Coevaluations

Solid Works and 3D printing

Well it was very obvious that this project was a challenge for us. Starting from the way of arranging the formulas, to integrating and adapting for 3D printing. We realized that it is not very clever to use scales specially when you’re using formulas with constant change (such as sine), it is better to work with real scales rather than proportions. We lived the complications of translating math to practical means but also realized how important it is the design for the materials and how practical it is to work with functions to understand dimensions or maybe even optimization with a different use. Overall, we tried to work together and help each other in what we could do best or maybe help the others understand the work better with its applications. Personally I think that this project made very obvious the way calculus contributes to industry, I can only imagine making a piece for a machine or product without the use of math, it would be a disaster! Math helps us define and control what we do, and I think this is of uttermost importance when applying it to industry or creation or planning or design or engineering or in other words, daily life. I think this is the answer to the question… ¿So when are we applying this in real life?

Volume calculations

The formula we used in order to calculate the aproximate volume of the piece printed was the one we saw on module 4 "volume by disks for rotation about the x-axis". Since it was an addition of three functions we treated them separately and integrated each one in the corresponding formula. 

So when calculating the first volume we encountered our first complication which was a natural logarithm squared but with a diferent argument as the ones seen in class. There were several ways to solve this problem, the first one was by "u" substitution and integration by parts, but also you could solve it by using integration by parts, then improper and proper fraction, these were topics seen in modules 5 and 6 in which we discussed integration techniques. The rest of the integrals were quite easy and almost made by an automatic process, by using trigonometry integration techiniques and "u" substitution. These complications were the same presented on the other process so you could take these in count for that process too. 

Geogebra and functions (design)

The geogebra first design 

 

Our idea was to try to keep it simple, we made a scale model of what we wanted to make (a jar). We decided to include some curves to make it resamble as most as posible to a jar. So you could say that we first made the image and then made the math fit in. Due to the extension and shape of the sine we decided that would be our middle function or the "body" of the jar. Then we realized that the logarithm could connect with a softer curve in order to create the base. Finally we added the polynomial to make the top, almost cup like to finish the vase. This looked very beautiful in scale but had many problems when we tried to adapt it to solidworks, speacially because the shape of the sine changes depending on the period. So even though we planned we had to change it all over again. 

The geogebra second design 

Taking as base the first design we modificated the original functions instead of thinking "scale-like". The first and very obvious change was the sine's period, and from that by trial and error fitted again the other functions. That meant that we had to re-do the whole integral process and calculus but it was easier to translate it to solid works and then to rotate it. 

New semester (Final)

Division

Module 3

Use of technological resources

Thanks to the use of online homework as well as the explanation offered by my math lab I've been able to clear a lot of my doubts, specially talking about the solving problems. Also it has helped me to see the things that I must review. In this case is more about the solving problems and rounding up decimals. But as you can see in the evidence of grades, I recovered after the 83 in the solving problems (mostly my mistakes were about decimals). Also it helped me practice for the mid-term quiz and partial. I actually like working with online homework because it's a very good practice to see what I do wrong and how I can make it right. 

 

Capacity to work with others

Part of our learning process is to understand the applications of all the theory we study. Therefore we gathered in teams and made some calculations (using all what we had been taught) in order to find some measures. I find this to be very useful and entertaining. It also taught me how to accept other points of view about how to solve. Sometimes I wanted to do very complicated things when they could've been solved rather in a much simpler way. 

Module 2

Capacity to work with others

The most important learnings we had this module were about the Basic and Reciprocal trigonometric ratios, and the special angles. Without the knowledge of those basic concepts, solving the next problems and understanding the other modules would be very difficult if not kind of impossible. 

I dedicated a lot of time to understand those concepts and to clear al my doubts about them so that when I had to work along my classmates I could properly contribute in teamwork to analyze problems and solve them. We helped each other and even though we solved the problems by ourselves we shared with the team how in order for everyone to understand. 

Autonomous learning

I know that we learn from mistakes and also that exams help us not only see our areas of opportunity but also how we overcame mistakes. I had a particular problem last semester with a problem of application of knowledge regarding angles and arc length, so by myself I dedicated to understand it and in the next exam I could solve it properly. 

Module 1

Critical thinking

At first instance this module was very easy, I seemed to understand how to do everything and once the mid-term quiz showed up. I had no trouble solving it. The problems were very simple and easy to solve. We were taught how to identify and properly name angles, to change from DMS to decimals and vice versa (by using a calculator), talking about changes we also saw the difference of degrees and radians and how to find its correspondent, we learned about reference angles, and coterminal angles (here we were also explained how to name quadrants, since they were relevant for the topics). 
So here is my evidence of the critical thinking being applied at the moment to solve the quiz. 

