Educational Myths

Reading the articles on each myth was eye-opening. They all seemed to surprise me in some sense: “I remember 10% of what I…” and “Are Your Students Engaged? Don’t Be So Sure” were the two that were the most surprising to me. I’ve seen the picture in “I remember…” multiple times during my journey through the education field. The citation was incorrect; the questions posed about the graph are interesting and really make you think about the fault in the “study”. Something that we’ve seen so frequently but holds no true value – this really caught my attention. As educators, we need to be on top of our sources and their credibility, even in a professional sense. Also, I thought the engagement article was quite interesting. It seems we sometimes look to technology as our ‘hook’… for the entire lesson; that adding technology will grab the attention of our students and never let go. This article definitely helped me think otherwise.

Dismissing the article on learning styles was the easiest for me. I agree that using multiple representations to instruct and gain knowledge is a reliable strategy, however, classifying students to a specific learning style is where things go wrong. It is just like assigning a student a reading level/color, then only allowing them to check out books from that level. We never want to limit our students, so why limit the way we teach them. I am surprised that the studies in the article were basically “called out” by the author in failing “to satisfy key criteria for science validity.” For a method we have been using for roughly 30 years, this is crazy to believe.

I agree with most of the information in the articles. However, to an extent: I don’t think learning styles and multiple intelligence’s should be completely debunked; teachers need to modify them. Using various methods of representation, media, and teaching strategies might help.

“They must be engaged…they’re having fun!” I have heard this, and quite possibly have said this, from time-to-time. Many students have mastered the art of “invisibly disengaged” that they have most teachers fooled. They are learning things on their own time, and ‘checking-out’ for their time spent in the classroom.

All of these myths are still floating around the education field to this day; I’m sure I’ve heard them all at some point. If I run into these non-evidence-based strategies throughout my career as a teacher, I would simply (and appropriately) show them the evidence! As educators, we should love learning just as much as we love teaching. Showing colleagues, and even administrators, these articles might sway their thinking. If not, use these “strategies” lightly; blend your knowledge of other strategies and techniques, with the research, to fix what is missing.

Trends & Issues with Technology

Trend: Interactive Whiteboards (IWB)

Interactive Whiteboards (IWB) have been used in schools for quite some time now, and can offer a more “interactive” approach to teaching. However, like all technology, “the boards are only as good as the people using them.” IWB seem to have a hit-or-miss appeal for educators: some rave about them, others criticize their use. When used correctly and with the proper training, IWB can get students out of their seats and hands-on with their learning. They can encourage student engagement and creativity. In retrospect, people feel that a tablet and a projector will work just as well, since IWB are quite expensive. Others note that teachers may talk-to-the-board, or take away class time fidgeting with an IWB.

As a teacher in the 21st century, any technology for the classroom seems interesting to me. I like learning about tips/tricks and seeing different approaches to integrate certain technology in the classroom. It’s interesting to read/hear about the pros and cons each technology comes with, including that on IWB. I guess I was more surprised to read so many disapprovals; IWB seem valuable, but with some limitations of course. I would try my best to learn about the IWB, and utilize it effectively, if I had one in my classroom.

I have never used an IWB as a teacher, but find them to be a valuable resource when used properly to meet learning objectives. As an elementary math teacher, IWB seem to be a great way for students to share their work (and save it to look over for assessing where students are at with the material). With all the disapprovals of IWB from the articles, I can say I am a bit skeptical for their use. I think there are students/teachers who would benefit from them: teachers who are tech-savy and interested in maximizing the purpose of IWB ; students who need to be up and moving throughout the day, and enjoy an interactive method of learning. However, it is up to the teacher to truly utilize them to the best of their ability.

Issue: Identity Theft

From The United States Department of Justice website: “Identity theft is a crime in which someone wrongfully obtains and uses another person’s personal information in a way that involved fraud or deception.” A persons Social Security number, bank account or credit card number, name/address, and driver’s license number are all examples of personal information connected to ones identity. Surprisingly, children are at a much higher risk for identity theft because the crime often goes undetected for years, when they begin needing to use those personal numbers.

A statistic from a Carnegie Mellon CyLab report states that “10.2% of the children in the report had someone else using their Social Security number – 51 times higher than the 0.2% rate for adults in the same population”.

The Center for Identity has developed an online game for children ages 8 to 10. The game titled “Beat the Thief” allows players to decide whether to share, or not share, different types of information on a social media platform. Players gain points if the information is safe to share online, and risks having their identity stolen if the information is unsafe to share. A “thief” character can steal the players personal identifying information if they choose the wrong information to share.

