Effective Uses of Technology Within the Classroom

New technologies are always emerging to make our lives easier. Many new technologies and gadgets such as Smartboards and graphing calculators have even entered our classrooms to improve the learning environment and classroom engagement. The use of technology within classrooms is also outlined within the Ontario Mathematics curriculum documents on page 8 it reads that,

"The prevalence in today’s society and classrooms of sophisticated yet easy-to-use calculators and computer software accounts in part for the inclusion of certain concepts and skills in this curriculum. The curriculum has been designed to integrate appropriate technologies into the learning and doing of mathematics, while equipping students with the manipulation skills necessary to understand other aspects of the mathematics that they are learning, to solve meaningful problems, and to continue to learn mathematics with success in the future. Technology is not used to replace skill acquisition; rather, it is treated as a learning tool that helps students explore concepts. Technology is required when its use represents either the only way or the most effective way to achieve an expectation."

 Note the final line highlighted in red font. Technology is actually required to be used when it is the best way to achieve a specific expectation within the classroom. For example, in an academic grade 9 mathematics class, many student's in the class may be struggling at understanding how the slope and y-intercept of a linear line can be used to generate an equation for that line. Platforms such as Desmos, an online tool used for graphing, can be used to engage students in graphing linear lines and also allows them to explore a variety of different linear lines by just simply inputting the equation of the line into the program.

Figure: Using Desmos to graph various linear lines.

The tool is easy and very quick for students to use. It will allow them to easily graph multiple lines and see how manipulating the equation changes the slope and y-intercept of the lines. 

Smartboards are another popular new technology present within many classrooms. Smartboards can be used to create interactive lessons that can help increase classroom engagement. The lessons can be created so that students can come up to the board and interact with various objects to solve problems, much like using manipulatives for factoring. 

Overall, technology should be used to help benefit the learning environment for your students. I believe it shouldn't be used to teach every expectation but should be used when it is the most effective way of teaching a certain topic.

Diagnostic Assessment

The Summer has just ended and the student's are coming back to school. Some students are excited and eager to learn while others are wishing the Summer would have never ended. A variety of different mindsets are entering the classroom and as the teacher it is your role to make sure that a positive learning environment is present for every student. One of the difficult tasks at the beginning of the school year for teachers, besides motivating students after a long holiday, is assessing the strengths of each student effectively. One of the ways this can be done is through diagnostic assessment, which is not always an easy task.

According to the document Growing Success, diagnostic assessment occurs before instruction begins so teacher's can determine student's readiness to learn new knowledge and skills, as well as obtain information about their interests and learning preferences. 

I remember back in high school each year when I returned back from Summer in my math class we would write a quiz to give feedback to the teacher about what we remembered from math last year. The issue with this type of diagnostic assessment is that sometimes students will forget certain topics if they haven't taken math in over a year (for example, last math they took was first semester of the previous year and they currently have math second semester of the current year) and they'll only need a reminder to refresh their brain on how to do certain topics. I believe a more effective method for diagnostic assessment would be to break students into random groups to allow them to work on questions together. This will allow the students to meet some new classmates and refresh their learning in a peer friendly environment. The teacher can walk around the classroom and assess the conversations being had about the math questions and assist groups in they are having troubles with certain problems. 

Figure retrieved from: http://media.oregonlive.com/portland_impact/photo/roosefreshenglishjpg-e31ff160773d042d.jpg

Diagnostic assessment will help teachers get a better understanding of the strengths and weaknesses of their students so that they can prepare their lessons and assessment tools accordingly as the school year progresses. 

Open Questions and Differentiation

One of the many goals in mathematics is to help students develop their critical thinking and problem solving skills. Open questioning is a method that can be used by teachers to engage a students inquiry. According to the asking effective questions document from the Ontario Ministry of Education, open questions are effective in supporting learning because they encourage a variety of approaches and responses. Open questions also intrinsically allow for differentiation, as the student responses to the questions will reveal their individual understanding and knowledge of the topic the question is based from. What are the differences between an open question and a traditional question though?

To use arithmetic as an example, a traditional question would be something along the lines of:

What does 5 x 6 = ? 

Students can do their procedural multiplication technique or use a calculator to easily find that the answer is 30 and then move on to the same type of questions using the same procedures over and over.

An example of an open question using this same topic would be something along the lines of:

Using multiplication, find two or more numbers that can multiply to 30.

This question has various answers and requires students to think about how multiplication works and could also even challenge their algebra and division skills as well. An example of some solutions to this open question could include:

1) 5 x 6 = 30
2) 2 x 5 x 3 = 30
3) -15 x -2 = 30

Notice the various complexity of the answers shown here. Answer 1) uses very basic multiplication to find the solution but still shows understanding of how to use multiplication. Answer 2) is a little more complex requiring students to think a little bit about their algebra skills. Lastly, answer 3) not only shows correct multiplication but also shows that two negative numbers multiply together to make a positive number, combining two different topics into one to solve the answer showing critical thinking.

Open questions can even be brought to the high school level and used for more complex problems. For example:

Create a linear function that passes through the y-intercept at the point (0,4). 
Students can come up with a variety of answers:

Figure: Different linear function solutions to an open question.

For this type of question students need to understand that the y-intercept component of their equation will not change, but the slope can be any number. This allows students to explore linear functions and see how manipulating the equation effects the graph of each function.

Overall I believe open questions are an excellent tool for testing student inquiry while also providing differentiating learning which provides great feedback for the teacher on how well students are understanding certain topics.