many more resources than I ever had but it also means they expect me to use the technology in my day to day teaching. So I have to make sure that whatever technology I choose to use is enhancing the learning experience and not there because I have to use technology.

I am on the committee whose job it is to rewrite the evaluation and I think we need to stick a component in that is strictly designed to look at the integration of technology even if it is just using a smartboard.

## Friday, January 23, 2015

### Part 3 on Math 42 and warm-ups.

Today I tried the calculator section with both Algebra II and Pre-algebra.

In pre-algebra, I had students type in the expressions under similar terms and it showed them the answer once all the terms were combined. They went to the combining tab and had them write down the work so they could see what was happening. Next week I will have them take a quiz on the material to see if this helped them. Many of those students struggle with math and have trouble figuring out what to do next. I decided that I'll put some of these problems as part of the homework so they get additional practice. The students loved it and the ones who struggled completed several problems without getting frustrated.

Later in the day, I had my Algebra II students use the same app but with quadratic equations checked. You can put in problems with an i and the answer is nice with the i. In addition, it will take the square root but i shows up there as the square root of -1 with an actual square root sign. This app will make it go faster for me when I need answers for their homework. I try to put answers in the form of a QR code.

I just started using my warm-up to pre-teach material in advance of the regular class time so I can build a solid base. I often also use those same problems as review for other classes and practice for others. So between homework and warm-ups, my students are being exposed to a variety of materials. I hope this helps them retain the material better for longer periods of time.

In pre-algebra, I had students type in the expressions under similar terms and it showed them the answer once all the terms were combined. They went to the combining tab and had them write down the work so they could see what was happening. Next week I will have them take a quiz on the material to see if this helped them. Many of those students struggle with math and have trouble figuring out what to do next. I decided that I'll put some of these problems as part of the homework so they get additional practice. The students loved it and the ones who struggled completed several problems without getting frustrated.

Later in the day, I had my Algebra II students use the same app but with quadratic equations checked. You can put in problems with an i and the answer is nice with the i. In addition, it will take the square root but i shows up there as the square root of -1 with an actual square root sign. This app will make it go faster for me when I need answers for their homework. I try to put answers in the form of a QR code.

I just started using my warm-up to pre-teach material in advance of the regular class time so I can build a solid base. I often also use those same problems as review for other classes and practice for others. So between homework and warm-ups, my students are being exposed to a variety of materials. I hope this helps them retain the material better for longer periods of time.

## Thursday, January 22, 2015

### Math 42 app and IXL

My Algebra II class is currently learning to factor and graph quadratics. With the new common core standards and the increase of technology use in everyday life, I have to decide what part of the material should be taught. In regard to quadratics, I have settled on factoring the standard form of a quadratic, imaginary numbers, finding the vertex equation and the quadratic formula because that is really all they need to know to work with quadratics. I do not even teach completing the square or vertex forms because most of the time, I can have students just graph the equation or use the quadratic formula to find roots.

I had my two T.A's try the training part of the Math 42 app and they struggled with it because they did not know the vertex form or even how to complete the square. This lead me to the though "Are apps keeping pace with what do students really need to know to succeed in today's society. They can download apps to their phones for use. My mother remembers when the computer at work took a whole floor and it was the latest. I had to learn all this because we did not have access to calculators or apps on digital devices. I had to know so much so I could graph equations.

I find that IXL has the testing part that allows me choices so I can decide if I only want my Algebra II class to factor or work complete the square. I can even have my Algebra I class take a quiz focused on the slope-intercept form or point-slope form

I think the Math 42 app will be better as an app to help reinforce learning.

I had my two T.A's try the training part of the Math 42 app and they struggled with it because they did not know the vertex form or even how to complete the square. This lead me to the though "Are apps keeping pace with what do students really need to know to succeed in today's society. They can download apps to their phones for use. My mother remembers when the computer at work took a whole floor and it was the latest. I had to learn all this because we did not have access to calculators or apps on digital devices. I had to know so much so I could graph equations.

I find that IXL has the testing part that allows me choices so I can decide if I only want my Algebra II class to factor or work complete the square. I can even have my Algebra I class take a quiz focused on the slope-intercept form or point-slope form

I think the Math 42 app will be better as an app to help reinforce learning.

