I've used Excel for many, many years and know a whole lot about ins and outs of the program. I'm also an expert on Googling, and can find answers to a whole lot of problems within seconds. Interestingly, these two different worlds often combine and help me to understand the limitations of a software like Excel for large data sets.
This problem came up a few times in my analysis of PCGS and the population report of US pennies. At first, I tried to collect the data from 1792 to present, but Excel was running extremely slowly and wouldn't even begin to graph or analyze trends from roughly 20,000 data points. I would run into a variety of errors, and so decided to cut down my data to just the wheat pennies in the PCGS population report of their penny grading. As we will see, this wasn't enough of a reduction. I still have around 3,000 data points from 400 subjects, and Excel maxes out with it's graphical analysis around 150 data points.
My first question dealt with the correlation between the mintage number and the number of pennies graded. The most rare coins are obviously the most sought after and graded percentage wise, but I wondered if there was a general relationship between these two variables. As you can see if you explore my data set and the visuals at the bottom of the document linked below, as a general rule, roughly 5,000,000 more pennies minted means that on average, around 100 more pennies are graded by PCGS.
Another question that I had was relating the mintage number to the year. I assumed that this was fairly highly correlated, but was also aware that many years, including 1921 and 1936 there were fewer pennies made than even 1909, so I wondered if the general trend was consistent. As can be seen in the graph and correlation calculation at the bottom of the document, roughly 53% of the variation in mintage can be explained by the year. Which is still pretty significant.
A final question that I explored was the relationship between the year and the total number of pennies graded by PCGS in that year. The answer was fairly surprising, there was no direct relationship (up to 10% variation) between these variables. That is to say, just because a penny is older than another doesn't necessarily mean it has more or less chance of being graded by PCGS. These are fairly independent variables. However, showing this graphically in Excel is impossible, as showing this trend would require roughly 400 different data points on either axis, which is impossible according to the variety of Excel boards that I read.
Anyway, this has been interesting. I much prefer using other software to analyze large data, but for now all that I have available is Excel. Maybe someday I'll do this analysis again in a more conducive environment for large data sets.
Here is a link to my Excel Document. Note that some functionality may be broken if you are not using an updated version or have the statistical toolbar enabled/installed.
https://drive.google.com/open?id=1axGsr4hjR9xPq15kpbDXviVYKU6d2jQU
Tuesday, April 16, 2019
Monday, April 15, 2019
Conference Connections
This past week was General Conference. This is a twice yearly event where we as members of the Church of Jesus Christ of Latter-Day Saints have the opportunity to listen to our prophet and apostles (and other leaders) speak about spiritual topics. This often includes teaching about Christ's life, how we can become more like Him, invitations to repent, and many more spiritual ideas.
Within one of my classes, we decided to all watch, read, listen to, or participate in General Conference in some way and specifically focus on how the teachings of the Gospel of Jesus Christ apply to our future math classrooms. This was a very interesting focus, and I feel like the principles that we pulled are applicable to all math teachers, not just those who may be members of our faith.
There is a problem, though. Conference was a total of 10 hours, and full of connections to education and technology. I'm going to spend the next few months going over all the talks again and again, and picking a single talk to focus on is quite difficult to do. This is part of the reason why this reflection is so late, I had a difficult time narrowing my focus to something that would fit in a single blog post.
I chose to focus on one single talk, Elder Bednar's talk Preparing to Obtain Every Needful Thing. Elder David A Bednar is actually an educator by profession, and acted as a professor, an associate dean, and as president of Rick's College. It's not surprising, then that there are many, many connections to education to be found in his talks. This talk is no exception. In this post, I will go through some of my favorite quotes that I found and relate them directly to our math classrooms.
"We should not expect the Church as an organization to teach or tell us everything we need to know and do.... Rather, our personal responsibility is to learn what we should learn..."
