“Are we going to do something fun in math today?”

I just completed the online course in Probability and am looking forward to my next course which is Statistics. I gain a depth of understanding that I did not previously have with every course that I take in this program. In each class I learn strategies for teaching and how students learn best which helps me to become a more effective teacher. In the Probability course I learned the importance of addressing both theoretical and experimental probability. A simple but powerful way to do this is by allowing students to play games of probability. How many times have students greeted you with the question “Are we going to do something fun in math today?” I have been asked this question countless times and now, when we are beginning a unit on probability, I can finally answer “Yes!” As students play a game, you can assess their understanding of probability by asking them the simple question “Is this game fair?” When they attempt to answer this question, one can ask them to explain how they know whether or not the game is fair. One can easily extend this activity by asking students to design a fair game. This hands-on experience helps students to learn about and understand experimental and theoretical probability.
In this course we had the opportunity to design a game that we could use in our classrooms to help students understand experimental and theoretical probability. We were asked to play this game with some children over the summer and report on our findings. I played the game I designed with children from the ages of 5 to 16 and saw the benefits and learning that occurred for children of all ages. One of my favorite memories this summer is playing the probability game on the beach with a daughter of one of my friends. The game was very engaging and the young lady did not realize she was part of a mathematical experiment. When I asked this child to tell me about her favorite part of the game, she simply stated “I liked that we could play this game on the beach and it was FUN!” I learned a great deal from this activity and plan to incorporate the “Fair Game” activity into my lesson plans next year as it is a powerful learning tool.

“Is it a Square?”

In each on-line class that I have taken at Lesley, I have been given investigations and problems that I can use immediately in my classroom. Every week, I anxiously wait to see what problems I will be given to investigate. I am able to select one or more of these problems and give them to my students to explore and solve. I often give one of the problems as a challenge problem. Some of my students have become hooked on these problems and are disappointed if I do not have one for the week. I have been amazed to find some of my students who are not motivated to finish other assignments tackle the challenge problems with enthusiasm. Their passion is contagious. They often want to discuss their progress with me and other students become interested. Soon more students ask for challenge problems to try.
While taking Geometry 1, I was working on a problem for my class. I typically do not give my students a problem until after I have solved it. A copy of the problem was on my desk and another teacher saw it and asked about it. Students overheard our discussion and asked for a copy of the problem so they could try to solve it. I warned them that I had not yet completed the problem, but their curiosity was peaked. It is not often that eighth grade students plead with me to give them a math problem, so how could I say no? I agreed to make copies of the problem during my preparation time. While making copies, two other teachers saw the problem and asked for a copy as well. The problem was simple. There was a diagram of a shape that looked like a square and the question simply was “Is it a square?” It was made up of smaller squares and some additional information was given. Students were also asked to explain their answer. I could see that this was going to be the problem of the day at our school so I solved it during my preparation time. I watched amazed at how engaged students were in trying to figure out this problem. They worked collaboratively and were very creative in their many different approaches. They celebrated when they came up with a solution and were able to prove their answer. They wanted to share their solutions with me and give the problem to their classmates who had not yet seen it. At the end of the day, one of the teachers who had asked for the problem earlier came to my classroom door and simply said, “Is it a square?” I replied, “What do you think?” Our answers matched. I then told him about a student who had solved it in about three minutes which was the record for the day! He shook his head in amazement as he walked away. I am grateful to have a new source of rich problems for my students. These problems bring math alive and help my students practice true problem solving skills. After one of my students solved a challenge problem I was rewarded with her final comment which was, “I think that is the coolest thing I have ever seen in math!”

“I Don’t Get What They Don’t Get!”

