My Thoughts on Assessment and Final Reflections

     As I conclude my final week in my Mathematics education class I not only got a chance to learn some important new information, but also had a chance to reflect on what I learned. Each week I learned more and more about pedagogical strategies I could employ to create a rich Mathematics program, but in the end it does not mean much without proper assessment.

Developing Meaningful Assessment 

     Assessment may not be the most glamourous task a teacher is responsible for, but it is one of the most important ones that they do. Experts continue to debate on the ways that teachers should assess, but I believe that the most important requirement is that it is meaningful. When I was a student my teachers would create an environment where all I cared about was the mark at the top. Was that meaningful to my learning? Of course not! Teachers need to create methods of assessment that provide students with detailed feedback on how they can improve. My belief is that teachers need to create assessments that focus on the learning during the process rather than the product at the end. If we do this, then students will focus on how they can improve on the next task rather than being worried for that one big test. In Mathematics this is especially true because there are many students that get anxious over tests, but if they clearly demonstrated their learning over the unit why are we so concerned about one test?

Here is a link I found helpful. https://www.edutopia.org/blog/making-assessments-meaningful-heather-wolpert-gawron   

   Just like our lessons, I believe assessment also needs to be differentiated for our students. I remember one student in my placement performing poorly on summative tasks like a test, but was always the most vocal during small group work and class discussions. I realized quickly that this student was an auditory learner and was able to clearly demonstrate her learning when I had conversations with her. It was during this time that I felt like I got the most meaningful evaluation of this particular student’s learning.

     Another important belief I have about assessment that I discovered this week was that success criteria for the assessment needs to be clearly outlined for the students. Students need to be able to know exactly what they must do in order to be successful. One interesting method I learned this week is co-creating success criteria for a task with the students so they have a voice in what needs to be met in order to be successful and teachers must be fair when they are assessing from this criteria.

Final Thoughts

There is certainly a plethora of ideas and concepts I learned in these past weeks. Most importantly I learned that Math is a subject to be explored, not memorized. It is its own language that students need to discover while the teacher guides them on the right path through rich tasks and deep questioning. Finally, I learned that teachers need to get their students to believe that anyone can be successful in Mathematics with perseverance. A message that I believe can apply to everyone, no matter what obstacle you are faced with. 

Blending Different Strategies and Tools for a Rich Math Program

     Welcome back to my readers! This week was another valuable week in my mathematics education as I learned about different tools and strategies I can use in my mathematics program. They are tools that can be used to enrich my program by not only engaging my students, but teaching them skills that are more relevant to real life.

Blended Learning

     In class we discussed the pedagogical method of technological integration and blended learning into math. We learned that blended learning combines the benefits of face to face teacher instruction with the exploration that comes with technological integration. I believe that blended learning strategies are the future of math education because our students are consumed with technology on a daily basis for recreation and need to learn how they can use technology to further their education. By completing my webinar this week I learned that blended learning is a really engaging tool when paired with activities that your students will find enjoyable and is able to stimulate meaningful discussion. The role of the teacher then becomes more of a facilitator that guides the students in the right direction and asks effective prompting questions that gets the students to think deeper about what they are learning. All of this is beneficial to students because it lets them learn at their own pace and have their own chances to explore.

Here is a video I found helpful about Blended Learning. 

Open Ended Questions

     For this week my webinar focus was on the topic of open ended questioning in mathematics instruction. Through my research and preparation in this topic I learned about how much our students can benefit from posing questions that can multiple solutions and multiple strategies to obtain an answer. With these questions the teacher becomes more focused on assessing the mathematical processes used in answering the question, rather than just being fixated on the final solution. In particular, students work on their ability to reason and make mathematical decisions based on those reasons. In my placement I tried as often as I could to pose a question to students which was completely open and had multiple ways you could use to solve the answer. It was this type of activity where I heard the most mathematical discussion between peers which I believe is essential to helping students grow their knowledge on a subject. Not only that, open ended questions allows for all students to be able to get involved because they are accessible enough for any student, yet students at the higher levels can have a chance to challenge their ability to justify an answer.

Here is a link I found helpful when trying to find examples of effective open ended tasks. 
https://www.youcubed.org/tasks/

Big Ideas vs Little Details      As I completed the online modules for this week I learned about the importance of teaching our students about the big ideas, rather than the minute details. I remember when I was a student how focused I was on the drill and practice questions that I didn’t understand what the main purpose of it was. I believe that teachers need to teach their students the main ideas of a topic and design questions in order to achieve that goal so students gain a deeper understanding of the topic without getting lost in the shallow details.

Creating a Meaningful Math Program

Hello once again to my readers! It is so incredible how fast this school year has been going but I am delighted to share with you some of the knowledge I gained this week.

Rich Tasks

This week in class we spent a large portion of our time together discussing how teachers can create rich math tasks for their students. In order to help me learn more about this topic I researched into other avenues of information to see what other experts say about this concept of rich math tasks (see link). What I learned was that there are certainly some differences in the way people define a rich task and the criteria needed to create one, but there were some key themes demonstrated.

http://nrich.maths.org/5662

One key theme I found to be incredibly important was that the task has to be engaging and meaningful. I believe that these two are interconnected because if you can achieve one you are most likely achieving the other. Too often I remember when I was a student answering repetitive math problem in order to develop my ability to grasp the concept. This was not only boring, but it also restricted my ability to use my knowledge to struggle with a meaningful problem. I would argue that students are much more engaged in their learning when they believe they are solving a real problem that could occur outside the classroom.

Another important point is that the problem must allow for all students to be able to participate no matter what their achievement level is. It should be easy enough so that any student can begin, while challenging enough for the students at a higher level. I believe that too many math problems are created where the student either feels it’s too easy and therefore pointless or too difficult that they cannot get started.

Multiple Avenues, Same Destination

We also learned this week about how there are multiple avenues that students can take when they answer a solution. For instance, we were asked to answer 18x5 without a calculator and I was amazed at the number of methods people used to solve the problem. It is critical that teachers be more open to the way students arrive at an answer and be able to anticipate the way they might do so. I remember when I asked my students in my teaching block a question that compared ratios and had them answer it in small groups. After they found a solution I asked them to write it on a poster and explain it to the class. Not only did the students all arrive at the same answer using multiple methods, they also were able to teach their classmates different forms they could use to answer the question (decimals, fractions, percentages, etc.).

Conclusion

Through my teaching experience and my learning this week I have seen the connection between creating rich tasks and allowing for different strategies in that it shows how math does in fact allow for creativity. Too often math teachers instruct math in a way that is too rigid when really it is a subject that allows for students to solve meaningful problems in creative ways that make sense to them. 

Here is a video I hope will inspire you to know your students and allow them to learn in a way that best helps them.