Inquiry-Based Learning through "Vroom, Vroom!!" Activity

Retrieved from https://goo.gl/Vwa70F

This week in our Mathematics Education class we did a great activity entitled "Vroom, Vroom!!". This activity included wind up cars and meter sticks. The goal of the activity was to develop a model that is accurate enough that when given a distance to travel, you are able to calculate exactly how far you need to pull the car back. The class was split up into groups and we were told that all the groups were going to be competing against each other at the end of the activity.

Our group started by collecting some data. We pulled the car back different distances and recorded how far the car traveled. We decided that we would pull the car back 5cm, 6cm, 7cm, 8cm, 9cm and 10cm. We choose these values because we found that when we pulled the car back 4cm or lower, it did not travel very far at all. These values were a good way to start to collect some data on how the car traveled after each pull. Once we got all this information recorded, we were able to make a scatter plot graph and find a line of best fit. Then with our knowledge of linear relations, we were able to create an equation that would model the distance traveled for our car.


Now came the competition part of the activity, which was the most exciting part as everyone got very competitive. We were told that we wanted the car to travel 210cm. So we went back to the equation that we created previously and substituted 210 in for the y-value. After some simple calculations, we concluded that we would need to pull the car back approximately 11.6cm for it to travel 210cm. In the end, our car did not travel the farthest, but it was a lot of fun competing against our classmates.

 I could absolutely see myself using this activity in my future math classroom. It would be a great way to get students to work together and collaborate while investigating linear relations.

This activity would be an excellent activity to use in the classroom as inquiry learning. Inquiry-Based Learning is described as "an approach to teaching and learning in which the classroom environment is characterized by the student being the active participant while the teacher’s role is decentralized" (What is Inquiry-Based Learning?). Which means that students are using investigation to discover their own learning, rather than being lectured by the teacher. Inquiry-Based Learning has been shown to help students gain a deeper understanding as they are figuring out the mathematics for themselves (What is Inquiry-Based Learning?). I think it's very important to allow students to learn through self discovery and investigation, as not all students benefit from being lectured. That being said, I also think that some students do benefit from the structure of a lecture-based lesson. Overall, it is important to give my students a variety of instructional techniques. In addition, to knowing how they learn and what works best for them.When this is done, we can continue to strive to be the best teachers we can be.

Technology and the Mathematics Classroom

Hello everyone!

This week in our Mathematics Education class we focused on technology in the classroom. According to the Ontario Mathematics Curriculum, "Technology can help to reduce the time spent on routine mathematical tasks and to allow students to devote more of their efforts to thinking and concept development.". Despite this, in my school experience, the only technology that I used in my mathematics classrooms was graphing calculators. Most of my high school mathematics classes involved paper and pencil techniques. While completing my undergrad I was able to take a class that focused on Technology in the Mathematics Classroom (MATH 4P96 at Brock University). This class opened my eyes to the world of mathematics technology. Through that class I was introduced to Buzzmath, Geometer's Sketch Pad, Geogebra and Journey Through Calculus; just to name a few. This was when I really started to see the importance of incorporating technology into my mathematics classroom.

Retrieved from http://support.desmos.com/hc/en-us

Throughout last nights class we were able to explore and play around with Desmos and Geogebra. Both activities were engaging and got the whole class involved in the mathematics. We started with an activity on Desmos called Polygraph. This online activity had a similar feel to the game Guess Who? which is played in twos by asking questions to your opponent to guess what person they had chosen. But instead of faces, we were asking questions about parabolas. One partner would chose a graph while the second partner would ask questions and slowly eliminate graphs from their screen. I found this activity very engaging because it didn't feel as if we were doing math, it just felt like a game. But we really were practicing our mathematics skills; as we were articulating questions to ask and as we were answering those questions. This activity requires students to apply their knowledge of parabolas in a fun way. I would absolutely use this activity in my mathematics classroom because I think that it would be a great way to get all the students involved and practice their mathematics skills.

Retrieved from https://mix.office.com/watch/tkg75uzi32m1?lcid=1033

The second activity was done as a class with Geogebra. Amy Lin showed us a video of a boy throwing a basketball, but we only saw half the video leaving us unsure if the ball went in the hoop or not. This started a class discussion about whether or not the ball went in the hoop. After a few minutes of discussion, we opened up Geogebra and started to model the path of the basketball to see if the ball would make it in or not. After modeling, we watched the whole video and concluded that the ball did indeed go through the hoop. This activity was great because it got the whole class involved in the math as we were all interested in whether or not the basket was made. This activity would be great to use in the classroom as a class activity. It required the students to work together to solve the problem.

After completing these activities and having time to reflect, I understand the importance of incorporating technology into my mathematics classroom. Tools such as Desmos and Geogebra encourage students to become more engaged in the mathematics content. When students are more engaged in the content, they will become more curious and excited learners.

Student Learning and Closing the Gap

Hello everyone! I hope everyone has had a wonderful Thanksgiving weekend surrounded by friends and family.

