Wednesday, January 31, 2018

Curve Sketching with the 1st and 2nd Derivative

I am a teacher by day, and an adjunct by night.  One evening, while looking out into the sea of college freshmen, during one of my "lectures" I noticed that their faces all had that glazed over look, they were not as engaged and all around looking miserable.  The college students humor me by laughing at my horrible jokes, and will even ask questions when they need, but I did not feel the room at all that night.  Later that week I was on Twitter scrolling through, and found an interesting Tweet by Robert Kaplinsky, "Who ever felt that lecture was the pinnacle of education?! If anything, we should be giving them our best instruction to prepare them."  Although lecturing is sometimes necessary to convey content, it should not be the sole way students of any age are taught.

Rubric: Curve Sketching Rubric
Project Example: First & Second Derivative Test Project

With that in mind, I also remembered that last year while teaching the same topic on curve sketching.  I was so excited by my examples and how to do the problems, that after I was done with the class I quickly assigned the odd problems from the text book.  Not thinking that each problem took about 15 minutes to complete, and giving 15 problems at 15 minutes a piece meant almost 4 hours worth of homework.  I did a complete disservice to those students with the assignment, and quickly had to apologize.  After reflecting on the previous year, and thinking about how I wanted this current semester to go, I figured out a new way of teaching the problem set and I feel I came up with a more interesting and collaborative way to practice the skill of curve sketching using derivatives.

Group 4's Project and Discussion were both great! 
Read below for more on the interactions of the group and the language used. 

Students were randomly assigned into 6 groups of 4.  I created a Google Drive Folder for each group and then made some adjustments to the problems from the text and my unit review.  Each group was assigned two functions to use the first and second derivative test, creating the curve sketching information that they needed.  Groups were to find the relative maxima, relative minima, any inflection points, where there was concavity up or down, and where the function was decreasing and increasing.   The groups added comments and edits, gave each other feedback and created a great collaborative final answer for their functions.  They also were to sketch the curve with Desmos, and find all of the points that they solved for mathematically on the picture instead of all by hand.  I had each group member turn in their perspective rough draft to have students show more than just participation in the online document, but the collaboration piece was key.  A lot of the discussions were really powerful with well thought out questions, leading to deeper understanding of the tables and sign charts groups created.    They learned from each other how to successfully apply the derivative tests to the function and what pieces would ultimately help them sketch the graph.  the groups also made their sign charts each in different modes through technology or taking a picture of their hand drawn chart.

Student Sign Charts were interesting and creatively made. 

Another Group's Sign Chart

After everyone had turned in their Google Doc, I also wanted to get a feel for the students' outlook from completing their group project. I created a Google Form and asked several questions about how they felt the project went. A majority of the feedback that came back said the group project was enjoyable, and it helped that students with understanding the process. I also saw a lot of good computational thinking in the form of their summative assessment following our fourth unit, and I think that I will use this project in years to come. My new goal is to create one collaborative or group project for each unit of my course to engage my college learners in a more enriching fashion. Next year I plan to facilitate another learning experience that will enhance my college course, and make the course even more engaging.

Sunday, January 21, 2018

One Hour of Code Initiative

After finishing two graduate courses on utilizing technology in the classroom, I was tasked with one for a collaborative research project.   The project consisted of classmates and I researching a technology trend in education and we chose coding in the classroom.  I was very impressed with the website and all of the resources that are available for free on the site, including their One Hour of Code Initiative.  I had students watch the five minute video from to get them excited to investigate coding.  Students then created a free account and started the process of completing the One Hour of Code initiative from December 4th through December 8th this year.

Following the One Hour of Code program, students were then given a set of Scratch coding activities that progressively increased in difficulty.  Students were tasked with creating an easy set of code that drew four different polygons.  Then they were given a second task to code a random polygon generator using some more complex coding pieces, which also had students create a block (their own code piece) to name the polygon that was generated. For the final project students were tasked with creating coding blocks to draw a Sierpinski Triangle.  (My code is attached below.)  I used these projects in my Saturday STEM Mathematics program last spring, and found that they would be great for school this year as well. 

The whole program took students about 5 days and an average of 5 hours to complete all of the coding projects.  Students were given a great opportunity to investigate coding.  To celebrate and reward their accomplishments with more than just a grade, I created a certificate of completion.  Students who successfully completed all of the projects and showed that they ran were awarded the certificate that they could then use in any resume.  My district is trying to increase the amount of experiences students are given for job and college readiness for PA State Act 339.  So the experiences in coding and computer science will give them more confidence in working on computers, and some confidence with job readiness skills.

