Assessing with purpose

Hi All,

This week we are talking about effective assessment strategies in Math. It is important to note that when talking about assessment it is always important to refer to the Growing Success ministry document. This document states that the purpose of assessment is to improve student learning thus assessment must be purposeful and must serve to benefit a student's learning progress.

(Google Images, Online)

I thought there were many tips that were given today that can help me in the future. For example, if student's are not responding to the way you are teaching, then stop teaching it! It is not working! So, as a teacher it is important to reflect on your own practices and on your students understanding in order for students to remain engaged in class. Another assessment strategy that resonated with me is the "leave comments, not grades;" I can relate so much to this because as a Math student whenever I saw my grade I always felt discouraged, so failed to go back to  review my assignment because often times there were no comments or there were vague comments. So, as a teacher it is important to offer descriptive feedback to students because it provides them with the opportunity to reflect on their own learning and to grow from those suggestions.

However, Pat stated that it is important to phrase comments in a way that encourages, rather than discourages the student. As such we engaged in an exercise whereby we got to view student work and assess their strengths, challenges and wonderings. Acknowledging strengths is important for students because they will not feel discouraged and pointing out challenges allow teachers to plan learner-specfic tasks. Wonderings allow for the teacher to provide instant feed back to the student in a manner that encourages them to continue developing their skills. For ex
ample: "I like the way you started...can you explain.'' Finally, it is through understanding the challenges, strengths and wondering that a teacher can write effective feedback to the student. As Pat and the Growing Success document stress it is important to provide ongoing and relevant assessment to students. This means ensuring that you are creating opportunities for assessment for learning, assessment as learning and assessment of learning–all at different stages of the learning process and all should be connected to learning goals and success criteria.

Their can be a variety of assessment tools and strategies that a teacher can employ. For example an assessment tool can be a specific application such as Wuzzit trouble and Dragon Box. These apps are very interesting because they can be very engaging for students, but they are also created in a way that engages students with the Math. This tool can be used as a self-assessment by the student to monitor progress and areas of improvement. Also there is a reporting tool available in the apps whereby teacher's are given information on student's progress. Below I have attached a video of an explanation of the apps. Finally, Patt provided us with a checklist for ourselves as we are providing ongoing feedback during the learning cycling. I think this is a very important tool to have because it reminds teachers that assessment is purposeful.

                                                        (Mindset Modules, Online)

      (Powerpoint, Online)

Work Cited
"Clipart." (2012). Social Brite. Google Images, n.d. Web. 18 Oct. 2016. <http://www.socialbrite.org/2012/11/06/tools-to-improve-your-online-fundraising/>
Lesson 6h. Perf. HTML Course. Youtube, 12 July 2014. Web. 16 Oct. 2016. <https://www.youtube.com/watch?v=NY7poNmNk4o&feature=youtu.be>.
McEachren, Pat et al. A Checklist for Planning Feedback During Learning. Digital image. Sakai. N.p., 16 Oct. 2016. Web. 2016.<https://lms.brocku.ca/access/lessonbuilder/item/33619208/group/EDBE8P54D12FW2016LEC001/Week%206/A%20Checklist%20for%20Planning%20Feedback%20During%20Learning.pdf>.

Blended Learning

Hi Everyone!

Wow! I can't believe that this course is almost coming to an end, I have learned so much over the course of these last few weeks!

This week we learned about blended learning which is a form of education that blends online and on campus learning in both content and instruction. Our class had the opportunity to experience blended learning, Pat provided us with a hardcopy and online worksheet that outlined five different stations that explained this topic. Blended learning is really unique because it allows for the students to study at their own pace online, but also allows students to engage with teacher in person. This type of instruction can be very useful in Math, as shown in the Blended Learning Unit for J/I Math video. In this video, through an online module, students are able to see the success criteria and learning goals prior to beginning online lesson. Then students engage in completing a set of variety of tasks such as e-practice and check own understanding. These types of tasks allow them to self assess and reflect. Finally, the module is completed in the consolidation section whereby students are able to make connections to other concepts. Allowing for students to go through this can be very helpful for them, however I also think that it is crucial, that in every online learning lesson students, students are given the opportunity to collaborate, share, and provided with rich final tasks that incorporate these types of applications they are using.