Correct use of mathematical language

Now, even though I could apply the concepts I've learned, I saw that I wasn't really able to accurately explain the process of what I was doing, specially when talking about the conversion of DMS to degrees with decimals and vice versa. That was put to test in the modular exam, where I saw my mistakes and had to re-check what I was doing so that next time I wouldn't make the same mistake. 

Capacity to work with others

Initial Reflection

With this e-portfolio I am hopping to be able to upload evidences that prove my work and learning I’ve had during this semester. To be honest, I also do it to comply with the tasks of my teacher (one of my main goals is to have a better average than last semester), therefore with this portfolio I hope to get a good grade. Still, it is not the only reason, it helps me track my learning process and to identify the topics I’ve had trouble with. I plan for this to be a place where I can expose my habits and achievements so that in a future it could be used as a guidance (made of evidences) for people who are interested in what I did in high school. In other words: a website that could help me open some doors for university.

My commitment with this portfolio is to upload at least three reflections (this is the first one), also at least two evidences for each module. I commit to choose the most representative works that might reflect my learning and therefore might be more helpful for identifying my areas of opportunity or my achievements.  I’ve had experience doing portfolios and they have proved to be very helpful, and I hope for this one to be helpful as well.

NEW SEMESTER

From this point on, we move to 4th semester. 

3rd Partial

Correct Use of Mathematical Language

Last partial I had problems with equations, this partial I have problems with word definitions. The mathematical concepts are easier to recognize in a practical way, but when I try to explain them in words I don't do a very good job. That is something I must study a lot, because some definitions are quite easy to understand but there are others that reacquire  a certain level of complexity to use the right words. I think its easier to define a circle than to define a Hyperbola in which you even have to imagine some elements in order to draw it.  

Here are my evidences and corrections:

3rd Partial

Collaborative Activity

During this partial we only had one collaborative activity in which we used the concepts of the two modules that we saw. 
In this collaborative activity we had to apply our knowledge in constructions of real life. We could choose from several ideas, (like to do a conic chair, a solar cooker, or a lamp) we chose to do the lamp. In the beginning we had a very crazy idea, and really cool, however as the due date came closer and all projects started to hit us (besides of the fact that I had a concert and a play) we had to adapt our idea to something much smaller. 
We did gave in the activity at the due time, but some elements were missing, although we had the idea our concept wasn't well applied.
Even though I did my share of the team, I feel I didn't involve enough in this activity. It could've been better if me and the other co-workers helped more Ana Isa at the time of building the lamp. 
At the moment of dividing the work we had some roles very clear, but Adrian wasn't involving enough and he never asked what would he do or in what he should help or which was his role. I was quite mad and had to do something extra work to organize him with the team. To be honest we somehow changed a bit the roles. Because the engineer (Me) made the design as well as the calculations. The designer (Ana Isa) chose the materials and did the circuits and connections for the lamp. The secretary (Samara and Adrian) both helped with the content as well as joining the parts. In fact the role of the leader was not very present and Isa, Samara and I were all collaborating and helping each other to organize and make the directions. I would believe that the only teammate I had a complaint was Adrian because he didn't involve enough. 
At the moment of defining the objectives Isa, Samara and I decided to stick to the ones in the rubric. Still some problems surged and also Adrian wasn't very clear with the objectives, I had to explain several times and make sure he was including everything. 
Because I failed to involve constructively Adrian to our team, I can't say I managed to create a collaborative dialogue. However I was very pleased to hear the ideas that Samara and Isa brought to the team. Specially Isa who was very enthusiastic about the lamp work, and she kindly offered to do it herself. 

3rd Partial

Critical Thinking

We have to be evaluated in critical thinking by our teacher, here is the rubric:

I noticed that this partial my critical thinking wasn't as good as the others, next semester it is a thing I must improve. However I would have loved to have some observations to know how I could do better next semester. 

2nd Partial

Correct Use of Mathematical Language

Next semester I definitely must improve my use of mathematical language. Especially now because I have been giving math advice to a lot of students. I find it very funny how I even manage to explain everything and yet I'm not being able to explain it in the exam. 

However, it's not like I'm really bad at this. I believe that more than anything I find that there are a lot of ways to solve things and I often think way too much about what they ask me for, and I get confused. As well I sometimes forget particular and important things, like sometimes I can't exactly tell the difference of when to use ln or log (although I know it is mainly their bases which tell the difference). 

