Blogging - Leaving Pieces Behind

I am writing this blog in response to Todd Nesloney's #EduLS Week 5 challenge. The assignment is to write a blog entry. For some it will be their first ever blog. For others this week's assignment will be part of their regular routine. For me, it falls in the middle. Blogging isn't something I do everyday or regularly, but something I have done sporadically. I have contributed to two blogs, this blog and Banana Daiquiris and Life Lessons. This blog is for my "professional life" while BD & LL is more personal. I am one of several (and certainly not the most entertaining/creative/cleaver/consistent/funny) contributors to BD & LL.

Back to the point. As I thought about the topic for this blog post, I read through some previous posts and a thought started to develop. There are lots of great reasons to blog. Jon Harper mentions a few of these in this video introduction. I find that blogging is a chance for me to think through some of my disjointed thoughts and attempt to make them understandable and relevant for others. As I read and reflected I also took a moment to look at my blog data. My blog is not followed by many people (actually only 1 and I think he was guilt-ed into it). However, by the magic of the inter-web and social media, my blog has been viewed 595 times. Certainly not very impressive and not even close to what more popular educational blogs see in one day.

Still I can't see this as a bit impressive. My first post was on March 21, 2014. In a little less than a year my little dinky, experimental, rambling, inconsistently contributed to blog was looked at 595 times. Not too bad. Granted some of these were friends and family, some were certainly repeats, some were probably even accidental. Still, it means that 595 times someone was exposed to what I had to say. I can somewhat confidently say that even if only half of those visits were from viewers who were somewhat interested in the content and took the time to read all or part of a post, my thoughts were shared with another human being around 300 times. That's pretty cool! And just maybe of half of those times - 150 times someone read something what I wrote and considered it. And just maybe a quarter of those instances (around 37 of those times - I should have used an easier number) someone thought further about or talked about or actually made a change to something that they do in their classroom or with their own children. Well that's pretty cool. And all I had to do was take 15 minutes and write some thoughts and post them to the magical inter-web. Pretty awesome stuff.

And how does this all relate to the title? I began to understand that writing a blog is like leaving little pieces and bits of information behind. And what's so impressive about that? Pretty simple. We all look for information on a particular topic daily. What's cool about blogs is that any time someone goes to the Google and types a question or topic into the search bar, there is a chance that that person will come across what you wrote. My job is to present PD to educators. I love my job and hope that I make a difference for students. However, I know that there are times when I present on a topic - let's say task-based learning for instance, and those that I am presenting to (or some of them) are not quite ready to use the information to make change in their classroom. Unfortunately this information may be lost. And lets face it 99.9% of the time they will never look at the materials given to them ever again. But then later (maybe 1 year, 2 years or 5 years later) they say, "Wow, I can really see how I could use task based learning to help my students understand _______________. I just wish I could find that stuff that one guy gave me." That's were the internet, including blogs, teacher pages, etc are great resources. They are little pieces of information left for others to find when they need it and when they are ready for it.

Now do I know if anything that I write makes a difference to anyone? Not really. But I think the odds are with me. Especially if I continue to blog, read blogs, consider their ideas, share their ideas, blog some more, post some more resources etc.

Happy blogging and thanks again to Todd Nesloney for putting us all to the #EduLS challenge! Maybe someday I will make his, or someone else's list of favorite blogs! And be sure to check out BD&LL. I like to think we are somewhat entertaining and will make you think about some things you never thought you would think about. Besides, we'd all like to be famous. And the only way for that to happen is if people like you read our stuff. Enjoy!

A Reflection

It's the time of year when many of us do some reflecting of one sort or another. For many, the winter break allows us a time to catch our breath and think about the changes we would like to make for the second part of the school year. Although my job as a secondary math specialists does not provide an official break from the job, it is a bit of a chance to prepare for the training that will be upcoming and to plan for some improvements.

The information that is gathered from session evaluations is helpful for looking critically at what I do and how effective it is in the eye of the teachers. One area of concern for me recently has been my ability to convey the connection between the various workshops that I have led and the AZCCRS (that is Arizona College and Career Ready Standards for those outside of AZ). 

In short, this post is more for me than any audience but perhaps it will inspire at least a few people to set some goals based on data. 

