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.

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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.

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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.

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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.

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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!