This directly relates to teaching our students. If our students expect us to teach and tell them everything that they need to know and do, they will never actually engage in mathematics. We have to instead help them to engage in the mathematics and take personal responsibility to learn. We will still help and guide and direct our students in their learning process, but if we can help them take responsibility they will be much more successful.
As a similar note, students can't just learn from a single source. If they learn all their mathematics from their teachers they will lose the ability to do math as soon as they forget the teacher. If they learn all their mathematics from a textbook they will lose the math once they set down their book. If a student learns all their mathematics from exploration alone they won't get very far (it's taken us thousands of years to get where we are mathematically, we can't expect our students to get there in a few years by themselves). If students rely too heavily on technology, they will lose the ability to do math when their phones are taken away. Students need to have many sources and internalize mathematics from all the rich opportunities they have available to them.
"If all you or I know about Jesus Christ and His restored gospel is what other people teach or tell us, then the foundation of our testimony of Him and His glorious latter-day work is built upon sand. We cannot rely exclusively upon or borrow gospel light and knowledge from other people—even those whom we love and trust."
This is in continuation of the previous idea, if our students only know what we tell them about mathematics, they will be on extremely shaky ground. It is important that we teach and help our students build their own understanding rather than relying completely on ours. It is important that our students can trust that we know the mathematics, but if that is all that they will ever have they are going to fall and their knowledge will erode away over time (just as a building built on sand would do). Students who build their own ideas of mathematics and can prove or justify them by themselves will keep these foundational experiences and truly engage in mathematical processes.
"A rich reservoir of resources exists in print, audio, video, and other formats to help us learn about [temple ordinances]..."
While this quote was specifically about the temple, this is very true for our math students. They have a huge variety of resources to learn from, including all the dynamic software and other technology we talk so much about. If we are familiar with these resources, we can point our students in the right direction so they can also have a taste of all the technology available for mathematical exploration.
Well, that's about enough for my perspective. If it wasn't the end of the semester and finals coming up, I might have explored a few more talks, but hopefully that is sufficient for now. And maybe you, my fine reader, can explore and dive into some other talks.
Anyway, a little about the discussion that I had with my fellow educators about General Conference: We focused a little more on the technological aspect of the conference. Something that Elder Cook said is that we should make technology "a servant instead of a distraction or, even worse, a master." This definitely applies to our classrooms. If technology is a distraction or a master of our mathematics we have failed as a teacher. This is true whether the technology is a distraction to us or to our students. We must use the technology to our benefit, not as a deterrent to learning.
There is a paper by Vince Geiger that discusses the use of technology in a math classroom that is very similar in the wording. Basically, Geiger describes a series of levels of using technology in the math classroom, beginning from the least useful to most: Technology as Master, Technology as Servant, Technology as Partner, Technology as an Extension of Self. We discussed this article and tried to determine where we were with various technologies. As a whole, we came to the conclusion that with most technologies, we are definitely to the point of servant, and hopefully to partner and as an extension of self. As teachers, we need to be familiar enough with the technology to be at a place where we can help our students not be servants to the technology but be able to use it to explore and further understanding.
We then furthered our discussion a little bit about how to get technologies in our classroom. We had the perspective of a professor who taught for many years in public schools before transitioning to teaching in college, and that was very interesting. He talked about the many types of grants that we as teachers can apply for, how we could get new technology gradually, how to help parents and administration be on our side, and how to show the benefits of new technology. Overall this was very interesting, and very useful. If in our future classrooms we have no technology we are actually slaves to that lack of technology, which is almost as bad as being slaves to the technology.
I chose to focus on one single talk, Elder Bednar's talk Preparing to Obtain Every Needful Thing. Elder David A Bednar is actually an educator by profession, and acted as a professor, an associate dean, and as president of Rick's College. It's not surprising, then that there are many, many connections to education to be found in his talks. This talk is no exception. In this post, I will go through some of my favorite quotes that I found and relate them directly to our math classrooms.
"We should not expect the Church as an organization to teach or tell us everything we need to know and do.... Rather, our personal responsibility is to learn what we should learn..."