Web-based Resources

In my final project for EDT 370, I plan to utilize Padlet – an “online wall” that is easy to use, and view, by both teachers and students. The lesson will be geared for 4th grade students. Students will work with a partner to research their assigned famous historical figure. Their Padlet will be the display of their biography, including websites, videos, and images to share their knowledge.

  • Teachers Pay Teachers
    • Title: Biography Research Reports (QR Codes & Scaffolding)
    • URL: https://www.teacherspayteachers.com/Product/Biography-Research-Reports-QR-Codes-Scaffolding-1117493
    • How I Found It: I’ve used TPT for a couple years now! I love looking at the resources people have created for ideas to use and incorporate in creating my own lessons. I went to the 4th grade Social Studies (Other) tabs to narrow my search results.
    • How I Might Use It: Though I probably won’t use this resource entirely, I really like the worksheet for students to fill out for their given person, and the websites they can utilize. These worksheet questions will be a good place for students to start their research to include in their Padlet presentation! I also like the list of biographical figures to use.
    • Standards:
      • GLCE 5 – U3.1.6 Identify the role that key individuals played in leading the colonists to revolution, including George Washington, Thomas Jefferson, Benjamin Franklin, Patrick Henry, Samuel Adams, John Adams, and Thomas Paine.

 

  • PLN
    • Title: History Is Elementary blog
    • URL: http://historyiselementary.blogspot.com/
    • How I Found It: This site showed up while Googling “Social Studies blogs for teachers to follow”. Now, I don’t specifically remember which list it was on of the best blogs to follow, but I know I found it on one!
    • How I Might Use It: This site is nice for getting historical information. This would be a tool I would share with my students for them to use, keeping in mind that this is a blog and not necessarily all true.
    • Standards:
      • GLCE P2.3 Know how to find and organize information from a variety of sources, analyze, interpret, support interpretations with evidence, critically evaluate, and present the information orally and in writing; report investigation results effectively.

 

  • Google
    • Title: 10 Uses of Padlet in the History Classroom
    • URL: http://teachersworkplace.net/2013/07/23/10-uses-of-padlet-in-the-history-classroom
    • How I Found It: I typed “biography projects using Padlet” into the Google search bar and found this website as the first to come up. Previewing the webpage, there are a bunch of great ideas for how students can use Padlet to display their research.
    • How I Might Use It: This might be something I share with my students while introducing the project to give them more ideas; or I might utilize it before giving the project, creating a checklist of criteria that students must have and/or ways to discuss and reflect on presentations as a whole class at the end.
    • Standards
      • GLCE P2.3 Know how to find and organize information from a variety of sources, analyze, interpret, support interpretations with evidence, critically evaluate, and present the information orally and in writing; report investigation results effectively.

 

Blogs in the Classroom

As a future teacher, I think blogging can really change the communication from the classroom to the home. Classroom reminders, picture slideshows, and helpful homework links can all be organized and easily accessible to parents when posted on the class blog. Teachers can keep parents up to date on what is going on in the classroom without sending multiple emails or flyers to take home. Google Docs and Word attachments are great, however can get lost in the mess of an ‘Inbox Folder’; blogs keep materials organized and accessible all on one website. I will definitely use a blog for my classroom! (:

Learner Analysis

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DJ Tanner is the oldest sister from the television sitcom Full House. Her father, Danny Tanner, raised DJ and her two younger sisters alone, but had help from Uncle Jesse and Uncle Joey. Danny works as an anchorman on the television news station in San Francisco, California.

DJ is an honor student and has always excelled in school. She dreams of going to college, particularly Stanford University. Although her younger sisters get on her nerves at times, she works hard to be a positive role model for them. DJ handles tough situations with ease, and thinks through things with a mature mind for someone her age. She enjoys music, movies, and hanging out with friends.

I would have loved to have DJ Tanner as a student in my class! She sets reachable goals for herself and works hard to achieve them. You can tell that she cares a lot about her education, and seems to be “college ready” even in junior high. I think DJ would definitely benefit from keeping a blog: a place where she can keep her thoughts and receive feedback from the blogging community; a place to make new friends that share similar opinions. She would truly learn a lot from the blog world!

About Me!

Hello education majors!

My name is Natalie and I’m a 23 year-old from Warren, MI. I have been studying at GVSU for a few years now, working on my Mathematics degree with an Elementary Certification. I love working with children and cannot wait to finally have a classroom of my own!