Last week in class we focused on techniques that we can use to help those students who are struggling in mathematics. This is very important to think about because we will have students who have difficulties with math and we need to know how to help these students become successful. According to Growing Success, as teachers it is our responsibility to "ensure that educational programs are designed to accommodate those needs and to facilitate the child's growth and development." This means that schools and teachers are ensuring that all students are growing and learning no matter what level he/she is at in their education. One way this can be done is through the use of modifications and accommodations. According to Growing Success, modifications are "changes made to the grade-level expectations for a subject or course in order to meet a student’s learning needs." These may include expectations from different grade level or a modification of the present grade level expectations. While according to Growing Success, accommodations are "changes in procedures that enable the student to demonstrate his or her learning." These could include more time on a quiz or test, allowing the student to work in a resource room or placing the student near the door so they can easily go for a walk if they need to.

Image retrieved from https://goo.gl/6drXNC

One of the first modification resources we were introduced to last week was the Gap Closing Resources through EduGAINS. These Gap Closing resources aim to assist and give additional support to students who are struggling in mathematics. As the name suggests, they aim to close the gap between students. In class, we were given two Gap Closing packages on Fractions, an Intermediate/Senior Student Book and an Intermediate/Senior Teacher Guide. The Teacher Guide including a list of Grade 9 expectations that linked to fractions and possible reasons for why students may be struggling. The book also contains diagnostic assessments, instructions on how to use the resources and a series of "thinksheet" answer keys. The Student Book contains the diagnostic assessment and a series of "thinksheets" that students can use to improve their fraction skills. These resources can be extremely useful to teachers because sometimes it can be hard to find the correct resources that will help struggling students and these resources were designed specifically for that purpose. 

In addition to teacher and student packages, the site also provides Gap Closing ePractice activities which allow students to practice their skills. This resource is excellent for students who have access to a computer and need that extra practice outside the classroom. This is just one resource that can help teachers provide modifications for students who need them.

Gap Closing is just one of many resources that can be found to help modify lessons for struggling students. Another resource that we discussed in class was TIPS4RM which stands for Targeted Implementation and Planning Supports for Revised Mathematics. This is another valuable resource that provides lesson plans and sample activities to use in mathematics classrooms, particularly applied classrooms. 

Overall, after this week I feel as if I am more prepared to enter a classroom with many different ability levels because I have been provided with a number of resources and sites that will guide be through the modification and accommodation process.

Hope everyone has a great rest of their week! Cheers.

Differentiating Instruction through Open-Ended Questions

Hello again, I hope everyone has had a good week so far.

This week in EDBE 8F83 we dove into the concept of open-ended questions. As we discussed in class, open-ended questions are questions that have many different strategies and answers, and suit a broad range of ability levels. In addition, in the case of math focused open-ended questions, they need to be focused on math that matters (Amy Lin, Personal Communication, Sept. 29th 2016). These are not to be confused with open-routed questions which involve one question, one answer and many different ways to get to that one answer. I know in the past I have mixed up these two, so it is important to note that these are different kinds of questions.

An example of an open-ended question would be:

The slope of a line is negative and travels through the point (5, -1). What other point is on this line?

In my past experience with mathematics I don't have much experience with open-ended questions. If I think back to my high school math experience, I don't remember my teachers giving my classes open-ended questions. And if they did, they weren't very memorable and didn't stick with me past high school. Once I got to university, there were no open-ended questions in sight. There was always a question with one answer and one answer only. University mathematics was very black and white.

Now that I have finished my undergraduate degree and am completing my Bachelor of Education, I am starting to truly understand the importance of using open-ended questions to differentiate instruction. Questions of this format "show children that their teachers trust them to have good ideas, think for themselves, and contribute in valuable ways." It enables students to take control of their own learning and take it in the direction that they see fit. These questions still aim to teach students a specific concept, but allow them each get to the understanding of that concept using a unique path. Open-ended questions get the entire class involved in the lesson by starting meaningful conversation about the topic at hand (What is Open-Ended?). Each student may start with their one unique way of solving a problem, but by the end of the discussion they may walk away with many different ways to answer the problem. Open-ended questions allow all students, regardless of learning style or ability level to get involved in class discussion. This changes the classroom environment from a lecture style where the teacher has all the information to a environment where everyone, including the teacher is learning from each other.

This image visualizes how each learner is different and unique in their own way.

 Retrieved from https://goo.gl/F1Ce1W

Additionally, in order to accommodate for the many different learners in each classroom, teachers need to make sure that their assessments also are differentiated. This is especially important in mathematics because often teachers gravitate towards tests and quizzes as the only assessments of learning in their classroom. But the reality is, not all students preform well on tests. Many students benefit from other forms of assessment in order to evaluate their learning. As we talked about in class, there are many different assessment techniques that can be used in mathematics other than tests and quizzes. Some examples are observations, discussions, interviews, and group problem solving assignments. By providing a variety of assessment tools teachers can accurately assess student learning in their mathematics classroom.

