What Would the Students Think?

This week in my class we took a focus on the student's perspective when planning a lesson. Below is a script we created showing student concerns after receiving instructions for consolidating the lesson. 

Teacher: Now, instead of solving an equation given to you, you are going to create your own equation with a partner and you must come up with a word problem that corresponds with the equation you create.

For example we make an equation, 29 - x= 13. One example of a corresponding word problem would be "Jenny is on the Price is Right and the price she guessed for a new toaster was $29. The difference between Jenny's guess and the actual retail price is $13. What is the actual retail price?"

Then you would solve for x and show all your steps.

Student 1: Miss, can we use any numbers?

Teacher: Yes, in your equation any numbers can be used and you must have one variable "x" to solve for.

Student 2: So do you have to show all the steps when you solve or can you just write "x = ..."

Teacher: When you solve your equation, I want to see all the steps you took to isolate or solve for x, and end by clearly stating statement "x = value".

Student 3: Can we do this in pairs?

Teacher: Yes groups of two only. Each group of two will hand in one paper with one word problem, equation and solution steps.

  

When planning any type of lesson or assignment, it is important to remember that explanations or instructions you hope to provide to the students may not be as clear and concise to them as they are to you. 

Always Time For Technology

            In today's classrooms one question teachers ask themselves when lesson planning is "How can I incorporate technology into my lesson?" There are numerous apps and websites available which can be used to enhance a lesson or for student aid. The challenge for teachers is to explore these methods of technology and decide if they are purposeful towards student learning.

            

       One purpose technology should serve in the classroom is to foster math talk. During our class this week we were working with the website Desmos, more specifically we used the feature Polygraphs. In this feature teachers create a class account and students use their own electronic device to login to the class game. This game is just like an electronic version of the board game Guess Who where students are provided with a grid of different representations and need to guess which picture their classmate has picked. In our case we were working on the quadratics section and were provided with multiple images of parabolas. In order to make an educated guess the students must ask questions (through the app) in order to eliminate the incorrect pictures. This process forced us to practice our math language and knowledge relating to quadratics and translations of parabolas. For example the first question a student may ask "is the parabola concave up?" If the response is yes then the student can eliminate all parabolas facing down. I found the game to be fun, interactive and it tested my math knowledge not only when I was the question person but also as the person answering. 

Class having fun with Headbanz

To compare to a more traditional lesson without the use of technology, we also did an activity called Headbanz. In this activity the teacher presented each of us with an equation written on a card which was attached to a headband. Without looking at our equation we were suppose to wear our headband and ask yes or no questions to our classmates in order to identify our equation. This activity was also excellent for fostering math talk as students needed to clearly explain their thinking in order to describe their equation. Both these games are great for the "Minds On" portion of a lesson as they get the students into the math mindset and prepare them to think critically. I'm sure positives and negatives can be described for both methods however I would not designate one activity to be better than the other since they both accomplish the same goal.  

            Another purpose for technology in the classroom is to make it easier for students to apply their knowledge to real life scenarios. Using Geogebra we were able to overlay a parabola on top of a freeze frame video of a man shooting a basketball towards the net. From the students perspective we were able to see what would happen to our graph as we manipulated different parts of the equation in order to match up with the path of the ball. I enjoyed this activity so much that for my next lesson plan I will have my students find their our picture or video of something that resembles a parabolic curve and have them come up with the equation of the curve using the tools in Geogebra.

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Closing the Gap

         Without question teachers should be prepared to teach to a class that has a range of learning levels however a classroom such as this is a constant challenge for teachers. In regards to math teachers, this challenge arises most often in grades 6-9 where each new concept heavily relies on the use of prior knowledge. Imagine teaching area and surface area formulas in a grade 8 class where a group of your students do not know the proper order of operations (BEDMAS) or do not know how to perform basic operations without the use of a calculator. This would be very difficult to teach to the entire class when a large learning gap exists between these students and students who can apply the new formulas to problems involving critical thinking. The goal of the teacher is narrow the gap and one method of differentiated instruction used is available through EduGains called "Gap Closing Resources". These resources include topic specific diagnostic tests which can help teachers pinpoint what concepts students are stuck on. Once a problem area is identified there are extra work sheets for the student to practice. I have personally worked with these resource sheets in a grade 7 math class. In a class of 26 students there were 5 students who were using Gap closing worksheets. After the teacher had taught the lesson the 5 students would work on problems in their Gap Closing booklet which were related to the lesson. They were required by the teacher to finish those questions before attempting the questions from the textbook or work book assigned that were assigned to the entire class. I believe these booklets do help, most of the students I worked with were making the same mistakes and after practicing questions in the booklet they were able to understand where they were going wrong and as a result they caught up to the rest of the class.             

