Last week I had the opportunity to volunteer at a middle school for a family math night where students from schools in the district can come with their families and visit math stations where they can play games and learn more about math. The games are lead by mostly college students and a few staff members. I was able to work with two girls from one of my classes and it was a great experience.
The game we played was called "hit the target" and we gave the student(s) four cards to choose from and a "target" card. The idea of the game was to use addition, subtraction, multiplication, and/or division of the four cards to get to the target card. In the future I would be interested in using this activity in my classroom. A student I specifically remember was in second grade she seemed to have trouble with subtraction. From my experience in other classrooms I would have thought that in second grade students should be past the point of struggling with subtraction. Another student that really interested me was an eighth grade student who was so interested in math. She came back to our table multiple times and was excited about doing math. Seeing that in a student is really inspiring because a lot of students lose interest in math as they get into the older grades. Keeping students interested in math will be something that I strive to do in the future. I think a lot of that interest comes from the interest that the teacher shows the students.
Last year I was a part of a family math night that was part of a class. It was at a different school district which gave me a whole different experience. At this night we did a game based on the book "how big is a foot". The students really seemed to like this activity. We traced the students feet and had them measure beds they made, like the one on the cover of the book. The students were able to pick from different measuring tools and it was really interesting to see what type of measurement tools the students picked. This observation and variety of measurement tools really helped me see the students understanding. Some of the students would measure the first foot then realize that they could multiply that measurement by the number of feet in the row. I think that I would defiantly use this activity in my future classroom, the students from family math night really seemed to enjoy it and that makes me confident that a group of my future students would also like it.
I hope to organize a family math night at a school I work at in the future, they don't already participate in one. Watching the way the students interact with their parents is very important because you don't see that in the classroom and during parent teacher conferences the students are not there to show their interaction. Observing how well or how much the students interact with their parents can give you a great understanding of why the student is performing the way that they are in your classroom.
This past week we were working on programing our own games or activities on scratch. I thought the programming was a little difficult and got me frustrated from time to time. I was able to program a pretty decent but very short game in the hour and a half that I worked before taking a break form the frustration. The idea of my game is to lead the dinosaur to the healthy food and avoid the junk food. My original idea for this program was to have 3-4 different stages each were the food got a little faster. For the lack of full understanding of the website and programming in general I was unable to finish the entire game, at this point. One thing I struggled with that kept me from moving forwards was I could not figure out how to make all of the fruit disappear once I had eaten all the healthy food. My main goal was to figure out how to get to the next stage without having to eat the junk food, I was unable to accomplish this and due to the frustration is caused I have not gone back to take a second try. I am sure soon enough I will try again but as of now, here is STAGE ONE.
After the sharing we did of our programs in class we had a class debate on if we would use programming in our classrooms or not. I was a head spokesmen for the side of the debate where we decided that programming should not be a part of our classrooms. We discussed that there is so much more math that is embedded into our curriculum that there is more important things to focus on then programming. We did agree with the other side of the argument that it could be used in the classroom as a introduction then the students could use it at their own leisure. It could be a fun activity for those who are interested but since it is not a necessary skill for all students it should not be a requirement. If every school was to introduce this at some point in their curriculum the students that were interested would have a chance to try it out. I think that in the higher levels or schooling, more into middle and high school they could make computer programming an elective and that would give the students who are interested a better look inside. So, now I think that I could use this in my classroom as a hook for some parts of math. I think with the grades I want to teach this site might be a little too advanced but if I was able to find a site that was for beginners it might be something they could try. But as I said before, this would just be something for fun like an extra choice.
Looking through the past 8 days of work with hexagon types we have done in class, I have realized how challenging it is going to be to teach this material. I don't remember any specific lessons or activities that I learned in elementary school and I want to make that a different story for my future students, but how?
Starting with the basics is essential, along with not teaching just the "regular shapes". Too many students get the idea in their head of a regular hexagon and can't get out of that hole, sadly I am one of those students. I have been working hard to see that a hexagon is a shape with six sides and six angles that don't necessary have to be congruent, but also can be. As a college student in a class full of future elementary teachers it has been a challenge to take my thinking back to the time I learned geometry for the first time. It is hard to look through the perspective of a child who has little to no knowledge of geometry shapes, like hexagons. To put ourselves in the places of our future students, we started creating hexagons and our own hexagon types. Each group of students came up with a new type and pitched it to the class so we could get a "standard" list of our hexagon types. Finding examples and non-examples was where the real fun started. It's so interesting to make up your own shapes that look like nothing you have ever seen before, but still fit the properties of a hexagon. Running through this activity with college students is a lot like teaching the elementary students real hexagon types and properties. Understanding the properties of each type helped me better my full understanding as well as move me forward in the Van Hiele levels, which is something I will need to do with my students.
It is time for teachers to get away from the cute activities that are fun for the students and get into the real meat of teaching these shapes. Teaching for understanding is something teachers struggle with, especially when trying to be creative. There is still room for creativity we just need to make sure we are doing the right types of activities, always touching on the big ideas. During our discussion we thought of some big ideas that should be a part of our hexagon lessons, as well as all math lessons we will teach:
In class this week we discussed and practiced the Van Hiele Levels. In the 1950s, a husband and wife team of Dutch educators, Pierre van Hiele and Diana van Miele-Geldof, developed a theory of how children learn geometry which is still widely accepted today. Through their research, they identified five levels of understanding through which children move sequentially on their way towards geometric thinking.
Level 0- (Visualization). The student reasons about basic geometric concepts, such as simple shapes, primarily by means of visual considerations of the concept as a whole without explicit regret to properties of its components.
Level 1- (Analysis). The student reasons about geometric concepts by means of an informal analysis of component parts and attributes. Necessary properties of the concept are established.
Level 2- (Abstraction). The student logically orders the properties of concepts, forms abstract definitions, and can distinguish between the necessity and sufficiency of a set of properties in determining a concept.
Level 3- (Deduction). The student reasons formally within the context of a mathematical system, complete with undefined terms, axioms, and underlying logical system, definitions and theorems.
Level 4- (Rigor). The student can compare systems based on different axioms and can study various geometries in the absence of concrete models.
Every teacher needs to learn how to understand our learners, and understand what questions to ask to help move students to the next level. Although we are always passing though the levels, typically grades K-8 are in levels 0-2. Watching students move through these levels is when they are understanding for example that a square is a square but that a square is also a rectangle.
I read the article "Developing Geometric Thinking through Activities That Begin with Play" and I can't help but think about when know when to start moving your students through these levels. I read on and discover that this all depends on the students' level of thinking. This makes all the sense in the world because how can you teach a student at a level farther then they have mastered.