Wednesday, 12 December 2012

App Review: Morfo

There are many apps for creating talking avatars. I recently blogged about Voki which is great and allows you to record talking avatars which can be embedded on a blog.

I came across Morfo last night. It is so much fun, and allows you to take pictures or upload them and do recordings which is synched to the avatar. More interestingly, as a math and science teacher, I thought they had immediate applications in an Ipad classroom wherein students are doing a lot of content creation. Here are some examples:

Other Applications/Ideas
  1. Create talking fruit for unit on nutrition
  2. Create talking organs (gross!) for study of the human body
  3. Create talking books for book reviews


Tuesday, 11 December 2012

Scaffolding Formative Assessments within Project Based Learning

I've had a breakthrough in assessment with Project Based Learning, (PBL). I presented a dilemma that I was having to my CFG group a while back regarding assessment within Project Based Learning. People that advocate PBL are quick to point out its life connections but don't seem to have a good grasp on assessment practices of it. This was my question:

"How can we ensure that during a PBL activity all students are assessed accurately and honestly in a way that help provides feedback towards mastery of learning standards?"

I've had too many instances of inflated group grades in PBL wherin the alpha student would do all the work and the beta students would reap the benefits only to be "called out" during a summative test. PBL has obvious authentic connections, but in my experience using this format for thematic learning, I've noticed that group work often takes a counterproductive effect as the "smart" students try and motivate the weaker students only because they feel that their grade will be impacted negatively. For some of these students the focus is on "the grade" rather than "the learning" or "the experience". We might see such cooperative learning as part of the real world, but it can take a toll on self esteem if the stakes are high and defeat positive connections we hope to engender through such experiences.

My Goals
My goals were simple in this protocol. I asked my group that the following recommendations be made:
  1. Students have the opportunity to work towards mastery of knowledge and skills.
  2. Students compact out (be excused) from dry boring summative tests at the end of the unit. Although these were in my opinion, accurate, they did nothing but share learning with me. The nature of PBL was that the learning be "aimed" at an audience.
  3. By the time the culminating project was reached, all students have had sufficient practice of skills thus eliminating the need for a final test.  
Other Challenges
I had about 15 benchmarks to teach and assess but didn't want to cram them all into the project. I did something akin to this with our recent unit on functions, but for our unit on exponents and roots I wanted students to have a real in depth understanding of the Pythagorean theorem along with artistic principles, and environmental implications of their design.
Enter Formative Assessments Through Group Conferencing
Formative assessments are those little check ups to indicate whether or not students have learned something and provide the opportunity to reteach if necessary.  I have used entry and exit interviews with my students at the beginning and and end of lessons in the past but one suggestion from my CFG group was that students manage their own learning. One suggestion that stuck with me is to frame approaches to PBL like a cooperative learning or literature circle roles, where one member is the "taskmaster" who is in charge of reporting whether or not people are on task or have met learning expectations. If not, help them and indicate them to the teacher so that they can provide help when needed.

This would take place during warm ups after lessons to give enough time to digest learning activities and apply them through subsequent lessons. Each group had a taskmaster who would report on the skills of the group which in no way affected student grades. All students chose their groups ahead of time and connected through Twitter and reviewed through skype chats prior to the lesson.

Students spend 5-10 minutes on a warm up when they walk into class. This entry interview has standards from previous lessons.
When everyone was finished, I met with group leaders about solutions while the rest of the class did extension activities.

A group leader debriefs the warm up with his group members to explain the solutions.

On this group's log sheet after our first warm up, group leaders indicate which members have gotten a problem correct to identify areas that they need to work on.

After our third warm up, students were beginning to show signs of mastery and ones that were not were given one on one instruction with the teacher or other enrichment.

The Project: Bridging Differences. GRASP Tasks

Final Projects
By the time the final project had rolled around, the need for assessing learning through traditional testing was gone. All students had demonstrated that they had met the benchmarks throughout the unit a number of times through formative opportunities, and were scaffolded and spiraled through harder and harder problems to ensure a higher level of understanding. I didn't need to follow up with banal questions afterwards and felt that all students had an individualized learning experience.