## Wednesday, January 21, 2015

### Math 42 app

Math 42 app has two modes. The first is how to solve your own equations while the second is using it to practice various facets of math.

With in the solving your own equations, you can choose linear, quadratic, etc for this to solve. I used x^2 + 3x +2 and although it came up with 1 and 2 as the factors, it showed solving it using the completing the square method rather than straight factoring. It does have a nice help button that gives you answers to most standard questions regarding use of the program.

First thing I did was try a simple combine like terms expression.

The app gives the user numerous choices on which step to look at. The student can look at the answer, how to combine like terms etc. So a student can learn by looking and by following the steps.

Furthermore, it allows students to solve linear, quadratic, derivatives, etc. This is a nice way to have students check their work.

Further more, if you have the student click on the graduation cap, you are taken to the testing portion of the app.

Students have a choice of training, test or other and its like a standardized test with multiple choices. You can choose what type of math you want to prctice. This app serves a double need in that it provides assessment and helps students learn to do problems so they can check as they go.

Unfortunately, it will sometimes choose a method of solving that I would not personally choose, otherwise it does provide a nice app for ongoing assessment.

With in the solving your own equations, you can choose linear, quadratic, etc for this to solve. I used x^2 + 3x +2 and although it came up with 1 and 2 as the factors, it showed solving it using the completing the square method rather than straight factoring. It does have a nice help button that gives you answers to most standard questions regarding use of the program.

First thing I did was try a simple combine like terms expression.

The app gives the user numerous choices on which step to look at. The student can look at the answer, how to combine like terms etc. So a student can learn by looking and by following the steps.

Furthermore, it allows students to solve linear, quadratic, derivatives, etc. This is a nice way to have students check their work.

Further more, if you have the student click on the graduation cap, you are taken to the testing portion of the app.

Students have a choice of training, test or other and its like a standardized test with multiple choices. You can choose what type of math you want to prctice. This app serves a double need in that it provides assessment and helps students learn to do problems so they can check as they go.

Unfortunately, it will sometimes choose a method of solving that I would not personally choose, otherwise it does provide a nice app for ongoing assessment.

## Tuesday, January 20, 2015

### Working in scaffolding.

As I add different types of knowledge questions to the warm up and standardized test, I am discovering student weakness. In my college prep class, one of my students admitted she has difficulty in using fractions. Another who is on their second time through Algebra one said he had no idea how to do a problem that required him to subtract one trinomial from another. Even some of my students have trouble remembering topics from one week to another. I think beginning next week, I am going to try to carve additional practice time within the classroom so students can work on areas they are weak in. I need to set up something in schoology or edmodo. so students can check for what I need them to work on so that I don't have to use valuable time telling them individually.

I don't spend enough time helping to shore up the weaknesses they have and that seems to get left by the wayside when I am planning things for my class. It always seems like I have one more thing to do.

As I am writing this I realized, I should give my students a test right now to identify the areas they need the scaffolding in. I have a paper copy of a placement test but I need to investigate if there is an online one that goes with the books I have so I can just send students there rather than my having to type it into the computer. I need to find a variety assessments so I can focus more on helping students have a better foundation in math.

I don't spend enough time helping to shore up the weaknesses they have and that seems to get left by the wayside when I am planning things for my class. It always seems like I have one more thing to do.

As I am writing this I realized, I should give my students a test right now to identify the areas they need the scaffolding in. I have a paper copy of a placement test but I need to investigate if there is an online one that goes with the books I have so I can just send students there rather than my having to type it into the computer. I need to find a variety assessments so I can focus more on helping students have a better foundation in math.

## Monday, January 19, 2015

### Building background knowledge.

As a math teacher I have always struggled with helping students build background knowledge especially those who skated through K to 8 by virtue of social promotion. I know, I know, "we don't have social promotions but most school districts are still reluctant to hold students back, especially if the student is older than the others in his or her class. This creates problems for the high school math teacher in that the students lack the necessary foundation to do well. I know I do not have time to differentiate the way I'm supposed to nor am i always able to scaffold the way I should. Due to living in a very rural community, I cannot plan a fully flipped classroom and expect my students to watch a video at home so they are prepared for the next day. I could post videos on the school wiki but not everyone has unlimited data plans and thus may not be able to download and watch the videos. Some times we run into the unreliability of the internet.