Overall, this week I learned that differentiating instruction and assessments is extremely important. By focusing on open-ended questions, teachers can give each student a chance to contribute to class and allow students to learn from each other. By incorporating open-ended questions into my classroom, I hope to help each student enjoy math class.

Making Connections and Incorporating Maniplulatives

Hi everyone!

I hope everyone had a great week, I know for myself school work is starting to pick up and I am feeling like I am a lot busier.

This week in class we started with an activity in which we were put into groups of 4 or 5. Each person was given either a word or a number. As groups we were instructed to make a sentence using all the words or numbers that we were given. The sentence was suppose to tell the rest of the class something about our group. My group was given the following words; almost, percent, 40, and 80. After a short discussion and brainstorming session my group came up with the following sentence: "Almost 80 percent of our group is blonde and 40 divided by 10 is the amount of people in the group". Kinda lengthy, but it got the job done.

Retrieved from https://goo.gl/rYHFJE

I really enjoyed this activity as an 'ice-breaker' because it got us thinking creatively as a group. I could absolutely see myself using this in my classroom. I think it would be a great way to get students to make connections between the different mathematical concepts that are being discussed in class. This activity also gets students up and out of their seats. This is important especially in mathematics classes because traditionally students in these classes are asked to sit the entire time. This can be very problematic for students who identify as kinesthetic learners. As stated in the article, Move Your Body, Grow Your Brain, by getting students up and moving encourages them to be more focused and less distracted during class time and in their learning.

In addition, we also talked about manipulatives and how they can be incorporated into the classroom. We were provided with four different activities they we could use in our own classrooms. The activity that stood out to me the most was the activity using pennies, chocolate and candy. Now initially this activity caught my eye because of the sweets that were involved. But after reading through the activity, I tried it out and really enjoyed it. I could really see how a student who is very visual could benefit from this activity.

Retrieved from https://goo.gl/h4GPIm

One thing that I realized as I was reflecting on my experiences with maniplulatives was that sometimes they worked for me and sometimes they did not. For example, as a Grade 10 student I remember using algebra tiles and absolutely hating them. They just didn't help me learn, because I was able to understand by just looking at the numbers and equations. But despite this negative experience, I was able to realize it is important to provide maniplulatives as an optional resource for students. Each student does not necessarily have to use the maniplulatives but by providing them to students, I will be giving them the opportunity to learning in their own way. Which is extremely important. I know that not every student I teach will share my love and passion for mathematics. But if I can make mathematics even just a little more enjoyable for my students, I believe that I will have succeeded as a teacher.

Problem Solving in the Classroom

This past week in EDBE 8F83 we finished the class with an 'Skyscraper' activity involving plastic cubes and a paper grid. At the beginning of the activity I know I was very confused and I think my classmates felt similar. The instructions were quick and vague and caused a lot of confusing as we started the activity. Instead of checking out, my group started to problem solve to see if we could figure out how the activity worked on our own. After a lot of discussion we to the conclusion that instead of counting the "levels" of each tower, we needed to count the amount of towers in each row.

Retrieved from https://goo.gl/zDzZrW

We would have never come to this conclusion on our own if we had been given explicit instructions from the beginning if the activity. It was beneficial for us to use our problem solving skills to figure it out on our own. And once we were able to understand the rules of the activity, we were able to complete the activity on our own.

In my own learning throughout high school and university I always found that when I had to discover something on my own, or with guidance from the teacher, I was always able to understand it better. This was because I came to the conclusion or answer my own way. This may be a silly example but I will always remember it. In grade four I asked my teacher how to spell the word awesome. Instead of simply giving me the proper spelling, she told me to look it up in the dictionary. And growing up I never forgot how to spell that word.

I would love to see something similar when I start running my own classroom. Instead of giving my students the answers, I want to be able to guide them to the answer. I really think that it is important for students to use self-discovery in the classroom. This makes their learning more meaningful. As Amy Lin explains in her TEDx Talk Thinking Math-ishly, it is important to probe students with meaningful questions in order to make their learning more valuable.

Introduction

Hello and welcome to my blog!

My name is Jordan Black and I am in my fifth year of Concurrent Education at Brock University. My teachable subjects are Mathematics and Geography, but I hope to eventually earn my third teachable in History. A few things about me outside of education; I am from Grimsby, ON so I am definitely a small town girl at heart. I love being active and working out, in fact I have been a dancer since the age of three.

I have created this blog to reflect on my time in Teacher's College and eventually on my career as a teacher. I think that reflection is a great way to learn and grow. And I look forward to what this year has in store. The name of my blog is two-fold; Algo-rhythm has a dual meaning. Algorithm as in my mathematics background but also algo-RHYTHM as in my passion and love for all things related to dance. I have been both a student and a teacher of dance throughout the years. I will absolutely be incorporating dance into my classroom one way or another.

I hope everyone has a great week!