This directly relates to teaching our students. If our students expect us to teach and tell them everything that they need to know and do, they will never actually engage in mathematics. We have to instead help them to engage in the mathematics and take personal responsibility to learn. We will still help and guide and direct our students in their learning process, but if we can help them take responsibility they will be much more successful.
As a similar note, students can't just learn from a single source. If they learn all their mathematics from their teachers they will lose the ability to do math as soon as they forget the teacher. If they learn all their mathematics from a textbook they will lose the math once they set down their book. If a student learns all their mathematics from exploration alone they won't get very far (it's taken us thousands of years to get where we are mathematically, we can't expect our students to get there in a few years by themselves). If students rely too heavily on technology, they will lose the ability to do math when their phones are taken away. Students need to have many sources and internalize mathematics from all the rich opportunities they have available to them.
"If all you or I know about Jesus Christ and His restored gospel is what other people teach or tell us, then the foundation of our testimony of Him and His glorious latter-day work is built upon sand. We cannot rely exclusively upon or borrow gospel light and knowledge from other people—even those whom we love and trust."
This is in continuation of the previous idea, if our students only know what we tell them about mathematics, they will be on extremely shaky ground. It is important that we teach and help our students build their own understanding rather than relying completely on ours. It is important that our students can trust that we know the mathematics, but if that is all that they will ever have they are going to fall and their knowledge will erode away over time (just as a building built on sand would do). Students who build their own ideas of mathematics and can prove or justify them by themselves will keep these foundational experiences and truly engage in mathematical processes.
"A rich reservoir of resources exists in print, audio, video, and other formats to help us learn about [temple ordinances]..."
While this quote was specifically about the temple, this is very true for our math students. They have a huge variety of resources to learn from, including all the dynamic software and other technology we talk so much about. If we are familiar with these resources, we can point our students in the right direction so they can also have a taste of all the technology available for mathematical exploration.
Well, that's about enough for my perspective. If it wasn't the end of the semester and finals coming up, I might have explored a few more talks, but hopefully that is sufficient for now. And maybe you, my fine reader, can explore and dive into some other talks.
Anyway, a little about the discussion that I had with my fellow educators about General Conference: We focused a little more on the technological aspect of the conference. Something that Elder Cook said is that we should make technology "a servant instead of a distraction or, even worse, a master." This definitely applies to our classrooms. If technology is a distraction or a master of our mathematics we have failed as a teacher. This is true whether the technology is a distraction to us or to our students. We must use the technology to our benefit, not as a deterrent to learning.
There is a paper by Vince Geiger that discusses the use of technology in a math classroom that is very similar in the wording. Basically, Geiger describes a series of levels of using technology in the math classroom, beginning from the least useful to most: Technology as Master, Technology as Servant, Technology as Partner, Technology as an Extension of Self. We discussed this article and tried to determine where we were with various technologies. As a whole, we came to the conclusion that with most technologies, we are definitely to the point of servant, and hopefully to partner and as an extension of self. As teachers, we need to be familiar enough with the technology to be at a place where we can help our students not be servants to the technology but be able to use it to explore and further understanding.
We then furthered our discussion a little bit about how to get technologies in our classroom. We had the perspective of a professor who taught for many years in public schools before transitioning to teaching in college, and that was very interesting. He talked about the many types of grants that we as teachers can apply for, how we could get new technology gradually, how to help parents and administration be on our side, and how to show the benefits of new technology. Overall this was very interesting, and very useful. If in our future classrooms we have no technology we are actually slaves to that lack of technology, which is almost as bad as being slaves to the technology.
Tuesday, April 9, 2019
Compositions of Transformations
Here is a link to a gsp file describing the composition of transformations:
https://drive.google.com/open?id=1lxVtvLpW3ZPYjupMBpPo-0mSLqwo4D8I
https://drive.google.com/open?id=1lxVtvLpW3ZPYjupMBpPo-0mSLqwo4D8I
Thursday, March 28, 2019
Parabolas for days
Here is an interesting exploration about parabolas. This involves a geometric and analytic dynamic representation of a parabola, including analysis of the directrix, focus, line of reflection, and vertex. Another very interesting piece of this exploration is how the vertex changes as a, b, and c vary from our general equation y = ax^2 + bx + c.
