Final: Integrating Technology Effectively to Further Understading in Multiplying Binomials

Final project Google Doc Link

For the final, I decided to use a lesson plan, which I previously worked on in my English Language Learners class. This lesson involved multiplying binomials using the FOIL method. The reason for incorporating a pre-assessment and vocabulary sheet in the first portion of the instruction is to get a grasp on what exactly my students need reviewed before moving along with the remainder of the lesson. During the pre-assessment, students will each be given a white board on which they could show me their answers. This way, I can very quickly look around the room and determine whether or not I can move on. Assuming the students understand this portion of the exercise, I would then move on to the vocabulary sheet. For this activity, the students would need an iPad with the app Math Dictionary installed. After finding the definitions for each of the terms outlined on the worksheet using Math Dictionary, the students could talk in their small groups, comparing the definitions they formulated using the app.

After the initial pre-assessments are completed, I could then introduce the next part of the lesson by modeling a few examples of multiplying binomials. While modeling, I would use the Think-Aloud strategy, telling students the steps to multiplying two binomials. After modeling a few examples, I would then instruct my students to find a video to watch (on the Pearson website or YouTube), explaining the steps for multiplying binomials. The reason I would incorporate both my modeling as well as a video modeling the steps is to provide my students with several ways of explaining the steps in order to maximize their understanding of the concept. When the students are finished watching the video model, I would model one more example to the students, this time using manipulatives. This way, the students who are visual hands-on learners can relate to the topic easier. Next, the students will be given a Real-Life Problem worksheet. Using the multiplication of binomials, the students will need to solve these problems in groups. For the worksheet, they could use any of the three ways they previously learned (the way I modeled the problems, the way the video did, or the way we used algebra tiles to solve it). I can use this time to formally assess the students’ progress by walking around the room and checking how the students are doing.

The next part of the lesson will give me a chance to more thoroughly assess the students. The students will work individually, completing a worksheet using a TI-Nspire calculator to check their answers. Having only used the calculator one other time, I will review how they could check their answers by modeling the steps in order to check the answers. By getting together with a partner, they will collaborate and communicate with their peers to check and discuss their findings with their peers. After pairing up, the class would come together and I would check the solutions to the problems, explaining misconceptions that might’ve lead to incorrect answers. These worksheets, although not graded, will provide me with a written record of how many students need more clarification on the topic.

The final part of the lesson involves more communication as well as producing a short presentation. Because the lesson is packed with many small activities for the students to get involved, I would assign a homework assignment. This homework assignment would require my students to prepare a short PowerPoint presentation about what they had learned about the multiplication of binomials thus far. This will be the graded portion of the lesson, for which they will receive formal written feedback. They will have to solve two real-world application problems using the multiplication of binomials, which they did as part of the lesson earlier on. In order to complete the project, they could use any of the sources with which they were provided during the lesson.

All of the activities in the classroom as well as outside will allow for my students to use technology in a very effective fashion. Also, the activities will promote their critical thinking skills and the ability to make connections between what they had learned in school and the real world. Most importantly, the students will not only get a chance to practice multiplying binomials, but also will be able to apply the properties of operations in order to generate equivalent expressions, and identify when two expressions are equivalent (part of the objectives for the lesson).

Students Aren't the Only Bullies In Schools

As future educators, we have read countless articles against bullying between students, never having thought that other teachers would be the source of such behavior. An article posted by the Huffington Post notes otherwise. Below is a link to a short video along with the article explaining what was said to Akian Chaifetz, son of Stuart Chaifetz, when he put a wire on his child before sending him to school.

Stuart Chaifetz, Father, Puts Wire On Son With Autism, Records Verbal Abuse From Teachers

Stuart Chaifetz also posted this 17-minute video on YouTube, explaining what happened to his son on this particular day, with actual audio recordings from the teachers' very inappropriate and hurtful conversations.

This is an extremely vile story about a few teachers who thought they could get away with inappropriate behavior in a classroom full of autistic boys, because they knew the boys could not relay the information back to their parents at the end of the day. Chaifetz, a concerned parent, wanted to figure out why exactly his son, who had never acted out before, was recently misbehaving, and acting violently. In his YouTube video, Chaifetz is clearly upset (and rightfully so) that people who were supposed to keep his son safe were, instead, verbally abusing him. It's a shame that teachers like this work in public school districts, but as future educators, we should take this as an example as to what NEVER to do in a classroom.

Robo-Readers Better Than Humans? Not So Fast...

According to Michael Winerip of the New York Times, "A recently released study has concluded that computers are capable of scoring essays on standardized tests as well as human beings do." Pearson graders can grade at most 30 writing samples in an hour, whereas e-Rater (an automated grader developed by the Educational Testing Service) can grade 16,000 in 20 seconds. Does this mean humans should be replaced by e-Rater?