Still, mistakes help us get better. So here are my evidences and corrections:

2nd Partial

Collaborative Activity

In this collaborative activity we created a document with all the right answers and procedures for all the problems covered in Module 5. 
We did gave in the activity at the due time, we only had a minor mistake because at the end we confused about who would have to print it but in the end we printed it and gave it on time.
I did participated and did my share of the team, I was assigned certain problems from the module to solve and I was in charge of organizing their process and answer, and putting their graphs.
The way we divided the work was by assigning problems. We took in count the abilities and availability of each member, because some times we couldn't do certain problems because that day we would have some personal thing that wouldn't let us work, but next time we divided the work different. In order to also give rests to the other team members and so that we worked somehow fairly and not overwork while some others would do nothing.
We defined our objectives by looking at the rubric and coped with what we were assigned to do. We shared a digital document so that it would be easier to help others and manipulate our data. 
I accepted several opinions, as well as I gave some. This in order to organize better and make sure that we would have everything complete. 

2nd Partial

Collaborative Activity

In this collaborative activity we made a video explaining the Euler number. 
We did gave in the activity at the due time, it was uploaded and deliver as the instructions asked.
I did participated and did my share of the team, I was the one to record the presentation and give the explanation. I was checking on my team members so that they would give me the information and the presentation on time in order to practice and record it nicely.
The way we divided the work was by assigning roles. Ana Isa was the researcher (the one to look for the information), Samara the engineer (the one assigned to make a presentation from the information), and I was the anchor (the one to communicate everything though a video).
We all chose and accepted their own roles, and by basing in the rubric we all agreed about our job. It is seen in the final job that we all compromised to it because we all did it in time and shared our part in order to give in a final job well done.
I accepted several opinions, because I had to cope with the products I received to work with. I was open  minded and worked with whatever they gave to me and if I had any questions I would tell them. 

2nd Partial

Collaborative Activity

In this collaborative activity we played a game in which we had to solve a problem about the module and then if we got it right we could go to the next question, and like that until the end, if we got it wrong we had to choose another one and do it until it was right. 
We did gave in the activity at the due time, even we had a bit of extra time because we worked very good together, we all knew the topics and also if we had any doubts we solved them between each other.
I did participated and did my share of the team, since we solved the questions by turn, it was just about doing the one I was supposed to do, and help my team members if it was necessary. 
The way we divided the work was by a common agreement, we all just tried to get together and choose what we liked the most. My team members were also my friends so it was really easy to work with them, besides we are all good at math so we did it very good.
As I mentioned before, because of our friendship and thanks that the activity was very clear  it was really easy to define objectives and to work together.
I accepted several opinions, since we were trying to make common agreements sometimes I had to accept what my other team members wanted and them as well.

2nd Partial

Critical Thinking

As an evidence of critical thinking you can see the evaluation of my teacher. It is based on classroom observations and questions indicated as critical thinking activities. Here is my rubric:

1st Partial

Correct Use of Mathematical Language

Something I am very proud of this semester is that I haven't had trouble with the correct use of mathematical language. From calling a composite function a composite function to recognizing certain figures, like D: , to know it means the domain and I must put it every single time I am writing the domain and that the domain comprehends x such that x, as well as other things. 

In this activity you can appreciate the correct use of mathematical language in the inverse function, that you know you must write f^-1(x) and to indicate that it is an inverse. Also that you can replace f(x) for y when you are in the process of making it inverse. 

Now at the composite function to indicate that f of g in an equation you must write f composed of g such that x and that you write it as f(g(x)). And vice versa if you must write g composed of f such that x and that you write it as g(f(x)). 

1st Partial

Collaborative Activity

In this collaborative activity we used composite functions in order to answer an exercise sheet. I really liked this collaborative activity, my team was really nice and cooperative. Although we worked in pairs instead of trios because our composite function did not had an assigned person. I was f(x) and she was g(x).
We did gave in the activity at the due time and even had extra time in the end. Everything was very fluent. Although I had some problems in the instructions at the beginning I quickly found my teammate. 
I actively participated since the beginning of the activity, asking questions and looking for my partner. I knew that since all the composite functions given were  f(g(x)) I was looking first for my composite function that had a something were I had an x. Then when I found it, I started looking for what replaced x (that would be g(x)) and I found my teammate.
Together we analyzed the exercises and questioned the processes we made. Was it possible to have a square root inside a square root? Why some square roots did not covered the whole equation? I was constantly asking my teammate if she understood all the processes and we wrote them together so we could analyze them. The activity was collaborative so we divided the work just a little, I wrote the process in a separate page and she would write the correct answer in the clean activity. However we did the exercises together.
I insisted on writing the process so we both would be completely sure of what we had made, and we mutually ask questions to be sure we understood and were applying our knowledge right. I was the first to find the composite function and was eager to find my teammate as quick as I could, she was looking too, so it was easy to find each other.
We had similar opinions which made it easy to work together and as I mentioned, questions helped us accelerate the learning process for each of us.