Once students finalized the projects, they began to investigate the math and history of fractal geometry, a mathematical definition of the patterns seen in nature.  Computer science has used fractals to create more and more realistic computer generated imagery in video games and movies.  Students got to investigate logarithms to define the fractal dimension and took in-depth looks at how the math has changed how we look at the similarities in nature.  For the last four years, I have been implementing and developing this two week unit before Christmas break. Leading up to students creating a holiday Sierpinski Tree.  I hope to one day inspire my students to investigate fractals even more, because the math behind it is very interesting.

Friday, October 20, 2017

Conditional Statement Story - Post Observation Reflection

Ever read the story, "If You Give a Mouse A Cookie" by Laura Numeroff?  I had not until I married an elementary school teacher, and read the book she had in her classroom.  Several years ago after reading the book I had an idea that was going to allow me to use the story for my students as well.  What could a Geometry Teacher do with a children's book you may ask?  Well it's simple, the entire book is written as conditional statements, if p then q.  In my second unit in the school year,  Reasoning and Proofs, we delve into the mechanics of writing conditional statements, their converses, inverses, even contrapositives, and using the symbols to write these statements.  The statements are used throughout my course to write and prove postulates, properties, theorems and corollaries.  Students immerse themselves in the logic of the statements and decide whether or not there is a truth value to a given statement.

6th Period Starting the Project
When I originally designed my project I had students write their own book and draw illustrations in it.  But now as I am becoming more tech savvy and more digitally in-tuned with my students needs. I figured why not adapt the use of computers to make a PowerPoint of the book?  The end goal is to make Google Slides the tool we use. But until students can log-in to a true Google Account and collaborate with students on the use of Google Apps, I am stuck with what little true collaboration my students and I have now.   Students are going to have to write their own Conditional Statement Story Project, much like "If You Give a Mouse a Cookie."  The requirements are that the story has 10 conditional statements, 4 original statements, 2 converses, 2 inverses and 2 contrapositives that flow together much like the story I read to them Tuesday.   Students will then work in pairs to write their story and illustrate it with pictures from the web.  I have a Google Slide set up to show them the proper uses of a Google Image Search to utilize photos for their presentation that have permission to reuse and distribute the image.  I added this component of Digital Citizenship to promote the Creative Commons that many other students already know about.  

Since students could not access Google Slides from the network computers we were utilizing,  I then had to change gears in my planning and have all students create their stories using Microsoft PowerPoint.  They then uploaded their typed rough draft and final PowerPoint presentation to my Dropbox account.  My Wiki page linked here allowed them access to the links I provided for my Dropbox, where I could then add the presentations to my Google Drive and convert them to Google Slides to easily share online.  One key characteristic of being an educator is that I am very flexible and while I would like to continue my journey in learning and utilizing Google Apps, I know that there are tools out there already that help me with technically updating my craft.  

7th Period Starting the Project
Wednesday I was observed by my administrator while students were working on this project and so I am using this post as my reflection piece.  (Lesson Plan Here)  Some thoughts I had while thinking back on my activity are; I would like to change my requirements for the rough draft for next year by making students label their statements, and also have them put the labels in the notes section of their PowerPoint or Google Slide.  Although most students completed a nice cover page some needed to be asked to do so, so next year I am going to add a cover page section into the rubric.  I feel students worked really hard on their stories, had good questions about the project, and I chose some of the best ones to share below.

 Please read and enjoy the great things these students accomplished while writing, creating and learning online.

Sunday, October 15, 2017

First Marking Period - Data & Committing to Life Long Learning

Recently the Keystone scores for Pennsylvania were released, and our Algebra 1 scores were not where we would have envisioned them.  Our English Language Arts scores saw growth, and a 9% gain in overall Proficiency, along with the Biology exam that is now given in PA.  Math took a 2% hit, although the numbers of students in the below basic category dropped and increased their scores, we need to re-examine the way we teach mathematics.  We believe student scores will increase if the math department increases the writing proficiency in Algebra.