In this project "Building Bridges" the students combined some mathematical use of the pythagorean theorum, artistic principles, and environmental awareness to integrate across disciplines.
Building Bridges Rubric

I'm proud of the work that students did during this unit of study. They're starting to utilize social media to discuss their learning, reflect on their own mistakes and work together for a common goal all the while while devoting some class time to independent practice of skills and as a time to work together on a project.

I feel for the first time that assessment was not distorted in any way which has always been a problem for me in the past. Each class had spiraling opportunities for assessment and debriefing with the student's group leader and myself to ensure working towards mastery of skills. After each lesson, we were able to apply each piece of learning to an architectural product.

Related Posts
Turning Student Failure into Information
Morphing into a Student Centered Environment

Sunday, 9 December 2012

Scaffolding Math Benchmarks with Blooms Taxonomy

I'm in the middle of a PBL unit and am designing a series of scaffolded formative assessments to help students achieve a mastery of understanding without the traditional summative test at the end. The walk in assessments have given some good insight to student abilities and I'm using small group peer evaluation and teacher one-on-one sessions while students work on their project to ensure that students are making progress.

I just saw "Waiting for Superman" and one of the points in the documentary was that there was an inconsistency between states, districts, and even schools of what "mastery" means. They used an example wherein a student could fail an assessment but then cross into a neighboring state and pass the same one. People are hoping that common core will eliminate the disparity but I think it will take 2-3 more years of implementation and resource acquisition before we see a more level playing field. Basically, people had different ideas of 'mastery'. 

What does "Mastery" Mean?
Why is there such disagreement about what "Mastery" means? I like to think that mastery means an "in-depth understanding of a mathematical concept that can be explained with critical thinking and reasoning" In short, something that cannot be easily measured through standardization. As a math teacher of 10 years, I've learned that there are many different answers and supporting reasons why something could be correct. Take this problem from properties of exponents wherein students learn some of the simplification processes of working with exponents with the same base:
Lower level rungs on Bloom's Taxonomy involve remembering principles, and summarizing or demonstrating that students can do them. Good for entry level understanding.

If they can simplify this to the correct answer which is 7 to the 7th power, they are correct. But have they "mastered" this understanding? I think not. All they have done is recalled the process of adding exponents with the same base and there is no explanation why this is supported. In fact, our textbook makes no mention of this as well.

Enter Blooms Taxonomy
Blooms taxonomy is a great model for designing assessments that work their way up towards the higher order skills of "evaluation" which we see in the pinnacle below. It can serve as a model to make the curriculum and learning of it "attainable" to entry level students in the beginning, but provide continual spiraling and scaffolding through subsequent more difficult tasks to develop cognitive abilities.

Photo courtesy of

In Practice with Formative Assessments
As my walk in "entry interview" I had a couple questions from the previous lesson. They all started at a very attainable level such as "Knowledge" and "Comprehension" but got progressively harder. In the case of properties of exponents, I tried to scaffold problems in a way that would lead to the higher order skills that I thought resembled "mastery".

Day 1-A low level question to check for basic understanding before moving on to higher applications

Day 2-An application and or analysis with many answers. Open ended questions can be differentiated by asking for supporting reasoning if needed.

Day 3-Evaluation and Synthesis to show reasoning and mathematical principles.

By day 5 within the unit, problems from our first lesson had been phased out, and students had been given one-on-one help with earlier concepts to tailor to a very individualized learning experience.

