Module 6 Reflection: The Importance of Self-Directed Learning

"This module has helped me think about self-directed learners and the role of differentiation in the following ways....."

The good news is that math education is by its very nature geared toward differentiation. Take for example the fundamental mathematical basis, the proof. There are a number of ways for students to arrive at the conclusion. Not every proof will feature the same theorems, definitions, or examples. Therefore, putting an emphasis on student proofs might be one way to differentiate the learning. (Of course, given the overwhelming feeling many students feel when confronted with mathematical proofs, providing an example and even a template of how to do show may be in order.)

Focusing on diversity of examples is another method I should employ. In a room with future teachers, engineers, artists, etc., it can be difficult to find common ground. However, if we are to believe the leading experts, mathematics is the universal language. It shows up in your medical reports, your bank statements, and even in your art show judges' scores. Therefore, relating these ideas and concepts to different examples across a spectrum can only illuminate.

Many students often want the path to "correctness" to be clear. And while we can and should provide some clarity, we also need to motivate these students to be self-guided or self-directed. Inquiry learning may be the ticket. Perhaps self-assessment of current progress might be in order, along with the feedback from the teacher. The important thing is that students have the resources available.

Therefore, student samples might have a rubric or template available from the start. Students can better know and better visualize just what is expected of them. Of course, the difficult part in all of this is not stifling the students' "creative juices." You could also place viewing/editing restrictions on PDF's or Word documents, along with many other methods. The ways around this difficulty for templates at the very least seem plausible.

The benefits of becoming a self-directed learner almost indisputably carry over to other areas in life for these students. Therefore, they transcend the learning objectives; transition objectives can also be addressed. So if there is one skill that may come back directly to haunt students, it is that of self-direction.

At the core of my teaching philosophy is the desire and effort on my part to see my students become successful young men and women. Therefore, it seems that an environment that fosters self-directed learning should be at the heart of my classroom.

Module 5 Reflection: All Good Assessment is Ongoing

"This module has helped me think about student-centered assessment in the following ways…"

I now realize that assessment is an ongoing process for teachers. Any unit of material should feature some sort of assessment strategy at its beginning. Otherwise, you are doing your entire classroom a disservice. Some material may be completely foreign to almost all of your students, or you may find that an overwhelming number of students have mastered some facet of your unit. (However, I should go ahead and say that I've only met ONE K-W-L chart I ever liked.)

So, assessment is no longer an endgame. It's a vital part of everyday instruction. Assessing students' learning during a lesson also helps you both then and later. If a particular instructional method is proving ineffective, you need to realize it as soon as possible so you can reach the students before they are lost. But you will also need to plan for future improvements. If your next class responds the same way as the first, then there's probably no point in trying your method all day.

Allowing students to have a part in assessment gives them a sense of ownership. It also gives them insight into the process of assessment, which can only make their future samples or activities stronger. 

For example, using a checklist or rubric provides clear expectations for everyone. There is no ambiguity or doubt. So, in addition to proving a good tool for teachers, these two assessment methods enlighten students. Therefore, an easy way to integrate students into assessment might be rubrics or checklists. Peer feedback and student-led conferences are two other methods for getting students involved.

For long-term projects, providing constant feedback or even a checklist can help students. Encouraging them not to procrastinate is probably an ineffective tool alone, as many students feel they are the exception to any rule--trust me, I was one! This is where a checklist or log of some kind can come in handy. Feedback is important for ensuring students are on the right track. While you may be encouraged by a student's determination and will, it will probably be irrelevant if they have gone completely off-course.

Questioning is always something I've relied on constantly. However, I like the idea of journaling, especially for math. They can work on their literacy skills while giving voice to concerns or comments they may otherwise be unable or unwilling to express via questioning.

This module has been incredibly helpful since I am not currently in the classroom. Hopefully, I can take a number of these methods with me as a new teacher. If it weren't for the innumerable benefits they can bring to my students, the personal challenge and excitement is reason enough.

Module 4 Reflection: Technology-Based Support and Assessment

How can technology be used most effectively to support and assess student learning?

Digital compilation seems the biggest avenue for effective use. Students have access at all hours and from a myriad of location. Whether they use a class blog, class website, or class wiki, a central hub of information is at the forefront of supporting student learning.

For example, a classroom website with links to downloads (syllabus, assignments, etc.), websites, and other tools gives students a constant in the otherwise ever-changing world of technology. Bookmarks prove ineffective when URL's change or become outdated, so a website would reduce the reliance on bookmarks.

A class wiki seems like a terrific way for compiling student research. I hesitate a little bit to include assignments here because a student could always sabotage another's work, intentionally or not. However, if all the students had something at stake (such as a assignment based on the data compiled on the wiki), that might reduce the risk of intentional sabotage.

Of course, relying too much on technology has its disadvantages, especially when the technology fails. Hard copies assignment could help here, but it doesn't work in the case where students make videos or podcasts.

When it comes to assessing student learning, there is always the risk that students may plagiarize. If a group of students were to do an Othello rap video (kinda PG-13), then they might copy another video almost shot for shot. Of course, given the nature of such resources, it's hard to envision how anyone could check the students' originality (like Turnitin).

However, if creative synthesis is to take place, then maybe resources like these should be utilized. After all, when we begin assessing the higher levels of Bloom's Taxonomy of Learning, we seek such creative endeavors.