In my Geometry course I am committed to help increase the perserverance in writing mathematically and technically.  To foster those skills I am utilizing more task problem sets to practice skills in Geometry.  Recently students investigated the use of areas in carpeting and tiling a first floor of  a house.  I used Carnegie Learning's Geometry course when I student taught and have found continued uses for the problem sets that are available in their old books.  I bought a student edition off of Amazon for $10 and have been using specific problem sets for my course to enhance the classroom rigor and relevance.
Carpeting & Tiling a Floor- Using Task Problems to investigate
area in a Geometry Classroom while increasing
writing in mathematics. 
I also am expanding my classroom set-up, with a new use for the white board in the back of my classroom.  After participating in a  Twitter conversation with some other professionals across the United States about mathematics and education, one topic really stood out to me.  What do you do with good student questions?  One educator said he had a Pressing Questions board, and I thought to myself, well I have a blank White Board in the back of my room, let's utilize it and discuss more questions with students. One question led us to a whole class discussion and deeper thinking while looking at a drawing on GeoGebra to illustrate what happens when polygons increase their number of sides.  My visual learners were fully engaged in the discussion and said they would like to use GeoGebra themselves.
New Pressing Questions White Board - Use questions students come up
with that cannot be addressed right away, or that are good enough
to keep coming back to. 

Students were also introduced to the use of Geogebra to start manipulating and working with digital drawings of mathematical concepts.  I enjoy teaching my students how to work with protractors and compasses, but this tool is much more efficient and easily understood, especially for my visual learners.  Throughout the school year I plan to utilize more Geogebra in the classroom to model mathematics in the real world, and maybe even in uploading photos for my students to modify and work with.   However, I'm finding that using our district network is making it difficult to continue with some of my ideas and the work I'm doing in my graduate courses.

Collage of Student Projects
Triangle Angle Sum, Interior Angles of Polygons
& Angle and Segment Bisectors

The only catch with all of the work in my courses I would like to continue with, is the fact that I cannot modify anything with my students and have them complete work in their own Google accounts, where everything can be saved to a cloud.  The school district I work for restricts the useage of student log-ins for any type of e-mail or account log-in.  Once we become a Google School I will be proud to share with them in all of the uses of Google tools in the classroom!  I even went so far as to become a Google Certified Educator, Level 1, and hope to continue this school year to gain Level 2 and even Trainer status to compliment my future master's in Information Technology Specialist.  I have a lot on my plate and continue to keep trying new things as an educator because I know my students deserve the best.  I want to inspire them in a way they have not been before, to look into technology and mathematics as a career and life-long learning process.

Topology Assignment for my Grad Class,
the computer lab system I work with, when
it works. 

Monday, September 4, 2017

Student Rapport

William Penn Senior High School, College Street Entrance
After thinking about the start of my eleventh year of teaching, of all the places I could have ended up with my career I never imagined this small town country boy would ever be successful in an urban education setting.  While I feel I will never have the perfect test scores, the high achieving grades from my students or become teacher of the year, I hope my students would all agree with me that I am successful in educating them.  In education the term prior knowledge is a buzz word that is applied to pre-assessment.  With every student I teach I not only look for prior knowledge but utilized the background of my students in reaching their needs.  I like getting to know each of my students and helping them learn the content of Geometry as well as thinking and planning for their present and future.

Wearing Black to support minority students in the community!
 - A student led initiative. 

Through taking online courses and experimenting with different content, I have started to prepare them for the real world with advancing their background in technology by incorporating more mathematics learning involving computer programs.  Growing up in this technologically advanced world we have seen the emergence in fractals from their usefulness in computer generated images (CGI), from film to video games, it is every where around us.  Fractal Geometry is not a term heard in every single school curriculum, it is in every computer animated image, but I have incorporated it with Logarithms to help my students prepare for diverse fields of study and pre-calculus.  As well, it allows  the chance to be artistic and creative in a sometimes otherwise thought of mundane classroom.  Through GeoGebra I have been able to bring precision and problem-solving skills to life in my classroom.  Utilizing Google Docs I have built in collaboration and peer editing projects.  With online research I have been able to bring ratios into social justice.  It is my hope that students come out of my classroom with a little bit more of an understanding of how critical thinking with mathematics can apply to their lives.