The last two days have been spent preparing for an upcoming session focused on increasing student engagement at a higher cognitive demand with a colleague. At the beginning of the process we wrote the goals for the session and discussed the idea that we wanted to stress the connection between the strategies we will be modeling and the AZCCRS.

Having the data has been helpful in helping me set a personal goal. However, the most important factor in me taking the first step toward reaching this goal is the collaborative process that has occurred over the last two days. Having another person to reflect and brainstorm with has been invaluable. Soon enough I will be able to see if this first step has been successful.

Happy new year!

Biggest Bang for your PD Buck

At our most recent staff meeting we were presented with some information regarding "effects" and their impact on student learning. The information was based on John Hattie's "Visible Learning for Teachers." This report is a synthesis of 1000 + meta-analyses which included 240 + million students and reported by Stephen Kendall-Jones. The basic idea is to see what types of things (teaching styles, teacher actions, school environment, etc.) are the most and least effective in terms of student growth. I have no specifics about the measurement of student growth or how the data was analysed. Some of the findings were interesting to me. Below I have listed the 10 least and the 10 most effective "effects."

Least Effective Influences

1. Whole language
2. Perceptual-Motor programs
3. Out of school curricula experiences
4. Distance Education
5. Teacher subject matter knowledge
6. Diet
7. Gender
8. Ability grouping
9. Teacher education
10. Mentoring

Most Effective Influences

1. Self-reported grades
2. Piagetian programs
3. Providing formative evaluation
4. Micro teaching
5. Acceleration
6. Classroom behavioral
7. Comprehensive interventions for learning disable students
8. Teacher clarity
9. Reciprocal teaching
10. Feedback

I must admit that I don't know what some of these are. I do have some observations. 

• Using evaluation to provide feedback is effective - I do not have the specifics and am unsure if this is regarding students or teachers. However, I do feel that it is important for both teachers and students to have formative evaluations. At times it is difficult for us as teachers to make changes unless we are given a nudge in the direction of improvement. Often times these changes are unnatural and uncomfortable for us. Focusing on these changes through the lens of a formative evaluation can be helpful if done in a supportive, non-punitive setting. I can see the same being true for students. Evaluations are an indicator of how a student is performing. We need to help students use evaluations to determine both there strengths and their weaknesses. We also need to help them improve in their weak areas through the development of a plan.
• Feedback is important - Feedback does help us grow. Others see what we have done and how we perform differently than we do. Through feedback we change our perceptions about ourselves and learn how we can improve our performance. This feedback must be specific and immediate (or as immediate as possible).
• High expectations - Most of us have no idea what we can really accomplish. We like to live comfortably and rarely reach beyond what is comfortable. Setting high expectations can be an effective influence if done so in a supportive environment.
• Self-reported grades - This allows students to take ownership for their learning. Students learn to be self-reflecting which teaches them meta-cognitive skills. Through development of these skills students will recognize where they need to improve and what skills they have to help them through learning difficulties. 

Although it didn't make the top 10 list, another influence that has a high effective is teacher-student relationships. If every teacher could make the extra effort to connect with all students (especially those that have not experienced success in education) we could see huge gains. It is not always easy to do this with our busy schedules. However, a concerted effort is worth every second of time spent. Doing this right away and staying with it can have a great impact on students who otherwise may not experience their true potential. Often times we get caught up in the logistics of teaching. We forget that it really is about kids and helping them reach their potential. They are people and often need our support outside of content. Life is tough for way too many kids. Letting them know that we do care about them not just as a math student can go a long way to helping them do things they never thought possible. 

Invert-and-Multiply...But Why?

If you teach division of fractions (the other "F" word) using the standard algorithm of invert and multiply, then you may have wondered, as I have, why it works. As a self proclaimed "math nerd," I have been thinking about this off and on for about a year now. As I started to work deeply with the AZCCRS (that's "Arizona College and Career Ready Standards" for those of you who do not live in AZ), I was really impressed at how the standards require the use of drawing and modeling with concrete objects to help students understand and make connections to procedures. I believe this is a key piece math education has been missing for far too long.

However, there was one common procedure (algorithm) that I could never connect to a model or drawing for myself - that is the standard algorithm for dividing by a fractions. The "Invert-and-Multiply" procedure is a mysterious procedure to most (if not all) students and I would guess to most adults, including teachers, as well. No matter how I tried, I was not able to connect a drawing to the standard algorithm of flipping and multiplying that you are probably so familiar with. Three education specialists (two math and one STEM) in my office have tried for months to find a way to demonstrate the connection for students. We were able to use drawings to answer division of fraction questions, but the elusive connection was always absent.