I was working with my co-teacher and we were planning math lessons for the next week. We were to begin a unit on linear equations which we had taught many times before. Many of our students struggle to understand the concept of slope even though we have come up with many creative ways to introduce and explore linear functions. Despite our best efforts, we were not reaching all of our students. My co-teacher turned to me and said “I don’t get what they don’t get!” That was a pretty profound statement coming from her considering that she was an expert in understanding how to help students “get it”. This made me pause and consider what I had learned in my on-line classes at Lesley. I remember learning that students need a strong foundation in ratios and an understanding of proportional reasoning in order to be successful in learning about slope. Was this part of the problem? We decided to give our students a pre-assessment and learned that our students were weak in proportional reasoning. As a result we spent several days exploring proportions and using proportional reasoning to solve problems. Students were finding success with this work because they had been exposed to ratios and proportions before and just needed more practice to solidify their understanding. The day came when we moved onto slope. A day or so into our explorations, one of our students practically stopped the class. He stood up and announced, “Wait, just a minute here. Could you say that slope is just a ratio and that’s all there is to it?” I gave this student a high-five and felt great relief. At times during the past week, I wondered if the work with proportional reasoning would make an impact. This was the first hint that it had indeed helped. My students were having less difficulty with the explorations and needed less support. Follow-up assessments showed that they were indeed learning and were “getting it”. We still had students who required interventions and support, but overall, we had found a better way to introduce a difficult topic.

I am now halfway through my on-line masters program in math at Lesley. This is just one example of how the math classes I have taken thus far have impacted my teaching practice. I am finding that with every class I gain new insights about student thinking and understanding. This allows me to develop tools that I can use to help guide my students toward mathematical success and true understanding of concepts. When I can figure out what they don’t get, then I have the opportunity to make changes that will help me become a more effective teacher in the classroom.

Why Online?

I have just completed my fifth on-line class in the M.Ed. in Mathematics Education at Lesley and am beginning my sixth course. I will complete this program in two years, taking one class at a time. I have been asked by my colleagues at work how I feel about being in an on-line program. Since I am half-way through my coursework, I am in a position to speak about some of the benefits that I have found from being in the program at Lesley. Every class that I have taken has aligned to what I teach as a middle school math teacher. Each professor has been excellent, not only because they are knowledgeable about the content, but because they also have experience in the classroom. They are passionate about their areas of expertise and go above and beyond to help everyone in the class grow as a teacher of mathematics. It is hard to explain how one makes a connection with on-line classmates so quickly. It happens because we are afforded so many opportunities to interact. We share mathematical solutions, teaching strategies, and work on group projects. We give one another links for teaching resources, trade lessons and discuss our successes and challenges. Most importantly, my classmates provide support and help whenever I need it and I am grateful when I am able to do the same for them. With the start of each class, I am excited to “see” familiar faces and find that I quickly make connections with classmates I am meeting for the first time. The online classroom allows me to experience diversity; my classmates come from all over the country, or I should say all over the globe. The on-line classroom experience is enriched because of our varied backgrounds. Collectively we teach in different places, use different curriculums, and teach at different grade levels. I picked this program initially because I live in a somewhat remote location and it would be a challenge to commute and attend class in person. I also liked the idea of being able to schedule the time when I would “attend class” and complete my coursework. I did not foresee all of the other advantages. I have grown in my understanding of mathematics and as a teacher of mathematics. I have been humbled as I continue to learn how much I have yet to learn!

New Perspective

My definition of equity has changed greatly from the beginning of this course until now. My initial thought was that equity in a classroom meant treating students fairly and providing everyone with an equal opportunity to learn. Making sure I call on the boys as much as I call on the girls, for example, is a big part of that. I thought that by pulling popsicle sticks with the student’s names on them I was fulfilling my duty of creating an equitable classroom. Equity also meant differentiating instruction so that all students are able to access the curriculum at a level manageable to them. While all of that still applies, my current definition of equity has expanded to include much more. My original thoughts were focused around the students; I was not factoring myself and other staff into the equation. Equity encompasses students, parents/guardians, teachers, as well as other support staff. Aside from the classroom core teachers, other teachers and staff may include special educators, ELL instructors, guidance counselors, speech and language pathologists, school psychologist, social worker, reading specialist, etc. It is each student’s job to set challenging, yet obtainable, goals that they’ll strive to either reach or beat on a daily basis. It is the parents/guardians job to keep up-to-date with what’s going on in the classroom and provide a supportive environment for student learning at home. Teachers need to continue to better themselves as educators by seeking out professional development, as well as any other opportunities that may come their way. Teachers and other support staff need to meet frequently so that everyone is “in tune” with what’s going on (or what’s not going on) with their students. All parties involved serve as a piece to the equity puzzle. When one or more pieces are missing, equity cannot be achieved. Everyone needs to be an active participant and fulfill their duties in order to create equity.