Les Pereleman, a director of writing at Massachusetts Institute of Technology, doesn't think so. Mr. Pereleman, in between teaching undergraduates, has researched algorithms like e-Rater, and found many flaws and loops in their development. He noticed that essays that are simply more wordy (although not as well-written) will be graded with a higher score. Longer sentences, paragraphs, and sentences not starting with the words "and" and "or" will score higher. Also, an essay which uses more complex words, no matter in what context, will get a higher score than an essay which doesn't.


Looks like we humans will not be replaced by robots in the world of teaching and testing just yet.


Link to article: Facing a Robo-Grader? Just Keep Obfuscating Mellifluously

Facebook Isn't Yours to Keep, It's Also The District's

In a recent article on Yahoo! News by Tecca, a Grade school teacher's aide Kimberly Hester was fired for refusing to hand over the password to her Facebook account. A parent reported an image on the aide's page and brought the issue up the school district, prompting the investigation. While teachers have gotten into trouble for posts on Facebook before, Hester's case was different because she got fired for refusing to grant access to her Facebook account.

Many other school districts are asking their employees to hand over the access information to their Facebook accounts. I disagree with their decision to fire Hester and also for the other districts' decision to require access to their teachers' accounts. Teachers should, however, be very careful with what they decide to post on their Facebook pages. Although Hester's page was set to private and she was not friends with any of her students, a parent did find pictures that he/she found inappropriate, ultimately being the reason why Hester was let go.

Teach Me How to Study!

For one of our interactivities, we had to come up with a list of helpful pieces of technology to use in a math classroom. One of those technologies, however, could be used for just about any subject. The website called SchoolTube, is very similar to that of YouTube. Instead of  a plethora of videos of dogs doing funny tricks or kids laughing at jokes, this website provides entertaining videos authored by students and/or teachers which have some educational value to them. One video really caught my attention, set to the beat of the popular song "Teach Me How To Dougie", but instead is entitled "Teach Me How to Study". It's a very clever way of getting across to fellow students some tips on creating successful study habits, all set to a beat of a song. We remember the lyrics to songs because we enjoy listening to them, so applying that same attitude towards educational concepts can be very helpful and entertaining in a classroom setting. Authoring/listening to educationally sound songs can help students retain information they might otherwise forget if taught by way of lecture and note-taking.

Here is the link to the video, "Teach Me How to Study" uploaded by user MsDumas.. Enjoy watching!

Interactivity 5: NETS Standards

I chose to interview an 8^th grade science teacher in the Clifton School District. For the purpose of keeping her identity private, I will refer to this particular teacher as Ms. Smith during the remainder of this blog entry. Ms. Smith teaches Physical Science, consisting of Genetics, Chemistry, Biology, and Environmental sciences.

Ms. Smith was not familiar with the NETS standards until I presented them to her during our interview. Although she’s never seen them, however, she noticed that many of the standards NETS outlines are ideas she already incorporates into her class on a day-to-day basis. Ms. Smith frequently uses a SMART Board in her lessons, and tries to make her science classes as engaging for the students as possible with the help of the technology she has available in her classroom.

After looking at the Clifton School District’s website along with asking Ms. Smith about the NETS Standards, I did not find any signs of implementation of the technology standards thus far. Ms. Smith did let me know that many of the classrooms at the middle school where she works are equipped with a SMART Board, and all of the classrooms have at least six computers for the students and teachers to make use of.

I was not very surprised at Ms. Smith’s responses, because after going back to my lesson plan spreadsheet for Interactivity 4 and adding in the NETS-S standards, I noticed that a good lesson already includes many of the standards outlined by the International Society for Technology in Education (ISTE). Ms. Smith also noticed this was evident in her personal lessons. She added that although the teachers in Clifton public schools are not required to align their lessons according to NETS standards, they do have to somehow note in their plans (by a simple way of highlighting for example) when technology is being used. She also said that another reason for Clifton not beginning the implementation of the NETS standards could be due to the diversity of the town. Because many of the students are English Language Learners (ELL’s), the teachers are required to not only align their lessons with their specific content, but also Language Arts. Adding yet another set of standards might be considered overkill.

As a future educator, I might try to make my fellow colleagues aware of these standards by talking with them about the NETS standards. Not only are the standards fairly easy to follow and straightforward, but they could also ensure a greater interaction between the students and the technology available in schools. We have seen that children today learn to use computers before they can read, so I think it’s safe to say that they could greatly benefit from having lessons aligned with the NETS standards.