This is a gsp file, so in order to open this you must have Geometer Sketch Pad. Sorry for everyone out there who doesn't.
Here is the file. Have fun exploring!
Wednesday, March 27, 2019
Secondary Student's Understanding of Geometric Transformations
Second day in a row here for the blog, today we will be discussing an article found in the NCTM publication from March 2004. This is quite a few years ago, in fact, this article is even older than some current secondary students! Which is kind of insane, but hopefully the information given in the article is still valid and helpful. The article can be found at the following link. Thankfully, this link doesn't require you to have any special access, anyone should be able to follow this! Good news!
Summary:
This article, written by Karen Hollebrands, describes a study of her high school student's understandings of the rigid motion transformations (translations, reflections, and rotations). The article then goes through each of these transformations and students understanding of these transformations. In short, students understood that reflections changed the orientation of the shapes but didn't completely understand how the line of reflection determined a unique image from a preimage. Students seemed to understand how a rotation works, but missed that a shape can be rotated around a single point and how that works. In her study, students understood that shapes can be translated but were unsure of how to define a unique image from the preimage. Overall, it seemed as though students understood that these three transformation maintained size, shapes, and angles but struggled to determine exactly how they were uniquely defined from the information given.
As I discussed this with a few of my peers, we found a few problems with this study. First of all, we found that while Karen Hollenbrands claimed that she was testing her students' understanding of the transformations she may not have actually been testing that, but testing their knowledge of notation and things that she had yet to teach. While it is a good idea to try to understand where students are in their understanding before we teach, we have to be sure that we are accurately representing their true understandings. One of the major issues we brought up was that when asking students to translate a figure they were given a translation vector, something that students had never seen before. It seemed that she was actually testing her students' knowledge of vectors, not of translations.
However, our discussion wasn't only about the faults that we found with the article. We discussed how the article suggested that students be given access to Geometer's Sketch Pad in order to understand transformations. This tool allows students to try a huge variety of different transformations in a short amount of time, allowing them to experiment and understand what the relationship between an image and preimage is for any given translation. It also helps students understand what is necessary for any given translation. We then spent some time discussing what is necessary to define a translation and what our students might believe about these transformations.
Critique:
The class discussion of this article fairly accurately sums up my thoughts on the article. I feel that Karen Hollenbrands didn't accurately portray her student's thinking with what she tested. It seems that the ideas and concepts of testing student understanding could be extremely useful but that the methodology of testing understanding would need to be improved in order to accurately represent student understanding. I do feel like Geometer's Sketch Pad is an extremely useful tool, not just for what has been discussed in previous blog posts, but also for transformational geometry. Students can use the dynamic capabilities of the software to represent a variety of transformations and really understand how a single change in the "givens" of a transformation can change the result. The article and discussion following the reading of the article really drew that out and helped me to understand the many uses that a dynamic software can have for helping student understanding.
Connections:
In my mind, students understanding that these 3 transformations are rigid motion transformations is an extremely important piece of student knowledge and the simple part of teaching about lines of reflection, centers of rotation, and how to represent translations is not as important initially. If students understand these, I feel that in my practice as a teacher I will be able to solidify and bring together all these ideas into what is mathematical practice.
Something that is worrisome to me is that there are many extremely useful tools that I can use in my future classroom, but I need to figure out which ones to use and figure out a way to have them all in my classroom. Geometer's Sketch Pad can be an expensive tool, and if I need to have this and a variety of other programs on a classroom set of computers that cost could add up quickly. I don't know how to petition administrators to purchase a variety of softwares or other technology to further learning, and I don't know how to learn exactly how to learn that either.