That all changed recently. As part of an effort to roll-out a math program to schools in Pinal County I have been participating in training offered by the Rodel Foundation of Arizona. The training is targeted at 3rd grade teachers. As part of the training we were asked to read selected chapters from "Teaching Student-Centered Mathematics - Developmentally Appropriate Instruction for Grades 3-5" by John A. Van de Walle, Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams. It is a wonderful resource and provides insight into helping students make connections so that they understand mathematics at the deep level required by the AZCCRS. 

I started reading the chapter on fraction operations as required. I expected to read another technical proof on why the invert and multiply routine works. I had seen multiple explanation of this and understand and agree with them. However they always fall short of making the connection using a drawing or model. As I read the section I was encouraged and finally it happened. As I worked through the suggested questions to ask of students, I began to use drawings to help me make sense of the problems I suddenly realized each time I was dividing my drawing by the denominator and then multiplying by the numerator. Although I know I was doing this with every problem, the secret for me to unlocking the connection between the drawing and the algorithm was the context that was given to the problem. It finally made sense! And I understood it! 

I worked several more problems just to make sure I understood it. Then the other two specialists and I practiced at the circular table in the middle of our office space. This is where a lot of great discoveries take place (or a lot of junk piles up - depending on the work load of any given week). We tried what ifs and asked each other to explain it again. After an hour or so, feeling accomplished, we went back to our individual tasks for the day.

A few weeks later, while I was working with a group of middle school teachers, who are working on studying the standards and writing effective lesson objectives in preparation for writing curriculum for their district, the question arose. How can we help students understand the process of dividing fractions. I pumped up my chest, and smiled and stated, "I can show you." Feeling pretty smart, I walked to the white board and asked for them to give me a question. They asked the question (of course it was a word problem) and I started. I drew some rectangles, divided them accordingly and then completely forgot everything that I thought I knew about making connections. (This ever happen to anyone besides me?) I tried another approach. Maybe a different context. Cookies! Yeah, there was something about cookies that helped me understand it last time.

I drew some cookies. No luck.
I drew some ribbon - you know for making bows. No soup.
Rates! - That was it. If it takes 2 and 1/2 hours to travel 3 and 1/8 miles how far can you travel in one hour. Nope - still couldn't put it together.

Every adult (7 middle school and high school math teachers and two math specialists) tried for 45 minutes to make the connections. Finally our time ran out. I left for 10 days of vacation and the teachers moved on to greener pastures. The first thing I did when I got back to work, was grab "Teaching Student-Centered Mathematics" and make the connection for myself again.

So now, after learning and forgetting and relearning, I decided it would be a good idea to have it where I can always access it. Isn't the Internet great! I can post it here, share it, get feedback, and find it when I need it.

First - start by asking students questions where the divisor is a unit fraction (i.e. 3 divided by 1/2, 5 divided by 1/4, 3 and 3/4 divided by 1/8). Also, to help students visualize, give them a context. (How many servings of 1/2 are in 3 containers?) This will help them create pictures to help them with the math.

This is how I approached the question "How many servings of 1/8 are in 3 3/4 containers?"

I first drew a picture of 3 3/4. I divided it into 1/4s. I kind of did this intuitively. I'm not sure if students would work with way at this point, but as they work and get stuck I may direct them in this direction later.

I then needed to decide how many 1/8 fit into the 15/4. I see that if I divide each section into 2 parts I will then have 1/8s and I can simply count.

Simply by counting I see that 15/4 divided by 1/8 is 30. Thus, there are 30 1/8 servings in 3 3/4. The standard algorithm would result in my multiplying 15/4 times 8/1 or (15*8)/(4*1). At this point I was still not able to make the connection. But I could see that in effect when I counted 2 1/8s for each quarter which means I multiplied by 2. 15 * 2 is 30. I can also see that if I had first reduced the fractions when multiplying by the inverse I would have multiplied 15 times 2 since the 8 would reduce to 2 and 4 would reduce to 1.