I felt that through my own experience, I was able to complete the assignment at my own pace, allocate my own time, and search for other resources to further my understanding on the concept. I think that blended learning can be particularly important in Math because students are able to take the time to read, reflect and discuss the content rather than being expected to understand instantly. Blended learning really provides students with an opportunity to really customize their learning which can contribute to their engagement. This type of learning is also mirrored in many high tech companies goals and strategies. To show an example of this, below is an infographic I found on the type of strategies that 'leaders' in organizations use to increase employee productivity:

(Google Images, Online)

Another important tip that I got from this week's blended learning experience is that when creating online learning opportunities, it is imperative that the teacher is cognizant of the applications they are using. That is, it is important that the applications, that one uses, work with the students and task that they help student reach those success criteria's. An amazing poster that I got from this week is the Pedagogy Wheel which lists the appropriate apps for the appropriate task. See below.

(Google Images, Online)

Bibliography

Carington, Allan. "It's about Transformation - In Support of Excellence." In Support of Excellence. Designing Outcomes, 22 Apr. 2016. Web. 7 Oct. 2016. <http://designingoutcomes.com/the-padagogy-wheel-v2-0-its-all-about-transformation-and-integration/>.

Sinclair, Ashley. "5 Tips For Success With Leadership Blends [INFOGRAPHIC]." Kineo. Kineo, 1 Apr. 2015. Web. 7 Oct. 2016. <http://www.kineo.com/blog/insights/5-tips-for-success-with-leadership-blends>.

The Importance of Rich Tasks

Hi All, 

This week Pat began the class by asking us which item in the picture did not belong. At first, I thought it was the font for the word "which," but there are other elements in the picture that do not belong such as the circle, square, color etc. Although this is not a rich task, this is a good illustration of what we want students to think about in Math. That is, we want students to think about a variety of responses and thinking about Math in different ways. This is a good ice breaker or introduction to rich tasks. 

A rich task allows students to broaden problem solving skills. They do not necessarily need to be open, it depends on the learner. However, a rich task should have a story that interests the student. An excellent example of showing the difference between a rich and non rich task.

Non Rich: 

   (Danielson, Online)

Which of these fractions do not belong:
3 1/2  2 1/3  5 2/7  1 1/9

Rich

Steven says that when you add two odd numbers with an even number, the answer is always even. 

Is Steve correct? Explain your reasoning. 

                                   

The rich tasks allow students to try out different methods of getting the answer and allows them to dig deeper into the concepts. Whereas, the non-rich task is the traditional right or wrong–no understanding type of tasks. A rich tasks allows students to use various mathematical processes when approaching and solving the problem. Rich tasks also allow students from various levels to get inside the Math. It also important to note that teachers should allow students time to collaborate with peers. The problem should also allow opportunities for extensions. I think the Pumpkin and Tractor trailer problem that was created by Pat was a really great rich tasks because it allows students to ask questions, collaborate, and reflect on the Math problem. It is important to allow students to try to solve problem rather than simply memorize the answer. I really think that Math is a subject where rich tasks should be incorporated the most because these tasks allow for students to gain a better understanding of the subject. 

Bibliography: 
Danielson, Christopher,  "Which One Doesn't Belong?" Weblog post. Which One Doesn't Belong? N.p., 2013. Web. 02 Oct. 2016. <http://wodb.ca/>.

Reaching all Learners

Hi All,

This week I will be blogging about differentiating instruction (DI) in Math class. DI is very important because it allows teachers to plan lessons in accordance with student's specific learning needs. Specifically, DI allows for teachers to meet students in their learning. While I was aware of how to implement DI strategies in other subjects, I was unsure of how to create differentiation in Math-apart from providing manipulatives. 

I think this has to do in part with the way that I was taught Math, so when Pat provided us with an open question in class, I was taken aback. I sat there unable to start on the problem because I was unsure of how to proceed. Where were all the given numbers that I simply needed to plug in? Why were there percentage? What do I need to figure out? 

After asking myself these questions,I read the question one more time and began to deconstruct the problem by putting myself in the situation. Also, I used numbers that I was most comfortable with, which helped me start! 