Socrative: A New Way of Assessing Students

Socrative, a way to "engage the class using any device," is a website I have recently learned about in one of my classes this semester. A virtual way to assess students' knowledge on any particular topic, socrative.com allows for an instructor to construct an assessment the class can take live, in class.

The assessments can be constructed in a multiple choice, true/false, and free-response format, so the possibilities are endless for assessing the students. During the actual testing process, the students have to sign in with a room number given to the instructor during the sign up process for the program (which is absolutely free!). The teacher can then choose between a student-paced test or a teacher-paced test. The student-paced test allows the students to move at their own pace and move through the questions as quickly as they wish, whereas the teacher-paced test stops the students after each question. The teacher-paced option can be especially good to check for understanding after each question has been answered by the students, in order to see what concepts the students still need to review.

Because the student response system allows for the students to use devices they are familiar with (i.e. a cell phone, laptop, or tablet) and use recreationally, this is a good way to show them that their device can be used for other, educationally rich activities. Also, because this is something I haven't seen done in many classes, I think it could be a way to get the students interested in the lesson, and interact with the material much more, since they are so comfortable with technology.

Not only can it be helpful and interesting to students; it can also be a great tool for teachers. "Socrative saves me 80 minutes per week in grading time," says Kristina Buenafe, a Boston Public High School Math Teacher. It's a great tool to save time while assessing the students and their knowledge on any material.

Engaging Students and Enhancing Learning Through Free Technology

Here is a very helpful link I found for educators to taken advantage of... and it's free! This e-book contains step-by-step instructions on how to construct a blogging website, twitter account, author a YouTube video, all while making the activity educational. I will most definitely try to take full advantage of this gem during my student teaching next semester, and during my teaching career in the future.

Below, you will also find a video showing just how many journals and newspapers agree that this source is of value:

Interactivity 4: Teaching Math Using Technology with Purpose

I chose this particular lesson plan because it incorporated many student-centered learning strategies. From past experiences as well as formal interviews conducted with current students, I believe student-centered learning is much more effective than teacher-centered learning. Being that this was a review lesson, it was the perfect setting for student-centered learning, since the students should be familiar with the material. It gives the students a chance, then, to think critically when being presented with a more interactive lesson.

I believe that the lesson met the goals set forth at the beginning of the lesson plan. If possible, however, I would use a SmartBoard instead of an overhead projector, because the SmartBoard allows for student interactivity much more than a blackboard or overhead projector, by way of programs such as Geometer’s Sketchpad. Before sharing their findings with the whole class, I would allow for the students to talk to one another in small groups. By first working in small groups, students can become more confident in their answer, and would be more inclined to want to share their findings with the whole class. Since students often feel more comfortable asking their peers questions about a concept they did not grasp rather than asking the teacher, this could serve as an opportunity for peer teaching to occur in the classroom.

The SmartBoard as well as the program Geometer’s Sketchpad were essential as far as showing the students how the movement of one point of a triangle can change its classification. It allowed for students to ask critical thinking questions and make assumptions about the different types of triangles that would be formed based on the orientation of the point being moved. The blackboard/SmartBoard/overhead also were necessary for students to take accurate notes when going over the proofs.

Links:
Spreadsheet
Lesson Plan

Let's Tweet About Something Educational For A Change...

At Roosevelt High School in Mineeapolis, Minnesota, students are being engaged in the classroom in a new way: Twitter. This video I found on YouTube shows just how engaging the activities in this particular english class can be.

I wonder how we could incorporate something as engaging into a more rigid curriculum such as Mathematics... any ideas?

Math Is Fun! Let me show you..

There are many fun, yet educational games out there for teachers to use. In one class this semester, we played a game called Math vs. Cockroaches, which can easily be turned into a review lesson on the slope-intercept form.

The game eliminates some Math anxiety by putting a mathematics concept in the form of a video game. I really enjoy this idea, as well as the educational purposes of it.

Interactivity 3: Generating Technology Inventory for Mathematics

This group assignment was different than any other I've ever done for a class at Montclair State University thus far. Although I did see 3 of my 4 group members in classes we share, this assignment was completed using only online communication. Like most group assignments, it required for someone to take initiative and start planning. I decided to not wait and sent out a mass e-mail to my group members, explaining what I thought needed to be done and by when, so that everyone was on the same page. After most of the group members inputted their technologies, I came up with the idea of color-coding the different categories, and lastly, organized them by grouping the colors together. We communicated via e-mail about any questions or concerns we had about the assignment, and kept each other in the loop on almost a daily basis on changes we made to the spreadsheet.

While this assignment seemed to have gone pretty smoothly, its efficiency had a lot to do with the fact that all of my group members held their own and completed their portion of the assignment by the deadline. We agreed to set the deadline to Monday night, so that all of us had enough time to write our Blogger entry before the Wednesday deadline.