The next question really got me on the way. "You have 1 1/2 oranges, which is 3/5 of an adult serving. How many oranges (and parts of oranges) make up 1 adult serving?"

More drawing. I started by drawing a representation for the oranges. 

I also knew the drawing would represent 3/5 of an adult serving. I thought to myself, if I could figure out what 1/5 of an adult serving is, then I could simply multiply by 5 so that I would have 5/5 or 1 adult serving. (Here's where I started to put this together.) If 3/2 of oranges is 3/5 of a serving then I divide the 3/2 into 3 equal parts (dividing by 3 - which is the numerator of the divisor) I will know 1/5 of an adult serving. 

Back to the drawing.

I know this mean 1/2 of an orange is 1/5 of an adult serving. Therefor multiplying 1/2 times 5 gives me 5/2 oranges or 2 1/2 oranges. I can now see with the picture that I divided by 3 and although I didn't multiply by 5 using the picture I can see the connection to the standard algorithm. I can see the light!

Now to try something a little more difficult, where the fractions aren't as friendly. "Aidan found out that is she walks quickly during her morning exercise, she can cover 2 3/5 miles in 4/7 or an hour. How fast is she walking in miles per hour?

I start by drawing 2 3/5 miles. I am also thinking that this represents 4/7 of an hour. Again, if I can determine how far in 1/7 of an hour, I will be able to determine how far you can travel in an hour, or mph.

To do this I need to split the 1/5 sections into 4 equal groups, or divide by 4. Since 13 doesn't divide into 4 even groups I will need to rename the sections. I know that if I split each 1/5 section into 4 equal parts, then I will be able to split the 52 sections in 4 even groups.

This means that she travels 13/20 of a mile in 1/7 of an hour. To determine how far she can travel in 1 hour, I multiply 13/20 times 7. This means that she can travel 91/20 miles in one hour, or approximately 4 1/2 mph or exactly 4 11/20 mph. So in summary, I divided 13/5 by 4. In order to do so I changed 13/5 into 52/20. When I divided I dot 13/20 miles for 1/7 hours and then multiplied by 7 to get 91/20 or 4 11/20 mph. I divided by the numerator and then multiplied by the denominator. I have made the connection using the algorithm to what I have done with the drawing.

I still think I can make this connection more explicitly, but I am much closer than I was and think I could help students connect these ideas. In some instances I think that students find this easier they have no knowledge of the standard algorithm and do not enter the conversation with misconceptions that we as adults sometimes bring to the situation.

Let me know if this makes sense to you and/or if you have another way to demonstrate this connection to help students make sense of and understand this often poorly understood algorithm.

Followup

I really enjoy my job as a math education specialist. However, I have had a lingering concern about the lack of follow-up that my job allows. Most of the time I work with teachers for very short periods of time. Sometimes as short as 1 hour. I then may not see those teachers for several weeks, months, or longer. This always makes me wonder how much of the information that teachers are able to effectively integrate into their practice.

How can I effectively follow up with teachers to support effective change?

This question has been following me since I began delivering PD to teachers in Pinal County over a year ago. Today I think I came up with an idea. Although I have not ironed out the details, I feel that asking teachers to report back electronically after a specified period of time will allow them to feel supported and to ask questions that come up as they attempt to change the way they operate within the classroom. Below are some ideas that I will think more about and use as follow up activities.

1. Using a forum on my website - I would ask participants to report what they have implemented into their classes after a given time (1-2 weeks) and their reflection on how it went. Also, they could ask any questions that may have arisen or ask for advice from myself and other participants.
2. On a PD blog - similar to using the above method however this would be more public. Perhaps a benefit of this format would be the reach. The questions, advice and conversation could potentially reach more people therefor allowing for collaboration on an even greater scope.
3. A scheduled Google Hangout - have the participants "meet" at a predetermined time to hold a video conference concerning what they have incorporated and the success and challenges they have faced. I like this idea the most, but scheduling will be a challenge.
4. Set up courses in Blackboard or Moodle - This would have the added benefit of having all of the materials available for participants in one location. As in using a forum on my website I would use the forum feature to facilitate discussions.

I'm sure there are other ways to do this and I would be super happy to have you share those with me. This is an endeavor that I feel is important and I have no idea of whether or not it will have any positive effect but as my Mom always told me, "You never know unless you try."

Happy mathing! 

To 3-Act Math or to not 3-Act Math?