Video Game Club 
Fractal Geometry - Students creating 3-D Sierpinski Triangles
and Menger Sponges before the holidays.
Using indirect measurement to calculate heights in Penn Park!
On top of teaching relevant topics, I always want my students to know I am a person just like them and will join in with their antics at times.  I strive to make them understand that I see them as human beings and care about not only their education but their well being, because honestly not everyone of them has that at home.  In our district students come hungry, are homeless, struggle daily and all in all do not open up to many.  I want my classroom to be a safe and inviting place.  Students know my passions and I proudly display my dorky habits of comic books, video games, and love of math, learning, and my family.  I coordinate with my co-worker and friend, Nick Naugle to run a Video Game Club where students can stay after school, organize tournaments or just play games, we have also gone to the local arcade to enhance their experience in gaming.  I participated in a student led protest to the treatment of minority students by others in the county.  During my 3rd period last year we created a Mannequin Challenge Video, which got twelve thousand hits on Facebook! (We went viral!)  And yes I know, this does not relate to education, but sometimes you just have to have fun because at the end of the day these young adults are still kids, and they deserve these little moments.

Viral Video on Facebook! Just having fun with the kids...
Students playing in Penn Park after their project is done.
Teenagers like the playground just as much as kids!

As I reflect through this post it is not my intention to brag about my accomplishments in my classroom, but to recount my past years in growing as an educator, to help others understand teaching is not always about the content.  Sometimes you need to bring life into the content and make the student's education a part of their human experience.  All too many times I hear stories about educators who try to bend the will of their students to the demands of the curriculum and their own strict procedures.  I am not like most teachers.  Through years of trial and error, I have found that if I want students to learn I need to meet them where they are, and teach them what they need to know in order to be successful in their post-secondary decisions, be it college, technical school, career or military.
Students working on GeoGebra and also using
Maps/Ratios to figure out social justice problems.

Although not every interaction is positive, I have always enjoyed getting to know each student, even those that are a bit of a handful.  I enjoy working with every student, creating meaning in our days together and observing their unique character qualities as they mature.  I teach about 125-150 students in a school year, and if I feel like I can reach at least one, I have had a successful year.

Tuesday, August 15, 2017

YCCOSP Stem Academy

While working with the YCCOSP Program (See my first Blog on my summer work) I have been given a lot of autonomy to create learning activities for my students.  This past Spring we had a chance to help design and implement a Saturday STEM Academy.  For four Saturdays, students were immersed in activities in Chemistry, Biology, Engineering and Mathematics.  Professors from York College of Pennsylvania created meaningful learning experiences for the YCCOSP students in the STEM field.  Since our school has discontinued all courses in computer science our students are never given the chance to experiment with coding or different computer programs.

While researching for a graduate course I found several articles on Edutopia about using Scratch coding from MIT to teach coding and mathematics.  Scratch is a basic system and teaches students coding using building blocks on the online coding program.  Several of the students had been through my Geometry class and had learned about the use and concept of Fractals.  Since our students have never been exposed to any type of coding programs I decided they needed to gradually be given steps to learn how to use the Scratch programming and scaffolded their learning activity with three different tiers of difficulty.

The first assignment took students through the basics of scratch code and taught them how to make the online icon do the simplest of moves to create a given polygon.  (Easy Scratch Coding Edutopia Blog)  The second assignment was then the intermediate level of coding which had students create a code to have the icon make a  random polygon and then name it based on the parameters given.  (Intermediate Scratch Edutopia Blog)  Finally students took the program to create the Sierpinski Triangle, a fractal program that made a recursive pattern within itself.  (Advanced Scratch Edutopia Blog).  From each of the blogs I found I created instructions and questions for the students to complete each level of difficulty in coding with the Scratch program.

Students were then tasked to share their code to their college Google+ account.  In the YCCOSP Math STEM Community that I created, students explained what they created and shared it with the world.  This allowed for another deeper conversation about the way one needs to convey themselves online and in social media.  I informed students that the sharing of their code and what their creations did, since it was put online they also had to understand that their words would be able to be seen by others in the social media.  This simple step created the sense that they as digital citizens must be precise in their wording and represent their own selves in a positive academic manner.