The DI strategy of providing students with an open tasks, not only supports the inquiry model, but it helps to meet every learners needs. That is, every learner is able to have an entry point and once they get more comfortable with the concept,they are able to build on the learning. Now, it is important to note that students do not magically understand concepts,rather there needs to be time for reflection, collaboration and feedback while students are explaining thinking. For example, a teacher could ask which mathematical processes helped the student in solving the problem or how was work represented? 

The key, for students being able to respond well to this DI strategy,is for teachers to  develop strong open tasks. Relatable, realistic, and personalized open tasks allow for students to see themselves in the learning and to engage with the material thereby deepening their understanding. 

Another DI strategy is 

(Capacity Building Series, p.8)

using parallel task which are open, but allow student's choice. This type of task allow students to choose a   question that they are most comfortable with and then progress to a more challenging one. This is the beauty of open tasks because they meet the needs of different learners whilst addressing the same big idea. In class, I thought that the parallel tasks were really meaningful because, as a Mathematical learner, I was able to choose a problem without feeling self-conscious about my  abilities. Moreover, I was able to create personal goals, for examples: I set the goal of completing the 'comfortable' question and then set another goal of trying to attempt the more challenging question.

Overall I think that DI is beneficial for students, however it needs to used in a way that meets the learning goals of the curriculum and of the individual, that is the only way DI can be successful–especially in Math. Open tasks, parallel tasks, engaging activities, different methods and collaboration are elements that must be incorporated into DI strategies in order for the learning to be meaningful. 


James P., N. (2016). 6 Golden Rules For Engaging Students; image creation and attribution via Sakai Math II

MOE. (2008). Capacity Building Series: Differentiating Mathematics Instruction. 

Providing a Math Experience

Hi All,

This week in Math class we discussed different ways of providing a meaningful experience for students. One of the main themes that we discussed was understanding the difference between knowing, doing, and understanding in mathematics. To me, knowing is about being able to know specific conventions when being given a particular problem. Doing involves actually being able to use those conventions in completing a task. Whereas, understanding involves actually understanding why you are using those conventions and reflecting on the problem. Although all are important, to me, it is the understanding that is essential for the Math learner. Being able to question these conventions and look deeper in order to gain understanding is more valuable for the learner. I think that making mistakes and communicating with peers is essential to the understanding. It is the Mamamdo- Half Triangle story that really cemented my own understanding about the value of making mistakes and how it contributes to everyone's learning. Click on the picture below to watch the video. In the video, Mamamdo is asked to explain his thinking of a one half fraction of a rectangle. The teacher calls Mamamdo to the front of the class and asks his peers to track his thinking and identify other possible ways of answering the question. The teaching strategy she used allows for the student not to feel as though they were wrong, but to allow them, through the help of peers, to identify the 'mistake' so that he could solve the question. This helps the student because he is better able to understand the concept.

Mathematics Teaching and Learning to Teach, University of Michigan. (2010). In Mamadou-Half-Rectangle [Online]. Available: http://hdl.handle.net/2027.42/78024

Another teaching strategy that contributes to gaining this mathematical understanding is the Math Daily 3 activity. It involves the teacher allowing time for the student to first, try out the question on their own. Second, consult a neighbour. And finally, write a mathematical sentence about the answer. This is a great strategy because it allows students to communicate their approach in different ways which allows them to further reflect on the problem.

Finally, in order to provide a rich mathematical experience for the learner, I think it is important for the teacher to think about the different ways of delivering Math questions. This week we looked at Math problems from an Indigenous lens through the story, Small Number Counts to 100. Please watch video below.  This is a story about a boy named Small Number who tries to count tipis. Through the story, students are asked how Small Numbers was able to determine which was the 100th tipi without actually counting all the tipis. This inquiry based question can potentially have students draw the scenario or actually create the scenario in order to figure out different methods of finding out the answer. These are very different approaches to Math because it gives students real-life problems to solve and allows them to use their imagination and ask questions in order to solve the question. Additionally, it allows them to understand ways that Math is taught across cultures. What is particularly interesting about this video is that it is offered in both Cree and Blackfoot languages. This way the video also offers the student an opportunity to learn about Indigenous traditions, culture and language in a more meaningful way.

Sinclair, R. “Small Number Counts to 100” (2009). Available: https://vimeo.com/29064016

Overall, I think that this week has been an eye-opener for me in terms of the different directions to take teaching and learning Math. I hope in the coming weeks; I can add more tools in my Math tool box.