Summary:
This article, written by Karen Hollebrands, describes a study of her high school student's understandings of the rigid motion transformations (translations, reflections, and rotations). The article then goes through each of these transformations and students understanding of these transformations. In short, students understood that reflections changed the orientation of the shapes but didn't completely understand how the line of reflection determined a unique image from a preimage. Students seemed to understand how a rotation works, but missed that a shape can be rotated around a single point and how that works. In her study, students understood that shapes can be translated but were unsure of how to define a unique image from the preimage. Overall, it seemed as though students understood that these three transformation maintained size, shapes, and angles but struggled to determine exactly how they were uniquely defined from the information given.
As I discussed this with a few of my peers, we found a few problems with this study. First of all, we found that while Karen Hollenbrands claimed that she was testing her students' understanding of the transformations she may not have actually been testing that, but testing their knowledge of notation and things that she had yet to teach. While it is a good idea to try to understand where students are in their understanding before we teach, we have to be sure that we are accurately representing their true understandings. One of the major issues we brought up was that when asking students to translate a figure they were given a translation vector, something that students had never seen before. It seemed that she was actually testing her students' knowledge of vectors, not of translations.
However, our discussion wasn't only about the faults that we found with the article. We discussed how the article suggested that students be given access to Geometer's Sketch Pad in order to understand transformations. This tool allows students to try a huge variety of different transformations in a short amount of time, allowing them to experiment and understand what the relationship between an image and preimage is for any given translation. It also helps students understand what is necessary for any given translation. We then spent some time discussing what is necessary to define a translation and what our students might believe about these transformations.
Critique:
The class discussion of this article fairly accurately sums up my thoughts on the article. I feel that Karen Hollenbrands didn't accurately portray her student's thinking with what she tested. It seems that the ideas and concepts of testing student understanding could be extremely useful but that the methodology of testing understanding would need to be improved in order to accurately represent student understanding. I do feel like Geometer's Sketch Pad is an extremely useful tool, not just for what has been discussed in previous blog posts, but also for transformational geometry. Students can use the dynamic capabilities of the software to represent a variety of transformations and really understand how a single change in the "givens" of a transformation can change the result. The article and discussion following the reading of the article really drew that out and helped me to understand the many uses that a dynamic software can have for helping student understanding.
Connections:
In my mind, students understanding that these 3 transformations are rigid motion transformations is an extremely important piece of student knowledge and the simple part of teaching about lines of reflection, centers of rotation, and how to represent translations is not as important initially. If students understand these, I feel that in my practice as a teacher I will be able to solidify and bring together all these ideas into what is mathematical practice.
Something that is worrisome to me is that there are many extremely useful tools that I can use in my future classroom, but I need to figure out which ones to use and figure out a way to have them all in my classroom. Geometer's Sketch Pad can be an expensive tool, and if I need to have this and a variety of other programs on a classroom set of computers that cost could add up quickly. I don't know how to petition administrators to purchase a variety of softwares or other technology to further learning, and I don't know how to learn exactly how to learn that either.
Tuesday, March 26, 2019
Creating Quadrilaterals from Existing Quadrilaterals
So here goes. The next few days are going to see more posts here than there have been for a few weeks. Life has been crazy and full of homework, and I've finally found the time to put together a few more posts.
Today I'd like to discuss an article titled "Creating Quadrilaterals from Quadrilaterals" that can be found here. It's an article written in 2016, but contains some interesting ideas about creatively implementing the Common Core curriculum using dynamic software.
Summary:
In this article, Wayne Nirode presents an interesting lesson that he designed around helping students explore a variety of student made conjectures about quadrilaterals. In essence, over the course of a few days, students created their own ways to make new quadrilaterals from existing quadrilaterals, observed how these new quadrilaterals were related to the old using dynamic geometric software, and finally attempting to prove these conjectures in a rigorous/semi-rigorous fashion. This created a very useful environment where students needed to use and develop vocabulary and proof skills in a creative and fun way. This activity exceeded the demands of the Common Core curriculum, but succeeded in helping students stay engaged in the mathematics and truly exploring.