The Saturday morning was filled with a lot of fun and students were very involved in the program. Students who had never seen code in their academic career were exposed to a new programming method that can help teach students.  Students were very successful in coding their projects and even commented that they enjoyed learning and "playing around" with the website.  The program ran very well and in the future I hope I can create as meaningful of a set of projects as I have here.  You can get all of my documents used in my TpT store for free! Coding Projects for STEM Mathematics

Tuesday, August 1, 2017

YCCOSP 2017 Summer Reflection

The YCCOSP Program

For the past three years I have worked for York College of Pennsylvania as an adjunct professor and as a summer mathematics instructor for the York College Community Opportunity Scholarship Program.  The summer program is designed to help our students succeed in an accelerated curriculum and prepare them to enter college.  The program offers enrichment to students who apply to the program from William Penn Senior High School. The groups that are in the program are either entering their sophomore, junior or senior year of high school.  I work directly every morning and afternoon with the Rising Sophomores and Juniors teaching them more mathematics problem solving and critical thinking skills.  They also take a course on reading and writing to help develop those skills.  The Rising Seniors take an entry level writing college course and can earn course credit with successful completion of the class.

The program is designed to enrich and has no set curriculum so I have the freedom to design whatever I want for the students to create and learn.  Working at William Penn and knowing the curriculum we offer helps me in structuring the summer class for the students' success for the upcoming school year.  The program helps emphasize critical thinking skills and advancing SAT preparatory skills.  Students in the program are either going into Pre-Calculus their junior year or doubling up their sophomore year with Geometry and Algebra 2.  We worked this past summer on skills involving critical thinking, problem solving, polynomials, geometry basics, trigonometry and even some statistics.  The ten students were also broken into three teams that were tasked with a culminating project called "Design a Winner."

2017 Project: Designing a Winner

Each year the students showcase what they have learned and/or worked on, so this year I found a project online through Curriki using geometric skills to, "Design a Winner."  Students were tasked with building a multi-sports complex with set criteria.  The question  was designed as open ended and each team created a company name, then they had to start preliminary designs, proposals, 3-D models of the final design and showcase mathematical computations they used to help in their designs.  The beauty of the project was that it tied into what is going on in the community already. We begun by reading the YDR article "Rutter's cornfield could become sports complex."

Students also got a special treat because there is one of the largest sports complexes in the nation right down the road from York in Lancaster.  We bused the group down Route 30 to the Spooky Nook Sports Complex, where two experts lead us on a tour of the facility and gave us facts and figures to start the teams on their brainstorming creativity.  Students took to Instagram for a scavenger hunt on the tour and documented the trip with facts and pictures of the facility to use in their projects.  Students then took to using Sketchup to complete 3-D models of their projects.  (Educators can get the $600 program for free with proof of employment by a school district!)


With the program running for 5 weeks and only Monday-Thursday time was limited on the project.  What made things run more smoothly was dividing up the aspects of the project between the student writing class time and mathematics class time.  Students wrote proposals, created Powerpoints and designed pamphlets for advertising in the writing class. They then created their model, used mathematical ratios and proportions to scale their models and created a poster to show off their designs and calculations in math class.  All components were then put on display during the showcase finale.  Students were also tasked with writing and orally practicing their proposal so they could discuss and answer questions about their project with the staff and parents who came to view their work.  

Students working on their project.

The last week I was really worried about how the project would turn out because I felt like we had rushed everything to be done on time.  We did not get to use trigonometry to talk about angles in the complexes the students were creating nor did we complete more calculations that would have intensified the math, but the students were excited to use the Sketchup program and learn about new designing software.  The thing that also did not help was that I did not have time to approach and have the campuses IT download or purchase a subscription to Sketchup for the students, I took my own personal laptops, I had 2, for the students to use and one student brought his own and downloaded the free version of Sketchup Maker.  The designs that came from the students were pretty amazing, although the time did not permit tons of detail they did come up with some interesting beginnings of designs.  

Athletic Era and their Project Design

The students were innovative and worked diligently in and out of the classroom, some utilized the Google Document Apps features to collaborate on one pamphlet or slide show at all times, which I did not even have to suggest.  By the end of the program my fears of the students being unprepared quickly subsided by looking at the posters and listening to the students discuss their designs to various YCP faculty members and their parents.  The students had a great sense of what the project was all about, they had stunning posters, great rate changes and an even better understanding behind design.  One group thought so much about the culture of York that they wanted to create a complex in the formation of a rose, since we are the White Rose City.  

AGibso and their Project Design

Although I did not feel like we got through everything that could have been done with the project, the time that I had with my students was invaluable in re-fueling the fire that makes me want to teach.  The inquisitive creative teams that I worked with were fun and impressed me with the work they completed.  The students did such a great job this summer that I feel a sense of pride in their accomplishments, plus I feel rejuvenated and ready to take on my regular geometry classes again! 
Clock Work and their Project Design