So over the past few weeks, I've been playing with using apps to help build or rebuild the foundation my students should have. Today, I had my Geometry students use constructions lite to help build perpendicular bisectors. What is nice is they could watch a demonstration or they could slow the demonstration down to step by step so they could watch each step and think about it before they moved on. After the demo, they practiced building a perpendicular bisector. One of the kids put in a perpendicular line and showed me he was done. I was able to point out that he had not followed directions due to no "pencil" marks. The next step after they practice both the perpendicular and angle bisectors is to apply these to actual triangles. I need to play around with it to see if they can put in a triangle before they add the bisectors.

So over the past few weeks, I've been playing with using apps to help build or rebuild the foundation my students should have. Today, I had my Geometry students use constructions lite to help build perpendicular bisectors. What is nice is they could watch a demonstration or they could slow the demonstration down to step by step so they could watch each step and think about it before they moved on. After the demo, they practiced building a perpendicular bisector. One of the kids put in a perpendicular line and showed me he was done. I was able to point out that he had not followed directions due to no "pencil" marks. The next step after they practice both the perpendicular and angle bisectors is to apply these to actual triangles. I need to play around with it to see if they can put in a triangle before they add the bisectors.

## Tuesday, January 13, 2015

### 7th grade math learning games

This is a nice little free app that can be used in the high school to scaffold struggling learners. I used it in my Geometry class. I had them work with the Ratios and proportions

then I had them choose the compute ratios.

The students had trouble with finding fractions of a ratio such as you have 5 gallons of milk and each container holds 1/5th of a quart, how many containers do you need. If you are wrong, the app tells you the correct answer but it does not show you how to get the correct answer.

This does tell students how they are doing overall and it does have a limit of questions that each student can do every day. I became aware of the limitation the first time I tried the app.

Over it is a good practice app.

then I had them choose the compute ratios.

The students had trouble with finding fractions of a ratio such as you have 5 gallons of milk and each container holds 1/5th of a quart, how many containers do you need. If you are wrong, the app tells you the correct answer but it does not show you how to get the correct answer.

This does tell students how they are doing overall and it does have a limit of questions that each student can do every day. I became aware of the limitation the first time I tried the app.

Over it is a good practice app.

## Friday, January 9, 2015

### Graphing and calculator apps.

I've learned that I need at least three different graphing or calculator apps on my ipads so my students can select the app most appropriate to the job they are doing.

Free graph calc is a free graphing app that has a calculator, graphing tab and a table. This one allows students to graph an equation and read numbers off a table so they can find important information. I find this one is good instead of say a TI hand calculator.

Desmos is nice for if a student just needs to graph and only needs to identify the vertex or zeros. This app allows them to touch a point and see the actual coordinate. My algebra 2 students are using Desmos to determine the zeros, vertex and axis of symmetry. So far they have not discovered a way to use a table on that one.

Finally, in my college prep math class, we just started working with logs and properties of logs. Even today many of the calculator apps will not process a log with any base other than 10 and you still need to utilize the change of base formula. I discovered that my script calculator will allow you to do a log with a base of 2 or 3 or any other base and get an answer without having to utilize the change of base formula. I am going to have my students check their work after they use the change of base formula to find an answer.

Free graph calc is a free graphing app that has a calculator, graphing tab and a table. This one allows students to graph an equation and read numbers off a table so they can find important information. I find this one is good instead of say a TI hand calculator.

Desmos is nice for if a student just needs to graph and only needs to identify the vertex or zeros. This app allows them to touch a point and see the actual coordinate. My algebra 2 students are using Desmos to determine the zeros, vertex and axis of symmetry. So far they have not discovered a way to use a table on that one.

Finally, in my college prep math class, we just started working with logs and properties of logs. Even today many of the calculator apps will not process a log with any base other than 10 and you still need to utilize the change of base formula. I discovered that my script calculator will allow you to do a log with a base of 2 or 3 or any other base and get an answer without having to utilize the change of base formula. I am going to have my students check their work after they use the change of base formula to find an answer.

