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

Friday, July 28, 2017


While working on my graduate courses and finding new professional development pieces for my coursework I stumbled upon this new movement, #ObserveMe.  I decided to go all out for the last few weeks of school and try out the new tool.  I found a generic observation form for mathematics, and then created a Google Form that was linked to a QR code outside of my room.  The Google Form contained a few questions a colleague could give me feedback on.

The objectives I wanted feedback on were:

1. Improving questioning skills to further student problem solving skills.
2. Have students persevere in making sense of problem solving.
3. Create meaningful activities for critical thinking and problem based learning.

With our district being inner city urban youth, we are constantly under scrutiny from all sides and from that we were tasked with creating a teacher to teacher observation tool within each building.  Through all of the meetings about what it would look like, and Distributed Leadership meetings that we were going this route, but we never got into the full use of the teacher observation and collaboration tool.  Since I found the tool I figured why not give it a try and open up my classroom to others.

Monday, March 27, 2017

Digital Media in Education

Throughout my career I have found different activities helpful for teaching my classes.  Students in my Geometry class have skeletal notes that they take in notebooks, they get practice in various forms, and sometimes I like to add extra information in the form of YouTube videos.  I have curated some interesting Geometry videos and rap songs written about geometry topics to help my students remember and understand the concepts that they are learning.   Some of the YouTube channels I have put together are below:

Triangles in Geometry - Involves triangle classification, Pythagorean theorem, Trigonometric Functions Songs 

Logic in Geometry - Helpful videos to introduce or enhance the understanding of Logic

Fractals in Geometry - Fractals in African Culture and a fun Doodle about Fractals 

Data Wall

Since I joined the Distributed Leadership team at William Penn Senior High School I have been pushing myself as an educator to do more for the school, and I have seen progress be made.  Simple things have helped change the culture in the building and letting students know where they are academically has been one of them.  The art teacher in my building came up with her simple data wall that the district had asked us to put up.  She had the template and I just copied and used it.  (Her class art can be shown here! The Muddy Bearcat )  My data wall is simple and lets students know how each class's grades are doing compared to one another.  I color coded the dots on each sheet to match up with those that are being used in the Commonwealth of Pennsylvania to show Blue for A's (Advanced), Green for B's (Proficient), Yellow for C's (Basic), Orange for D's (Below Basic) and Red for F's (Little to No Work).

Saturday, March 25, 2017

Journaling in Geometry

While sitting through a Professional Development two years ago, I found myself excited to learn and ready to get back into the classroom.  Our presenter was enthusiastic, knowledgeable and fun and I really started to get into the ideology of writing in a mathematics classroom and how I wanted to implement that as a new procedure in my classroom.  I had always had students do a Problem of the Day that they recorded the problem and solved it on a sheet that would be turned in at the end of the week as part of a small formative grade, but after listening to our speaker I decided I would try journaling instead.  Since I have taught in an urban setting for all of my career my colleagues and I asked how to get students to build their writing skills.  Following the different ideologies from Collin's Writing and how to Build Stamina for Writing we discussed the three following types of writing that are useful in developing understanding and writing in a mathematics classroom:

1.  Descriptive Writing: the first step is to just get students to write their thoughts on paper; ask for a specific idea or concept that students should already know.  A way to differentiate would be to give a list of 5 specific questions or topics and have students pick at least 3 to write about, and students who can or need to be pushed can write about all 5.

Ex. Describe the classifications of triangles.
a. Give a description of each classification of triangles by their side lengths.
b. Give a description of each classification of triangles by their angle measures.

2.  Procedural Writing: The second type is to expand and have students write about procedures, such as How to make a PB & J?  Students should summarize a process, explain how to do correctly solve a problem.  It is a good way to start having students process steps in mathematics and give more information.

Ex. Explain the process in drawing a right scalene triangle.

3. Conceptual Writing: The third is then to convey understanding  check for clarity, correct vocabulary usage, correct mathematical concept usage.

Ex. a. What are the differences  between the given triangles?  Explain how you found those differences.

b. Can a scalene triangle also be a right triangle?

Using these three types of writing in a sequential order, students become more comfortable after doing multiple descriptive writing responses, and you can expand on their writing by making more procedural writing prompts, or conceptual writing prompts later in the school year.  Finding prompts (Journal Prompt Search) is always easy as well, Googling Math Writing Prompts yields many results with various forms and formats.

While using this process I have found a systematic way to have students complete the journal each day before class.  Every Monday Wednesday and Friday students write on their Geometry Journal Page.  I also found these Stamina Building Phrases to be useful.  Since we write on certain days of the week, the other two days in order to help with understanding and fluency in mathematics I have also implemented Number Talks, which helps me build not only students writing but also their oral fluency in mathematics.   Students in my classroom are writing and discussing to build on their understanding, they are writing to learn mathematics, not learning to write.  With these formative tools I feel I have improved my classroom understanding.

Reading and grading all of these journals seems like a tedious, time consuming event, but if done right no teacher has to read all of the journal responses.  The instructor during our professional development explained that in order to validate writing, students need to have their writing read, so to make sure everyone has their responses and opinions read, students in my classroom trade journals with a partner and then do a partner response.  Usually the response is for students to read their partner's writing and give one piece of advice or to state whether or not they agree with their partners writing.  Having the partner response and original response be a combined grade on the page holds everyone accountable.  I usually assign 2 points for each individual response and then 1 point for each partner response on the page.  Then I only have to glance at each section on the page to grade the journal page, making grading easy.