Wednesday, October 28, 2009

Differentiation of Math

As a classroom teacher one of the challenges I face is finding the time and resources to differentiate instruction in a way that is truly effective so that all students are able to learn at their level. My typical math classes of about 26 students consist of a diverse range of learning styles and needs. There are usually about 6 students on IEP's, 8-12 Title One students, several Hi-Cap students and students who are in the range of being at gradelevel. The challenge this presents for math is finding activities that are both engaging and appropriate so that students are able to work the zone of proximal development.
In the Math Masters Program, every concept we have explored has been approached from a very multi-modal aspect. The activities are geared specifically toward building conceptual understanding. Many of the activities we do provide a variety of ways to make connections and build upon prior understanding. A great example is; currently in my Geometry class we are studying about angles and constructing perpendicular and parallel lines to create a transversals. Instead of simply using a compass, we approached the concept from several aspects. We used paper-folding, which was a very tactile,concrete way to see the "why". We also did a compass construction and had to tie those two methods together by explaining why the compass construction worked, and then we used a computer program to create and construct the same figures and properties.
By exploring this concept in multiple ways, it showed how you can approach differentiation in the classroom by using non-traditional methods of exploration that build on conceptual understanding, and appeal to different learning preferences and needs. My own understanding of the concept has deepened immensely by having experienced a familiar concept in new ways. This particular lesson has given me a whole new set of activities for which to approach differentiaion when I teach Geometry.
I would like to add that the experience I've had in Geometry class has been typical of my experience in all the math classes I've taken. There are so many approaches to learning math that are rich, engaging and multi-modal and they are an absolute necessity for differentiating instruction compared to some of the more traditional methods that have been taught in classrooms in the past. These experiences have directly effected how I design my lessons, which has had an immediate effect on student learning. It's been a very exciting and rewarding journey over the past year. As always I look forward to the classes ahead.
Jennifer Nelson

Sunday, October 25, 2009

We all can't wait until Monday!

After completing a self-evaluation three weeks ago, I have found that my science instruction has not followed the model of inquiry very closely. I have been engaging my students in traditional, old school, recipe-like labs that require the students to follow a list of instructions in order to reach the predetermined goal. These types of lessons are filled with mostly right and wrong answers. The activities do not give the students a chance to develop, explore, or test their own ideas. My students are missing out on inquiry, missing out on real science.
Fortunately, I am now learning how to adapt my large inventory of science activities, which I’ve been using up until this point, so that they can start to shift towards learning through inquiry. This semester’s class is focusing on improving classroom “facilitation” (not instruction-move away from “teaching”). There are two strategies that I’ve already incorporated.
The first strategy is one that I call “What & Why?” It’s a form of questioning used to probe for student ideas. I have started to use this when my students are in the predicting stage of their investigations. More specifically, I ask them “What do you think? & Why do you think that?” when making their predictions. I’m trying to stress that their reasons for their prediction are just as important as their hypothesis. I’ve seen this become a great asset to discussions before and after the experiment/test portion of the investigations. Just last week, I had a discussion with my classes about the results from their “Metric Mass” investigation. They were faced with surprising evidence that contradicted their predictions. They could actually share why they were wrong by looking back at their written reasons. They could see how different their ideas were before testing their hypothesis.
The second strategy I’ve applied to my “facilitation” of inquiry is one that encourages formation of student ideas. I introduced a new “Journey North” project by passing out an unknown object (Emperor Tulip Bulb) to pairs of students. (Thanks Sally Crissman!) I did not tell them what it was, but I asked them to record any questions they had in their new science journal. We discussed the questions they had without answering them. I took one of the questions, (What is it?), and turned it into a “What & Why” prediction. This was followed by a “Where & Why?” prediction about where I got the objects. The students recorded and shared a wide variety of ideas about what the object could be. They thought it could be an onion, garlic, potato, seed, nut, plant, man-made object, radish, or a turnip. Only three students were convinced it was some kind of a bulb. As the students passed in their journals and exited the classroom, they begged me to tell them what it was. I said, “We’ll find out on Monday.” I spent about $17 on the above produce that I plan to share on Monday. They will be able to see if their predictions were correct… without me telling them. We all can’t wait until Monday!
-Mark H.

Friday, October 23, 2009

Examples for direct classroom use


A quick background – I am a mother of 3 school age children, went back to work recently after being a stay-at-home Mom, found my dream job as a Technology Integration Specialist (K-8) and don’t have the ability to physically attend classes for my desired Master’s degree (not enough hours in the day!). The solution – Lesley University’s TIE Master’s program where I found superior professors & classmates from around the world and courses on topics that I can implement right away in my classrooms.


We are teaching our students about the idea of “global community” and “flat classrooms” in which the physical walls of the classroom can be broken down through use of technology so that students can see and interact with others across the world. Imagine how empowering this is to a student when they realize their voice and their work can be seen and heard by an audience greater than what we find in the confines of the physical classroom!


Let me share a couple of examples with you. In ECOMP5004 (Technology in Language Arts) we did a version of the Monster Exchange. Paired up with a partner, each of us created a monster. I used the drawing tools in PowerPoint. Next we wrote and revised descriptions of our monsters and exchanged them (our pictures were not posted yet). From the written description, I had to draw my partner’s monster. I posted my picture, she posted the original, we compared them, and reflected on the process. She did the same for mine.