Aside from school, I love being adventurous and exploring the great outdoors. I enjoy rollerblading Kent Trails, setting up my hammock to read, or finding local food/music with friends. Grand Rapids has introduced me to the craft beer scene, so exploring breweries has become another one of my favorite pass times. Also, I absolutely love thrifting! My family and I have been searching for treasures since I was a kid; now, I direct my focus towards teaching supplies (books, pencils, bulletin borders…you name it). My attic is filled and ready to stock my future classroom!

I am an outgoing and passionate individual. I love to make people laugh and bring a smile to everyone’s face. The video below was taken this summer during a study abroad trip to Tanzania, Africa. This experience was life-changing; I learned so much about the people and the culture. I like to express myself in various ways – and dancing is one of them. Though I am not the best at dancing, I do like to try!

Natalie Dancing in Tanzania!

Growing up this day in age has truly developed my understanding of the versatile roles technology can play in the classroom. Various apps and websites for teachers and students to use really change the education system. Children are used to such technology at home, so why not bring something they are comfortable with into the classroom as well. I have made a few lessons with technology, but am excited to dive into more of the tech-world to see what else it out there for teachers!

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Teaching Class 5 Science in Arusha, Tanzania! 

Looking Back

This semester I took my capstone class, MTH 495: The History of Mathematics. On the first day of class, we were asked the thought-provoking question: What is Mathematics? Looking back on this day, I really didn’t know how to go about answering this question. Math is such a broad concept; there are different fields, developments, and relations to mathematics that defining it seems rather impossible. My initial blog about this question is posted a couple months back.

downloadSpecifically in one class this semester, we debated about another question: Is Math a Science? From the get go, I said yes – math is a science. I said this with some un-sureness in my voice, since I would prefer to say “Math is related to science”, or “Math plays a key role in science”, or even “Math is a nice umbrella to science”. With more discovery and concepts in the course, I feel more comfortable responding to these questions such as these.

At the beginning of the semester, I said math is just a logical way of explaining the world around us; a science of not being wrong about things. Now, this means even more. Throughout this course, I have seen countless examples of math involved in areas I had never thought of. Some examples: the Fibonacci sequence in plants, fashion, and what seems to be everything; repetitive wallpaper patterns that actually relate to specific symmetry groups; and doodles that do more than just take up class time. Most people think of the difficult concepts, like calculus and algebra. But mathematics is everywhere, and not everyone realizes that.

I was embarrassed to admit how little I knew about the history of mathematics. When asked, I could hardly name major people in the field, let alone what their contributions were. Now, I am much more comfortable to talk about Riemann and his connection to calculus, Euler and his famous line, or this sequence of numbers Fibonacci discovered that people are always talking about.

In order to truly appreciate math, one must know how big of a field it really is. Without the struggle and perseverance of mathematicians before us, we would never have the concepts and advancements that we have today.

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The 17 Wallpaper Groups

“Wallpaper groups”? What does that mean anyway…

For the final project of my capstone class, my group and I decided to produce a tessellation coloring book. Since we are all future elementary math teachers, we thought this was a perfect, relaxing idea. Make random designs, generate them on a computer, bind them together, and BAM…a coloring book! However, our professor thought to challenge us and introduced us to the 17 Wallpaper Groups. wallpaper definition

Each of the 17 symmetry groups is made up of translations, rotations, reflections, and glide-reflections, or any combination in between. I started researching about each symmetry group so I could decide how to incorporate it into our project. There was a lot of information on each group, such as: lattice type, IUC notation, rotation orders, and reflection axes. Here, is a spreadsheet to organize my findings.

After looking at all of these properties, I started to wonder about the history of these specific groups. Who was/were the mastermind behind our symmetrical wallpaper?

A brief summary of events, as told by Natalie:

It turns out the 17 plane symmetry groups were discovered during the 19th century. A collection of people throughout mathematical history added to the development: first, the Pythagoreans discovered that there are five regular solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron). These were used for a variety of purposes, but shined in architecture and decorative art. A man more famous in astronomy, Johannes Kepler has influenced work in mathematics as well. He is generally credited for the first systematic explanation of the set of tessellations known as Semi-Regular or Archimedean. There are 11 specific examples of these tessellations which are composed of regular polygons.

Nimage014ext up, Robert Hooke looked at
different ways atoms could be arranged to form crystals. Then, in 1831, Hessel classified the 32 three-dimensional
point groups that correspond to the three-dimensional crystal classes. A crystal is an endless repetition of some point group operations in a 3D plane, or “wallpaper”. The wallpaper, or space lattice, is generated by tessellations of this symmetrical point group.

Now, in 1835, Frankenheim (possibly related to Frankenstein?) geometrically found all the symmetrical network of points that can have crystallographic symmetry.