Recently, I was tutoring and a student asked me for help with what I found to be an interesting question.

"There are 2 stools, one 3-legged and one 4-legged. One of the stools wobbles slightly.

• Which one is it? How do you know?
• Suppose that each stool is placed on a flat surface that is slightly sloped. Do you expect either of the stools to rock side to side? Explain why or why not. 

 Life experience led me to the correct answer yet I had to think for a moment to consider how to help the student understand the underlying concept that any 3 points make a plane.

Concurrently, I was thinking that a much better way of presenting this question to the students would be during an inquiry activity. It would allow students to discuss their ideas with one another and collaborate in order to make a precise statement defending their position. It would allow students to make a connection between "real-life" and mathematics - an opportunity to understand that there is a mathematical explanation for an what many students may have already observed during their lives. It demonstrates that people use math to explain the world around them. This idea also has applications such as the use of tripods.

I thought more about the question as I drove home and considered how I might have introduced this to students and what tools I may provide to them in order to experiment and get them interested in the task at hand. I turned to my PLN for ideas and posted the question and asked "Could this be improved? How could tech be integrated?"

A conversation followed between myself, +Jeremy Bell, and +Kyle Pearce. They both offered suggestions. The conversation then turned to whether or not the concept warranted the creation of a 3 Act Math Task or not. I would argue that this is an opportunity for students to have a math talk about a concept that is pretty simple, yet difficult to explain without mathematics vocabulary. Perhaps I view this activity as one that could be done at the beginning of the semester in Geometry. It could be used as an opportunity for the teacher to demonstrate to the students how to engage in math talks and share ideas. Also of emphasis could be that learning will take place through inquiry and discovery activities. This is a significant change for many students as they have been taught in a more traditional direct instruction model.

I also understand the other side of the argument. The same idea may be conveyed through a quick demonstration or even an explanation. The concept is not one that is of great focus in Geometry. It may be wasted time to create a 3 Act Math Task for this small concept and it may be a waste of time to have students work through a process.

So the question stands. Do you think that a 3 Act Math Task is an effective way to help student uncover the idea that 3 points always make a plan, or is it wasted time and resources for this particular topic?

Mini Goals

Lately I have been working hard to try to stick to a workout schedule. With the start of the school year (yes in AZ it starts at the end of July or beginning of August) it means my wife will be going back to work and I will once again have the pleasure (or duty - depending on the day) of transporting our three year old to daycare a preschool. Sticking to a workout schedule becomes more difficult. I also tutor at Grande Sports Academy, a residential soccer program, three nights per week. So the schedule gets more hectic and getting up with the alarm at 5 gets tougher.

While running earlier this week I found myself wanting to take a walking break after running just over a mile. With another 1.5 miles to go, I was having a sort of internal struggle over whether or not to take a short walking break. My hip was hurting, I was out of breath, and my allergies were causing issues beyond the normal. The struggle led me to keep setting mini-goals. Keep running to the next intersection, then the stop-light, then catch that guy that is walking, then to the corner in front our house. Before I knew it, the run was over and I never did take a walking break. I find myself doing this when I work out. One more set of 10 burpees, 15 more seconds planking, 3 more sprints, etc. I break down a workout that seems overwhelming into a series of mini-goals. This helps me keep from giving in to the aches, pains, or lack of motivation.

Amid the argument in my head, I began to realize that this strategy can apply to other areas of life. I specifically thought about using this strategy in education. Instead of being overwhelmed by a larger goal you may have (integrate technology, implement problem-based learning, etc.) break a larger, long-term goal into one mini-step at a time.

As a trainer this is something that I sometimes fail to do. I fail to help participants break an overwhelming task into smaller more attainable mini-goals. This is one great weakness that I see in the model of PD that I am sometimes asked to deliver. One-time, all-day PD sessions often have excellent content, strategies, resources etc. However, they truly lack in follow-through and support. Fortunately many schools are beginning to ask for follow up support as their teachers implement the new _______________ that has been presented. It is more effective and it seems that teachers are much more willing and able to truly change their teaching when this support is provided.

My goal is to be more cognizant of what my long-term goals are and work to create mini-goals that lead me to the finish line. Although, if you are a runner you know that one finish line leads to another start.

What are your long-term goals and what are some mini-goals that will help you get there?