## Thursday, January 8, 2015

### Fraction Basics and more on lion grapher.

Today, I had students check their math work by using the point mode for lion grapher. Today students were finding the slope from two points. After they completed the first four problems I had them go to lion grapher and use the point mode to check their work.

In this mode, they input the two coordinates and it graphs a line from one point to the other and expresses the answer in the slope intercept form. I had the students read the equation to check to make sure the two slopes were the same. Tomorrow, I will have them do this again to check work as I am hoping to create a connection between the idea of the slope formula and both the point slope and slope intercept equations.

My pre-algebra class is still struggling with fractions so I had them go to fraction basics, a free app, that has videos with examples so they can watch the videos independently.

I like that they have the lesson and a separate topic for examples. If you click on say equivalent fractions, it has a 4 min introductory video. The next topic is examining fractions visually by multiplication, followed by the reasoning behind equivalent fractions, then a section on can we get equivalent fraction by division and finally, can we get equivalent fractions by addition or subtraction.

What is nice is that it has several videos on each topic showing students how to do each part and they can listen to the video at any time and go at their own speed. I used it today and the students started with dividing fractions.

This particular class is a combined pre-algebra and algebra class. I think I am going to have my pre-algebra work on this app while I give the main lesson to the algebra class so they get the scaffolding they need and be engaged in learning. This allows them to work independently.

In this mode, they input the two coordinates and it graphs a line from one point to the other and expresses the answer in the slope intercept form. I had the students read the equation to check to make sure the two slopes were the same. Tomorrow, I will have them do this again to check work as I am hoping to create a connection between the idea of the slope formula and both the point slope and slope intercept equations.

My pre-algebra class is still struggling with fractions so I had them go to fraction basics, a free app, that has videos with examples so they can watch the videos independently.

I like that they have the lesson and a separate topic for examples. If you click on say equivalent fractions, it has a 4 min introductory video. The next topic is examining fractions visually by multiplication, followed by the reasoning behind equivalent fractions, then a section on can we get equivalent fraction by division and finally, can we get equivalent fractions by addition or subtraction.

What is nice is that it has several videos on each topic showing students how to do each part and they can listen to the video at any time and go at their own speed. I used it today and the students started with dividing fractions.

This particular class is a combined pre-algebra and algebra class. I think I am going to have my pre-algebra work on this app while I give the main lesson to the algebra class so they get the scaffolding they need and be engaged in learning. This allows them to work independently.

## Wednesday, January 7, 2015

### Back from holidays with lion grapher

As my algebra I class has just gotten back from holidays, I am reviewing how to find the slope. Yesterday, I went through a smartboard presentation on the three ways of finding slope. Today I had the students go to lion grapher to do the lion mode.

In this mode, they are given the formula as y = blank/blank + b up in the corner. The students are expected to find b and then figure out the change from the y intercept to the lions head and write it as rise over run. Once they have filled out the y/x values for slope, they can then hit the graph button and if the equation of the line is correct, then it gives them points and a new position of the lions head. The only issue that may cause a problem is that it is timed and when students are first learning to use this program, they may only get one or two problems completed before they run out of time.

I see this mode as a nice way to head students towards learning to read the slope-intercept form. Since slope intercept form is the next topic in this class, I feel that this app will help prepare them for the topic and make the transition easier.

I know I've spoken of this app before but this is the first time I've used it in my classroom.

In this mode, they are given the formula as y = blank/blank + b up in the corner. The students are expected to find b and then figure out the change from the y intercept to the lions head and write it as rise over run. Once they have filled out the y/x values for slope, they can then hit the graph button and if the equation of the line is correct, then it gives them points and a new position of the lions head. The only issue that may cause a problem is that it is timed and when students are first learning to use this program, they may only get one or two problems completed before they run out of time.

I see this mode as a nice way to head students towards learning to read the slope-intercept form. Since slope intercept form is the next topic in this class, I feel that this app will help prepare them for the topic and make the transition easier.

I know I've spoken of this app before but this is the first time I've used it in my classroom.

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