As I discussed this article with a few of my peers we found some interesting points that Wayne Nirode didn't specifically pull out of the activity. Something that we found interesting was that this could be a fairly vulnerable activity as a teacher. In this activity, students were asked to create their own conjectures and really engage in mathematical research. The teacher provides scaffolding for the initial exploration with the three examples of how to create new quadrilaterals from an existing quadrilateral and asked the students to explore from there. In response, the students in the article created 150 unique constructions, allowing for a huge pool of mathematical conjectures and actual mathematical practice. When students come across these conjectures, they are extremely likely to struggle with the mathematics and may in fact be unable to prove using the tools they have. As teachers we have the duty to allow these students to struggle with the mathematics enough to promote understanding but not enough that they become discouraged. This can take a variety of different forms, and in my view is possibly the most difficult part about being a math teacher.
Critique:
One problem that I have with this activity is the amount of time that this activity requires. Students were given a few days in class to create their constructions, a few days to create conjectures about these, and a few more days to create and present their proofs. All in all, this seems as though it would take at least a week of daily classes in order to finish this activity. While this seems like quite a bit of time, students are extremely likely to come out of this activity with having an understanding of special quadrilaterals (squares, trapezoids, kites, etc) and have some practice with creating a variety of proofs and struggling with mathematics. However, it seems that if a teacher isn't careful with managing time and helping students stay on task a lot of time could be wasted.
As a group, we also brought to light an interesting dilemma about engaging students in mathematical discourse. Can we really engage all our students in true mathematical struggle? What would happen if one student becomes distracted and begins to distract others from the mathematics? How do we balance the need for exploration and the need for discipline in our mathematics students? These questions are very interesting and fall into the realm of classroom management. I don't have all/any answers for these, I'll leave these answers for another post/author.
Connections:
Something that really stuck out to me from this article is the usefulness and necessary aspect of dynamic geometric software for this exploration. It would be almost impossible to do a similar exploration without software, students would need to create hundreds of examples by hand, something that could be done in a few minutes using a computer. One of my biggest worries about having technology in my classroom is that students could easily be distracted and get lost in their Facebook feed rather being lost into the mathematics. This article and many others like it have helped me to understand the extreme benefit that technology can bring into a mathematics classroom, largely outweighing the potential disadvantages of technology.
I wonder if there are great advantages to having phones in class. I've largely seen phones as distractions in math classes, but at the same time I have a graphing calculator on my phone. That is extremely useful for me, but as a teacher I'm initially reluctant to give students free access to their phones in my classroom. I guess that's going to be a problem that I will need to address with my school and fellow teachers on what my expectations should be in my classroom.
Today I'd like to discuss an article titled "Creating Quadrilaterals from Quadrilaterals" that can be found here. It's an article written in 2016, but contains some interesting ideas about creatively implementing the Common Core curriculum using dynamic software.
Summary:
In this article, Wayne Nirode presents an interesting lesson that he designed around helping students explore a variety of student made conjectures about quadrilaterals. In essence, over the course of a few days, students created their own ways to make new quadrilaterals from existing quadrilaterals, observed how these new quadrilaterals were related to the old using dynamic geometric software, and finally attempting to prove these conjectures in a rigorous/semi-rigorous fashion. This created a very useful environment where students needed to use and develop vocabulary and proof skills in a creative and fun way. This activity exceeded the demands of the Common Core curriculum, but succeeded in helping students stay engaged in the mathematics and truly exploring.
As I discussed this article with a few of my peers we found some interesting points that Wayne Nirode didn't specifically pull out of the activity. Something that we found interesting was that this could be a fairly vulnerable activity as a teacher. In this activity, students were asked to create their own conjectures and really engage in mathematical research. The teacher provides scaffolding for the initial exploration with the three examples of how to create new quadrilaterals from an existing quadrilateral and asked the students to explore from there. In response, the students in the article created 150 unique constructions, allowing for a huge pool of mathematical conjectures and actual mathematical practice. When students come across these conjectures, they are extremely likely to struggle with the mathematics and may in fact be unable to prove using the tools they have. As teachers we have the duty to allow these students to struggle with the mathematics enough to promote understanding but not enough that they become discouraged. This can take a variety of different forms, and in my view is possibly the most difficult part about being a math teacher.
