Differentiated Instruction and Consolidation

Differentiated Instruction (DI) can be simply understood as providing your students with a variety. It is critical to ensure that all of our students are provided with an equal opportunity to learn and in order to accomplish this we must differentiate our instructional techniques. Edugains describes DI as “effective instruction that is adaptive to students’ readiness, and learning preferences”. The website also suggests that attending to these preferences we increase the chance of students connecting the new knowledge to prior knowledge and ensures that the students stay engaged in their learning.

https://aae.boisestate.edu/know-your-learning-style/

A student’s learning preferences will usually include their learning styles. In my opinion a learning style is a situational preference that depends on the subject matter at hand and the end result of the task. I learn strategies and tactics in games though participation, while I understand scientific and mathematical problems when I hear their explanations. As we differentiate how we teach students we will be allowing a wider variety of students to succeed. I feel as though the mathematics classroom is both a beneficial environment for DI, but can also present a variety of challenges. These challenges include the traditional math setting that was very teacher centered as well as the students who have become accustom to this type of teaching. While there should still be some aspects of teacher-centered education it is critical to ensure that students are giving time to explore all of the learning styles. Utilizing models, manipulatives, videos and games can be a very effective way of adapting to the needs of your students.

In addition to ensuring that you instruction is differentiated I feel as though it is just as important to differentiate your assessments or consolidation pieces. As students are kinesthetic learners , visual learners or verbal learners, some students may only be able to express their knowledge using the same mediums. In saying this it is not fair to give an assessment to the entire class and expect them to succeed. As teachers, we must provide a variety of tools and options for students to show us what they have learned.

http://www.theflippedclassroom.es/dandole-una-vuelta-a-kahoot/

One tool that I am excited to explore is an online tool called Kahoot. In our second class of the semester we played a Kahoot quiz based on our introductions, and I was impressed by the learning and enjoyment that took place. We were learning about one another and I gained more knowledge during the ten minutes it took to complete the quiz, compared to the time I spent reading blogs online. The scoreboard and other game-like features encouraged me to explore it more. After looking into it I feel as though it is an appropriate tool to use in any classroom. You can make your own quizzes and ensure that students are engaged in their learning. The website also provides the students with the opportunity to hear the questions and see them on the screen as opposed to simply reading them off their tests. The game like environment also encouraged students to collaborate with one another in order to help their peers reach the top of the leaderboard.

Mr. Moore

Reference: http://www.edugains.ca/resourcesDI/Brochures/DIBrochureOct08.pdf

Mathematical Reasoning and Logic

Reasoning is defined by the Merriam-Webster online dictionary as “the process of thinking about something in a logical way in order to form a conclusion or judgment”. This logical thinking is critical in mathematics in both the real world as well as the educational setting. Ensuring students can think about their answer and understand if it is right or wrong is critical for student success. As teachers we need to ensure we are asking students if their answers “make sense”. Do the answers fit with the question or does there seem to be something that is backwards or out of place?

           

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Earlier this week, this concept of reasoning became apparent in a question presented in my University math class. The question presented an inverse relationship that discussed a specific number of workers completing a job in a specific amount of time and asked how long would it take a larger number of workers to complete the same job. When solving this question it was interesting to hear the logic that was used to explain how we found a solution. I was intrigued when a member of the class explained that the answer that he found “was higher than the original time, but that did not make sense since there were more workers”.

           

This is a prime example of thinking about something in a ‘logical way in order to form a conclusion’. Thinking logically allowed him and many other students in the class to realize that when there are more workers present, the amount of time should decrease, not increase. As teachers we must foster this thinking as it can be applied to everyday scenarios. Not only does logic influence their decisions in the mathematics classroom, but also when using math in the real world. Using logic will ensure students connect other pieces of information that they know are true to the problem that they are attempting to solve. This concept of connecting knowledge to the current problem is presented in the video below.

https://www.teachingchannel.org/videos/student-self-correction

In the case of the problem presented in class the students knew that as more people work together the amount of time spent on that task should decrease, not increase. A real life example could include as they give the cashier more money for an item they should receive more money in return for change, or as they work more hours their pay cheque should increase by a set amount. Students must be encouraged to think about the answers they are giving, rather than simply writing or responding with the numbers that the calculator spits out.

Thanks for reading!
Mr. Moore 

Reflecting on Open Ended Classroom Instructions

Hey readers!

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Welcome to the new Mathematics category of my blog! As some of you already know my name is Mr. Moore and I am a teacher candidate from Brock University! My major is physical education and my second teachable is mathematics at the intermediate senior levels. This section of my blog is going to explore the experiences that I have had both in an academic setting, as well as my personal experiences involving math in the real world.

     Today I am going to reflect on an experience I have had in one of my University classes. At the end of the lesson the instructor gave us skyscraper puzzles and snapping cubes. Now if you are like me, you have no idea what a skyscraper puzzle is or how they work. She instructed us to complete the puzzle using the snapping cubes, but was very limited in the amount of rules and directions that she gave. Immediately there was a level of confusion and frustration within the class, as not many of my fellow students knew where to start or how the puzzles worked.

     After reflecting on this after class, we realized that she was encouraging us to become problem solvers, to think creatively, and to visually solve the puzzles at hand. She purposely left the instructions incomplete to ensure that we met all of these goals and were not simply following the directions that led us to the final result. It also gave us the opportunity to develop living skills such as teamwork and communication with not only the people at our table, but other tables as well.

     Even though this activity was successful in our classroom, it does not mean this type of activity will be as successful in all classrooms. Earlier in the day we discussed all the different options and streams available for high school students once they reach grade eleven. The curriculum suggests that there are strands for university preparation, university/college preparation, college preparation and workplace preparation, but there is also a stream that includes mathematics for life (Ministry of Education, 2007). While completing the skyscrapers activity I could not help but think about the streams of high school education. As a university class completing this activity we were all engaged and interested in solving the problem. We have all taken university level math and have a personal connection with problem solving.

Ministry of Education, 2007

This personal connection made me think about the students who do not care about solving the problem or cannot think critically enough to come up with solutions. These students may get discouraged and as a result I feel as though we must ensure that our instructions are sufficient for the variety of students that we are teaching. Streaming students in high school may group them together by destination, but also results in a mixture of previous knowledge and interest levels. Some students may only be in university level mathematics to ensure they can enter a specific program, while others who are gifted in mathematics may be in the college level courses since they want to work with hands on problems.

     It is critical that with any activity we ensure that our instructions and goals are appropriate for the audience, but still encourages them to become problem solvers, and creative thinkers. 

Mr. Moore