I also really liked that we could view when changes to the document were made, and by which of the group member(s). It created a sense of accountability for each and every group member, wiping out any opportunities for any of the group members to “coast” their way through the project. All in all, this group assignment surprisingly turned out to be a very positive experience.

"Why Are We Learning This?"

Photo credit: http://www.glasbergen.com/math-cartoons/

It's a dreaded question asked by students in school, especially in a math classroom. "Miss (blank), why do we need to know this?" Student motivation is one of the most important aspects of a successful classroom, so we need to keep in mind that students want to learn things they don't only need to learn, but want to learn. By making the material relevant to their lives, we can better get through to them.


I thought this cartoon was a good way to sum up the fact that the way teachers sometimes believe students need to learn the material because they just need to learn it, no questions asked is very different from the way that students perceive school and learning.

Interactivity 2

"One machine can do the work of fifty men. No machine can do the work of one extraordinary man."

Picture credit:

Wade, Cindy. "Internet Puts Homeschoolers on Even Keel with Public School Monopoly." Web log post. Guerilla Homeschooling: Unschooling the Child and Deschooling Your Mind! Blogspot, Feb. 2012. Web. 14 Feb. 2012. <http://guerrillahomeschooling.blogspot.com/>.

Interactivity 1

Olivia's story is a very interesting one, but not surprising. By that, I mean that a lot of teens experiment with technology and learn to become very savvy with the various different pieces of equipment Olivia uses on a daily basis. What I found very interesting was that while Olivia did not have access to a computer in her apartment, she found ways to gain access to one, whether it was downstairs in her building, at school, at a friend's house, or even (my favorite of her resources) the Apple Store. Through research, she learned how to use HTML codes to enhance her and her Big Sister Dawn's MySpace pages. Because Olivia was so interested in learning about these topics, she went out of her way to get her hands on a computer, whatever measures it took. This is an important piece of information to know about Olivia as her teacher. The passion she has for technology can be incorporated into the classroom, and her interests can and should be incorporated into the curriculum as best as possible. By being passionate and working hard, Olivia achieved being one of the top 3 at her high school. Olivia was not the only one to have learned something from Dawn or her teachers, however. They all learned from each other, and that's the type of approach I plan on taking in my future teaching practice -- to collectively learn from one another as part of a community.


In the second video titled "Learning to Change, Changing to Learn," the students in the clip did not only use the computer to play video games. They also learned how to speak Chinese, to read/write/play music, develop a website, and to coordinate with others in a video game setting. I found it very intriguing that they went out of their way to teach themselves because they were interested in finding out more. Technology acts as a great tool for these students, helping them learn on their own about the things that really catch their interest. As one of the students at the end of the video put it, it's learning in a non-traditional way; they are given a certain amount of resources, and then need to decide which ones to turn to in order to reach their final goal.

The three technologies I chose as the most important, I chose because I use the most. My iPhone is almost always at my side, because there are endless applications on it to help me stay connected. I can send/receive e-mails almost instantly, similar to text messaging. I, like Olivia, keep my phone to stay connected with my family and friends, and use it often to check my Facebook account or Twitter. I have occasionally gotten updated on current events in the news via my Facebook/Twitter, because people have posted about them. While this can be a good thing, there's a downside to it as well: the information may not always be accurate. There is an upside to having my iPhone, however. If I ever don't understand what something means, I don't even have to be near a computer to do a quick Google search about it and inform myself in less than a minute. Although I've only had a smart phone for a few years, I can't imagine going back to a time when I did not have one.

My Macbook is also an essential piece of technology I find myself using every day. Being a college student, there's always a paper to write, research to do, etc. Having a laptop is good in that I can use it at home if I need to, but I can also bring it to class and take notes. Because I took a typing class in high school, I can type a lot faster than I can write, and so in classes that require a lot of writing, I avoid taking handwritten notes and instead type mine into a word document and print them afterwards. Also, with websites like YouTube, learning "How To" do anything at all has become much easier. If I ever forget how to do anything in math, I just have to type it into the search bar on the website and it's right there for me, with someone teaching me step my step. With YouTube, I use my Macbook similarly to the way students in the second video do, i.e. to reteach myself math concepts I'd forgotten.

Lastly, I chose the television. While I use TV mostly to relax and unwind after a long day of school and work, I can also watch the news on it, or even learn how to cook with Rachael Ray on the Food Network. Technology makes learning things faster if you are innovative enough. As future teachers, we need to be aware of this and familiarize ourselves with as many of these resources to maximize the learning of not only our students, but also our own learning.