        To assess just how wide the learning gap is in the classroom, teachers can incorporate a variety of websites and apps into a pre-lesson or pre-unit "warm up" as opposed to a traditional test of existing knowledge. In my class this week we explored a website called "Which One Doesn't Belong" where four pictures within a similar category are shown together and students must describe how and why one picture is unlike the rest. The website organizes the pictures into the sections; Shapes, Numbers and Graphs and each section has pictures that range in grade level. I think a great idea for teachers would be to combine the concept of this website with a Kahoot presentation. Not only can teachers use the pictures from wodb, they can create many similar questions focusing on the same specific mathematical concept. By using this anonymous forum, students may feel more relaxed and inclined to answer honestly instead of guessing or not answering on regular tests. Also by customizing their own Kahoot, teachers should be able to get a general idea of the knowledge gap in their classroom. In the end this teaching strategy would not be a loss because for students who are struggling this exercise could possibly help them better understand a concept and for students who are excelling this is a great way to review and strengthen their skills before moving on to a new unit.

References:

Gap Closing. (2016). Edugains.ca. Retrieved 11 October 2016, from http://www.edugains.ca/newsite/math/gap_closing.html

Which One Doesn't Belong. (2016). Wodb.ca. Retrieved 11 October 2016, from http://wodb.ca/shapes.html

Kahoot!. (2016). Kahoot.it. Retrieved 11 October 2016, from https://kahoot.it/#/

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Learning Gap. (2016). Retrieved from https://www.quora.com/I-always-hear-people-advising-JEE-aspirants-to-get-their-concepts-cleared-But-how-do-we-get-clear-concepts

Open Question, Open Mind

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The one thing about math I have always taken solace in is the fact that there is one answer. That one answer poses a challenge that I feel I have to meet. It is just like reading a book, doing a puzzle or even watching a movie I need to see it all come to one concrete end. Conversely to these thoughts, I have also learned that math is not always straight forward, it can be messy and complicated with multiple answers or there are those questions that remain unanswered. Of course I still love the straight forward questions but as I continue my work in mathematics, now through a teaching lens, I realize that the real learning took place while working on the "messy" questions. In order for students to work on these types of questions teachers need to develop confident, independent and critical thinking in their students. One way to gradually develop these skills is to implement open ended questions in a lesson plan. I can tell you that at first trying to use open ended questions in math is not as easy as english for example, but with practice it becomes second nature. In my teaching mathematics class this week we discussed some common and effective examples of open questions. Questions that leave a lot of room for student interpretation are comparison questions; asking students how a figure or an equation compares to another. Another key point we discussed was how teachers should provide enough information to form a problem but not too much information to completely restrict the question. Using words such as "approximately", "minimum" or "maximum" can open the question to multiple solutions. Below are two examples of open questions where the approach was providing the answer and having the students work backward to formulate the questions. 

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               In one of my placements during my undergrad, I taught the unit on area and perimeter to the grade 7 class. One assignment I gave to the class was similar to one of the unit problems from the textbook however I tweaked it making it more of an open ended problem. The students were required to create a patio design under some restrictions including using only the five specific shapes. (Prior to completing the problem I had marked out the five shapes on the floor using tape and the students calculated the area by measuring the floor tiles.) In the end each student had submitted a completely unique patio design. As long as the design included the five shapes and met the minimum area requirements then each of the designs were 100% correct. I think this assignment was a good balance between open ended and closed questions. After asking the students to formulate their own solutions to the design, I then asked all of them the same closed questions which they had to answer in relation to their own individual design area. I believe problems such as these are beneficial to all students because at the very least everyone can make an attempt and as I mentioned before this is a step towards building their confidence when dealing with math. 

Patio Problem

Resources

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