Final Stage of the Unit
By the time the end of the unit had rolled around, students had had enough practice with earlier concepts through spiraling to eliminate the need for a final summative test. The cyclical nature of using progressively harder formative assessments did the following:
  • Gave multiple opportunities to show learning though mistakes and peer and teacher conferencing
  • Allowed the opportunity to apply previous learning foundations to new situations
  • Eliminated the mandate for a final test
  • Provided inflection points to raise the bar with higher order thinking questions
  • Gave indicators over what benchmarks students were beginning to understand, developing their understanding or mastering their understanding
  •  Got rid of the "Remember this, because you'll be tested on it in two weeks" mentality.
Since the above criteria were met, I could focus on an in-depth understanding of the Pythagorean Theorum for the final project which contained elements of roots and exponents and our own PBL slant on the unit with some integrated artistic principles and technology expression as well. I didn't feel chained to the 15 benchmarks of the unit and had essentially broken down the test in a series of warm ups.

More Ideas on Scaffolding
There are other ways that others are exploring the use of scaffolding for understanding. Here are some ideas that I've learned from educators around the world.
  1. Provide "Challenge by Choice" materials. CBC is offering the curriculum through different tracts. entry level, standard level and advanced level. It's not modifying the curriculum in any way, but rather making it more accessible or challenging to any heterogeneous population of students. 
  2. Experiment with math stations. Such activity centers give opportunities to apply learning to a real-world authentic problem which can be shared to the class or online.
Related Posts
Formative Assessment in the Math Classroom
Turning Student Failure into Information
Challenge by Choice

Monday, 3 December 2012

Tweeting in the Math Classroom

If you've never read Steve Wheeler, check him out. He has a lot of great ideas about digital education, but he recently wrote a post on next generation learning that alludes to web 3.0 interfaces and what that might look like. It blew me away.

He uses a term that I had never used before which he calls "Rhizomatic" which be definition is a root sending out shoots in all directions. As students use various sources to learn from in this day and age, we might instinctively think that learning this way is the new norm. However, what really struck me from the post is the notion that students can create "learning communities"amongst themselves that help them learn. Research shows that students are aided by online collaboration, social media and many students would rather work with another student than a teacher anyway. The question is, how do we develop students to build their own learning communities?

Student Learning Communities Redefined
It's serendipitous that I just finished "Educaction Nation" by Milton Chen last week. Chen also advocates for more digital literacy and makes the good argument that blended learning communities are a good start, but that learning shouldn't start and stop during class time. Real engagement is when students share ideas outside of class and keep the discussion going long after the bell. Some ideas that I wanted to grow to fruitation:
  1. Students being able to access, share and evaluate resources together. 
  2. Students willing and able to help other students, not merely from our own classroom.
  3. Develop partnerships with other students to share ideas and resources.
Enter Twitter
Our school uses Google Apps and a number of 2.0 tools, but they're constricting to the mere students in the classroom. I gave a good lesson on Twitter Do's and Don'ts, Hashtags, and inappropriate and appropriate us so that we might "branch out" in a Rhizomatic fashion to teach and learn from others in the world. We cannot choose connections for students, but we can educate them on how to make good choices. Since our students are already Facebook fiends I gave a two minute spiel on using social media for learning.

Students give thanks to their group leaders that helped clarify and reteach after a warm up.
Students hypothesize a conjecture about whether a number with a negative exponent can ever be greater than 1

Students tweet about a lesson as formative feedback to others and the teacher

The Response
The response was great. Since implementation, we used Twitter for a variety of formative assessments at the beginning of class and I must say that the exchange of verbal and kin esthetic learning with a steady stream of tweets underlying the learning made for a very rich learning environment which students could draw on and enter at their own risk. Twitter allows for making a customizable widget which can be embedded onto a blog. In the following case, I embedded the conversation widget that we have in the back channels in math onto my classroom blog site. Parents can see little snippets of their child's conversations, resources shares, and general feelings about the subject at hand. There are settings within the filter that do not allow profane or obscene language to be posted to the timeline.

Continued Applications
Twitter will not teach my students math. However, it's shown to be a valueable tool in talking about math, asking for clarification, offering help and asking for it too. Is that not the predecessor to learning?

Related Posts
Blended Learning