Science Talks

At the beginning of the equity course we were each asked to come up with our own equity question to investigate. Examples of some of our questions are:
- Do students participate more if the science lesson caters to their learning style?
- Which gender, boys or girls, are earning the higher report card grades in my seventh grade science classes?
- Who takes the leadership role during small group work, boys or girls?
- How do lower level students compare to the other students when it comes to participating in class and doing labs?
- Do girls or boys have the scientific knowledge and attitude needed when they enter a departmentalized 4th grade science classroom?

In addition to collecting classroom data, we’ve also been on the search for related articles to help support our findings. Information we find pertaining to our question often leads to pondering more questions. Cindy Ballenger mentions something similar in her article titled One View of “Does a Plant Grow Every Day?” The focus of the article is on “science talks,” which are whole class discussions based around questions that arise from the children. They are not questions that have a definite answer; rather they are speculative and lead children to “trying to imagine phenomena, to connect a variety of events or experiences, to theorize about why and how.” Throughout a science talk, students use their prior knowledge as they draw upon their ideas and engage in a meaningful conversation with their peers. As mentioned above, “any questions they answer usually lead to more questions.”

One of the features of a science talk that makes it such a success is that the teacher’s main role is to facilitate student turns. Some teachers are more involved than others, but generally the teacher is not the main participant. Other teachers may feel that by being more involved they can guide the students in the direction they want and can interject with questions as they please. Another important feature of a science talk is that “students talk to each other and in a manner that is more associated with social situations outside of school.” In their discussion about whether or not plants grow everyday, a student in Ballenger’s article (3rd or 4th grader) commented that “I think I can kinda’ see myself grow because one day I putted on my socks and they was too small for me so I can fit in my mom’s socks now.” She made a connection between a plant’s growth and her own growth. Personally, I would like to incorporate more science talks into my lessons next year. Students who are less likely to raise their hand may contribute something to the conversation they would otherwise be more hesitant to say. Ballenger mentioned that these children “often add significant depth to the learning taking place.”

What Happens Inside The Classroom Is Just As Important As What Happens Outside The Classroom

This past week in Sharon J. Lynch’s book, Equity and Science Education reform, we read about how a student’s family, peers and surrounding community all influence student learning. We arrived at the understanding that science equity goes beyond the day-to-day happenings within a classroom. Who students interact with outside of school is just as important as who students interact with inside of school. As educators, it is important for us to be as aware as possible of the life our students live outside of school. We are sometimes quick to judge a situation, but we need to remember to take a step back to understand where the child is coming from. Children are products of their environment. A child with a tougher home life may not be as “put together” as other children. Understanding each child is a big part of the foundation of creating a classroom environment that supports equity. The most important thing for us to do is show the students we care. My principal's motto is "kids don't care how much you know until they know how much you care." If our students know that we care about them, then they should look forward to coming to our class each day. Some students spend more time with their teacher(s), peers and other staff more than they do with their own families. The classroom may be where they receive the most guidance, support and structure. Whether or not a child in need decides to seek out his/her teacher for help in a time of need is unpredictable, which is why showing the students we care is so important.

On another note, here are some common questions (and my answers) asked by those interested in the Science in Education online experience…

Do you feel as though you could have done the work you have had in your classes without being a classroom teacher or would it have been difficult?

Certainly, it does help to have your own classroom while completing the online courses, but it is definitely doable without one. Do you know of any elementary or middle school aged children to work with if you don’t have your own classroom? A relative? Family friend? The work done in the classroom setting can easily be done with students around the same age in a different setting. Working with students does not take place each week. It ususally happens toward the end of the course. You use what you've learned and then apply it to working with children.

Have you found that you have fostered relationships with people in your classes, without having met them, easily?

YES! During the first course I took (Try Science) I exchanged numbers with a few of the girls in my group to talk about an assignment. As it turns out, we all don't live that far away from each other so over the Christmas break we all met for lunch. It was so nice to put a face with a name! It's been great... we call each other often when we have questions, comments, concerns... I love it! We all began at the same time and have signed up for the same courses since.