For example, if students are to have their own blogs where they post reflections, assignments, etc., then they would learn 21st century skills along with time management--namely, being responsible for keeping up with it over an extended period of time.

Technology has its place in today's learning environment. While any adjustment can be expected at the outset, teachers and students unfamiliar or unacquainted with technological tools will find their benefits most welcome.

Module 3 Reflection: Integrating the Internet

"This module has helped me think about the impact of the internet on my students’ learning in the following ways..."

Prior to this module, my perceived impact of the internet on my students' learning was fairly basic. I'm talking about like e-mail and maybe a classroom blog (not even a website).

Part of that has to do with own technological ineptitude. But another part was concern I have over technological restrictions of my students (means, funds, etc.). I get that students for the most part resort to last-second internet research most of the time. Meaningful interaction, though, is what I worried about.

However, students need practice with 21st century technology skills. While some already possess a small scope of these skills with social media and smartphones, many will almost assuredly need these skills for future opportunities.

Incorporating technology components as major resources may also require students to consider critical thinking skills they may not otherwise utilize: for instance, they will need to consider the validity of open content or the legal and ethical ramifications of misusing sources.

Therefore, I think a class wiki would be a great idea for certain assignments and compiling research or other data. An assessment geared toward information on the wiki would create a sense of ownership while giving the students' work a sense of urgency.

A classroom website is another great tool for communicating weekly, daily, or emergency notifications. It also serves as a readily accessible, central hub of resources for both parents and students. A blog, while effective at times, doesn't seem to carry the weight that a website does.

Hopefully, we can also learn how to efficiently and effectively research material via the internet. Managing your internet resources is a useful tool for anyone who uses the internet. Plus, the internet offers an abundance of resources and tools that can help students learn (as apparent through all the Cool Tool presentations).

The internet is an integral part of academic life, both for teachers and for students. If I can get my students and myself to use it effectively, then we all benefit: not just for the present academic year but also moving forward.

Module 2 Reflection: Holistic and Thoughtful Planning

"This module has helped me think about using standards, CFQ’s or formative assessment in the following ways……"

Frankly, having neither public school nor education backgrounds has provided the biggest challenge, in terms of learning the terminology and expectations of becoming a certified teacher.

For starters, I had never heard of a "standard" before. I never even realized standards were the building blocks of teaching units. Since identifying what we want students to learn in the initial step of planning a unit, standards provide the best (and mandated) guide for that.

As for the learning objectives themselves, they should include a mix of the vague and specific, the explicit and open-ended. Particularly the CFQ's, another term I was unfamiliar with entering this module.

We want clearly defined CFQ's at the essential, unit, and content levels. Respective examples of each include the following:

• Is math more than numbers?
• How does the addition of fractions compare to the addition of monomials?
• What is an isosceles triangle?

These CFQ's are the guide stones. Planning a unit without them may make me and my students lose focus. Because PBL, along with other types of learning, requires a holistic approach, I should make every effort to compose CFQ's thoughtfully and completely. This includes having CFQ's link past and future units.

Continuing the in-the-dark theme from above, formative and summative assessments were also terms I was unfamiliar with. The concepts are straightforward and were not unknown to me, but the carefully planning of them is something I never really considered before. Summative assessments are emphasized more it seems. However, the formative ones are the key to student learning.

I need to be thoughtful of how my formative assessments gauge my students needs, provide self-direction and encouragement, and engage metacognitive skills. Therefore, my formative assessments should be appropriate, thorough, and effective. This includes embracing a range of formative assessments, including but not limited to direct questioning, essay, journals, peer review/feedback, and tests.

Module 2 was helpful at a base level simply for introducing me to foreign but intuitive terms and concepts. However, I was able to discover that planning is more than just time management and allocation. If I want to be successful, I need to take my unit planning seriously. Students will be able to see through any BS, but--more importantly--they will not reap the rewards of their time and hard work.

Of course, any teacher worth his or her salt should reflect during and after every day, week, unit, semester, etc. I hope that these blogs will create this habit within me, if nothing else. I have no problems with self-assessment, but putting aside the time for it will prove my biggest challenge. I must guard against self-contentedness. Ensuring that is a necessary condition for ensuring the best for my students.

Module 1 Reflection: Evolution of Thought

"This module has made me think about my role as an instructional designer in the following ways..."

I'll be the first to admit that project-based learning (PBL) is an afterthought for me. As a teacher of mathematics, I'm very proud of our methods of instruction. In fact, we all probably swear by the same tried-and-true methods that our teacher's teachers taught.

However, Module 1 has illuminated that archaic way of thinking. At a time where we are struggling to keep up with 21st century technology and innovations, PBL seems almost necessary.

Why would I not want my students to have exposure to skills vital to today? PBL is a way to get the students to become their own educators. To an extent, it's already the case, but PBL accents their critical thinking, technology, and work environment skills in a way that traditional teaching methods cannot.

I have to become a facilitator for my students. They need to collaborate together, whether it's through a class/project wiki or interactive field trips to the McWane Center. PBL allows them to do this.

I must also accommodate varying needs. Different levels of cognitive function affect behavior, sociability, and performance. Therefore, students need a chance to experience all these while having an opportunity to shine in maybe two or three facets.

Having students be at the center of learning gives them something at stake. Whether it's an innate feeling of ownership, motivation for being self-directed, etc., these benefits outweigh any disadvantages of PBL.

And that's something that three weeks ago I just wouldn't have believed.

- Jordan