Critique:
One problem that I have with this activity is the amount of time that this activity requires. Students were given a few days in class to create their constructions, a few days to create conjectures about these, and a few more days to create and present their proofs. All in all, this seems as though it would take at least a week of daily classes in order to finish this activity. While this seems like quite a bit of time, students are extremely likely to come out of this activity with having an understanding of special quadrilaterals (squares, trapezoids, kites, etc) and have some practice with creating a variety of proofs and struggling with mathematics. However, it seems that if a teacher isn't careful with managing time and helping students stay on task a lot of time could be wasted.
As a group, we also brought to light an interesting dilemma about engaging students in mathematical discourse. Can we really engage all our students in true mathematical struggle? What would happen if one student becomes distracted and begins to distract others from the mathematics? How do we balance the need for exploration and the need for discipline in our mathematics students? These questions are very interesting and fall into the realm of classroom management. I don't have all/any answers for these, I'll leave these answers for another post/author.
Connections:
Something that really stuck out to me from this article is the usefulness and necessary aspect of dynamic geometric software for this exploration. It would be almost impossible to do a similar exploration without software, students would need to create hundreds of examples by hand, something that could be done in a few minutes using a computer. One of my biggest worries about having technology in my classroom is that students could easily be distracted and get lost in their Facebook feed rather being lost into the mathematics. This article and many others like it have helped me to understand the extreme benefit that technology can bring into a mathematics classroom, largely outweighing the potential disadvantages of technology.
I wonder if there are great advantages to having phones in class. I've largely seen phones as distractions in math classes, but at the same time I have a graphing calculator on my phone. That is extremely useful for me, but as a teacher I'm initially reluctant to give students free access to their phones in my classroom. I guess that's going to be a problem that I will need to address with my school and fellow teachers on what my expectations should be in my classroom.
Thursday, March 7, 2019
Geometer's Sketch Pad
It's been a while since my last post, and this is a pretty small post. Sorry to the one dedicated reader of my blog. There are going to be more posts in the near future.
I've recently been playing with Geometer's Sketch Pad. If you haven't ever played with it, I highly recommend it. It's been a lot of fun, even as I've run into some limitations of the software. But some of the most fun things that I've done is to create a bunch of constructions. Software like this allows the user to go through thousands of creations and dynamically view a construction in many, many ways. And if you make a single mistake (like I do often) you don't have to completely erase your entire drawing. Instead, just hit Ctrl Z and go back to having fun.
Anyway, here are a few of my most recent constructions in GSP. They are all created as tools, and are fairly cool. If you want to see how they were made, you can view the script view and walk through the entire construction.
Here is a link to a copy of my gsp file (you'll need GSP in order to view these, sadly).
https://drive.google.com/open?id=1r4mseSTA-rgLa3ez4TTFAXd6axeayZNG
I've recently been playing with Geometer's Sketch Pad. If you haven't ever played with it, I highly recommend it. It's been a lot of fun, even as I've run into some limitations of the software. But some of the most fun things that I've done is to create a bunch of constructions. Software like this allows the user to go through thousands of creations and dynamically view a construction in many, many ways. And if you make a single mistake (like I do often) you don't have to completely erase your entire drawing. Instead, just hit Ctrl Z and go back to having fun.
Anyway, here are a few of my most recent constructions in GSP. They are all created as tools, and are fairly cool. If you want to see how they were made, you can view the script view and walk through the entire construction.
Here is a link to a copy of my gsp file (you'll need GSP in order to view these, sadly).
https://drive.google.com/open?id=1r4mseSTA-rgLa3ez4TTFAXd6axeayZNG
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