A French mathematician by the name of Camille Jordan discussed a general method for defining all the possible ways of regular repeating identical groups of points (that’s a mouthful). Through this theory, he discovered 16 of the 17 wallpaper groups. It was not until 1891 when Fedorov, German mathematician Schonflies, and English geologists Barlow, proved that there were only 17 possible patterns in “The Symmetry of Regular Systems of Figures” (two-dimensional crystallography groups). And alas, the 17 Wallpaper Groups were born.

wallindex


 

The discovery of these groups dates back a long time, with mathematicians and scientists from all over adding their insight. This was rather interesting to learn about and will be extremely helpful to my project!

Is Math a Science?!?

Is math a science? A question that seems so simple to answer, yet is far from it. To classify ‘mathematics’ as a branch of science seems a bit much to me. Yes, we use math to do science, and yes, we sometimes use science to do math. However, the two have certain distinctions that keep them separate. Based on research and my own thoughts, I would say that math and science are closely related, but not one in the same. Here is why…

The main difference between math and science: how ideas are tested and accepted.

In science, the task is to figure out what rules/laws are operating by observing the results following the rules. If your predictions conflict with your experimental data, then you need to change the set of rules you picked. Math is the opposite though: we choose the rules, with the task to discover what the results will be when choosing this particular set. Here, our choice in rules yields no specific right or wrong outcome. If the results produced are interesting enough, another mathematician will surely keep playing with them.

One of the criteria on the Science Checklist is relies on evidence. This relates to science, of course – evidence can make or break a scientific theory. Science NEEDS evidence to be accepted! And the more evidence, the better! However, there is always new evidence being discovered. Constant revision of theories means scientific ideas can never be absolutely proven. Again, math doesn’t work this way. Mathematics relies on proof. No proof? No deductive reasoning? Shot down! Not accepted!

Doctor Ian, from mathforum.org, summarizes his response to the question quite nicely:

“Science is the pursuit of the correct description of this particular world; whereas math is the pursuit of interesting descriptions of possible worlds. Whereas scientific theories are right or wrong, mathematical ‘theories’ are merely interesting or uninteresting.” – Doctor Ian


References:

Book Review: How Not to Be Wrong

I recently read How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg. My feelings about the book roller-coastered until the last page. Overall, I did enjoy this read.

One afternoon this summer, I was exploring Holland with my sister in town. We walked into multiple shops and boutiques, but of course found ourselves lost in a bookstore on the corner. Here, was my first encounter with Ellenberg’s book. As soon as I walked in, How Not to Be Wrong was featured in the front; the red dart and word “mathematics” on the cover caught my eye. I read the back, flipped through a few pages, and took a picture of the cover so I could read it in the future. Lucky for me, this book was on the recommended book list for my capstone class, so of course I jumped right on it.

Initially, I loved this book. I loved it so much I hardly put it down – I even got splashed in the face by a sprinkler while I was reading and walking to class…not okay! Ellenberg begins the book with a perfect explanation to a high school student about what mathematics is. I quoted a majority of it in my blog post, What is Math?  He states: “Math is woven into the way we reason…it is the study of things that come out a certain way because there is no other way they could possibly be.” And then dives into the story of Abraham Wald, a mathematician asked to analyze bullet-hole data from planes returning from World War II sorties. Wald shocked the military when he suggested putting more armor where you don’t see the bullet holes. The reason: planes hit in such spots did not return to be included in the data. This is the kind of “mathematical thinking” Ellenberg highlights throughout the rest of the book, “the extension of common sense by other means.”

After finishing the first couple chapters, my feelings began to develop. The book is divided into five major mathematical topics, each with one or two chapters on specific events/stories to help better understand that topic in general. Here is where my loss of interest started. I noticed myself going back a line, a paragraph, or sometimes an entire page, just to make sense of what I read. His stories are relevant, but fail to the overall connection: when am I going to use this? Ellenberg points out complex mathematical ideas from our everyday lives, and tries to simplify them for anyone with a high school education to understand. His result: a long, confusing chapter, over-explaining what he is actually trying to get across.

Although Ellenberg takes on a lot to chew here, he does make it a point to keep his voice active throughout the entire book. I caught myself laughing out loud multiple times while reading, something that really helped in finishing the book. Even though I had to go back three times to read the same passage, I didn’t mind if the description of the +/- sign in the quadratic formula “looks like a plus sign and a minus sign that love each other very much”.

In conclusion, I would recommend this book to anyone who truly loves mathematics. The stories are in fact eye-opening, only once you understand the point he is trying to make. I think Ellenberg just needed to connect his final thoughts on each story to his main point of the book: mathematics is everywhere and anyone with some mathematical background can see that.