This is something I can implement in a classroom immediately. Having the first hand experience of being a student in the process gives me insights that will be invaluable in bringing the activity into a classroom. This was a fantastic assignment that brought strong literacy skills together with technology.


A second example comes from ECOMP7010 (Emerging Technologies). I am fascinated with Google Earth and all the potential this resource has for use in the classroom (such as Google Lit Trips). However, it was a bit daunting to try tackling the learning of such a vast resource on my own. An assignment in this course provided me a structured activity to explore and create. Along with the guidance of my professor and input from my peers, I tackled Google Earth. I can now teach my students and help staff members create Google Earth trips and all are enthusiastic about getting started!


Challenge yourself to learn about the educational technology that fascinates you and learn in a constructive, positive environment. Learn to use technology to enhance curriculum rather than just decorate it. Check out the TIE program at Lesley. It was one of my best decisions.

Sunday, October 18, 2009

Factor Lattice models

Last spring in my number theory class, one of my favorite activities we did was creating 3 dimensional factor lattice models. I'm just about a week away from implementing it with my current students. You use toothpicks (primes) and clay (vertices)to create a 3 dimensional model for a number. I wanted to share this activity because many of us from grades 4-12 are beginning our school year by either teaching or reviewing factors,prime factors and greatest common factor, least common multiple. The activity I will share with you is such a fantastic tool for exploring and making connections across concepts within math and allows students the opportunity to experience these concepts in a very tactile way. There are also endless patterns within the models for students to discover, and a nifty way to tie in technology.
You begin by choosing a number,and finding it's prime factors. Next you start with a vertex from which each prime factor(color-coded toothpick)will extend in a different direction. (Two prime factors will result in a 2 dimensional model, and 3 will result in a 3 dimensional model.) From there, each toothpick represents a multiple of the prime, with a vertex connecting them. Once your model is complete, you can use the primes and vertices to multiply and label all remaining vertices. When finished, the number of vertices is the number of factors, and each factor is labeled on the model. From there you can determine the GCF and LCM of the number by navigating through it.
Students can then create a digital model using Microsoft word, and write about the process. My class did these last year, and we displayed them in the office hallway showcase and had many visitors that wanted to hear about them. The really great thing was that the students could talk about them in detail and relate the math concepts they learned. It was truly a learning experience that allowed all students to explore and experience math in a new way.
I realize that the directions for making these models is not complete in my post, but I just wanted to give enough of a description so that the general idea was clear. If anyone would like step by step directions for this along with a photo of an example, I'd be happy to send that via e-mail.
And finally, I would like to say that this project is just one example of the kinds of exploratory learning we have done during classes in the math program and how beneficial they were to my own understanding, and how easy they were to incorporate into my own classroom. My e-mail for anyone interested in the activity is: jnelson7@lesley.edu Happy Teaching! Jen Nelson

Sunday, October 11, 2009

I can talk the talk, but can I walk the walk?

It’s now been a month since I’ve been back at school, and I’ve got to be honest here. I have to admit that I haven’t been working too hard at trying to incorporate what I’ve learned from Lesley this past summer. I haven’t been writing little notes to remind myself to "give reason", or to create lists of probing questions to ask my students. I haven’t been sitting down trying to come up with new ways to get my students to share their ideas about science. Many of those things that I thought I’d be doing to make my lessons better, aren't even getting a second thought. I guess I should feel somewhat guilty, but I don’t.

I don’t feel guilty because I don’t have to think twice about what I learned this summer! Everything is coming out naturally. I’m asking my students to make their predictions and support them with their own reasons. I’m listening to their ideas and asking, “Why do you think…?” The words “tell me more” roll off my tongue. On some occasions, I consciously caught myself giving reason to “abstract” student responses, which in the past wouldn’t have caused hiccough in the day’s lesson. It has been so easy to follow the path that I tread this summer. Students in my classroom are already benefiting from Lesley almost as much as their teacher.

I’ve found the easiest way to get my students to share their ideas through predicting! I don’t know why I rarely did this before, but I’ve only now started asking my students to give reasons for their predictions. Now, I want to know why they predicted something to happen just as much as I want to hear their prediction. For example, we investigated leaves using qualitative and quantitative observations as few weeks ago. The students needed to predict what kind of leave they might find on a tree, in the woods, behind our school. Then they were asked to supply reasons for their hypotheses. On the first day, they drew pictures and wrote down predictions for shape, color, length width, texture, disease, insect damage, and etc. They also had to share that all important reason for each prediction they made. I liked these: “The leaf will be green in color because it contains a green pigment called chlorophyll” Or, “The leaf will be multicolored since leaves change color in the fall.” (These questions would set up so many probing questions to explore.) I didn’t accept any one-word answers. They had to tell me more! The second day, involved the data collection in the field. On the third day, I passed back their papers to compare their predictions and actual observations. I got quite a surprise as each student was handed his or her papers. The kids were visibly shocked by what they saw on their sheets. Some gasped when they realized how far off they were, while others couldn’t believe how close there predictions were to the actual leaf collected out back. I heard comments like these: “What was I thinking?” “I knew there were oak trees out there, and that’s what I found!” “I thought the leaves would have changed color by now!” “I think a caterpillar was eating my leaf.” We had a great time, sharing their ideas as well as the reasons why! I want more!

-Mark