Graphing Understanding

One of the things I would like to do with my students is have them graph their understanding of different objectives and mathematical practices. This would help them visualize their progress at different points throughout the semester. It would also help me see where they know they need help. Both asking questions in class approaching a teacher after can be intimidating and a bit nerve-wracking for some, so I think this would be a very low-key and passive way for them to tell me how they think they’re doing. I imagine something like a y-axis of levels of understanding, including statements like “I do not understand this at all,” “I understand parts of this,” and “I fully understand this.” On the x-axis would be the different elements students have been exposed to.

While this would not be used to grade them, I would use it as an informal, formative assessment to help let me know what to reteach or which students needed intervention. I think another way this could help my students is to visually show them that they have, in fact, learned something over the course of the class. If they start with a graph at the beginning of the year with low levels of understanding and increase over the semester or year, they will be able to give a tangible answer to the question, “What have you learned this year?” It would also be useful to show parents during conferences as a way to illustrate (albeit self-reported) learning or during interventions to show which elements the student definitely struggles with. It would also be interesting to see if some students understand past elements better after applying them to newly learned material. There is no doubt that students need to learn certain information before moving on. But would the deliberate practice and application help increase that learning after they did move on? Also, I wonder if I were to measure their understanding immediately before and after breaks, would there be a drop in knowledge due to the time off?

This is an activity I would like to take class time to go over at least three times a year, though ideally it would be done once every month. I think it would be helpful to me as an informal, formative assessment and a good illustration of self-reported knowledge for students, parents, and administrators. Let me know what you think in the comments!

Substitute Survivor Guides

I’ve been considering how substitutes will regard the lesson plans I’ve been writing. I’m trying to make them as clear as I can, assuming they know (and remember) 10th Grade level math. But what I’m really worried about is how they will get through the day. I remember subs in high school having nothing but a seating chart to go on, and those days weren’t very productive. Some classes were filled with responsible students, and we were able to read the plan and go through the lesson helping each other. Unfortunately, not all classes are like that.

I’ve found a lot of ‘survival kits’ for substitutes to bring or fall back on, but want to focus on what I can do as a regular teacher to make anyone who comes into my classroom have an easier time getting by. Here is what I’ve been able to find so far. Please add recommendations in the comments!

  • On a Clipboard:
    • Substitute Feedback Forms
      • These tend to have things like overall class behaviour, absences and tardies, and concerns. I plan on drafting one of these for my class, to give substitutes a voice as well as enable me to address any problems or successes after my return.
    • Sign-in Sheet
      • Having a back-up sign-in sheet would be great in case the sub is unable to find the attendance program on the classroom computer.
    • Period Overview
      • I found one PDF that consisted of each period, the lesson plan topic, and trustworthy students. When my mom first started driving our middle school bus route, she relied on a couple students to tell her where to go and which houses to stop at each morning and afternoon. I imagine having a go-to student (and even fellow teacher) for questions would be helpful and reduce stress.
    • What to Do/Where to Find
      • Another PDF I stumbled upon had two columns: What to do about… (attendance, homework, tardiness) & Where to find… (lesson plans, grade book, class lists). Having a compiled list like this would be a godsend if I were to substitute at this point, so I plan on making this available to my subs.
  • SubPack
    • Many resources talk about kits called ‘SubPacks’, which substitute teachers can bring into a new school. This usually has things like school supplies, activity ideas, and motivators. I’d like to have a small kit of something similar, that would have extras of things found around the classroom. Locating materials in a new environment can be tricky (just ask anyone who’s tried to find something in my mom’s kitchen), so I plan to have the necessary supplies stored in one place for the convenience of any newbie. One resource also listed first aid materials as a kit element. While I assume most classrooms will have this nearby, having some basic items (gloves, band-aids, etc.) would be handy.
  • Guidebook
    • I’ve found a printable document that lists virtually every policy and classroom activity that a sub might need to address (like evacuation plans, classroom procedures, and special education info). It is left blank, so that teachers can fill in the information for their schools and classrooms. I will definitely be making my own one of these.
  • Welcome Letter
    • I didn’t actually find this in any of the recommendations I viewed. But I think it’s a good idea to give someone filling in for you a nice greeting. I would appreciate it, anyway. It will not only have a basic welcome and thank you, but some basic info that may not be covered in the rest of the kit, as well as where to find the elements of the kit. Maybe some tips, too. Like who near the school is quick with to-go orders or who owes me favours they can spend. Something like that.

Brochure for Parents

I designed this for a class I’m taking, and was hoping for some feedback from others. (Technically, I’ve just submitted it, so I haven’t received any feedback yet.) It think this is a good introduction to parents, and a few of the MOOCs I’ve taken have mentioned writing to parents. Would this be a better replacement for or addition to a letter to my students’ parents/legal guardians?

Parents' BrochureParents' Brochure 2

Constructive Feedback

I’m currently drafting a stock lesson plan to use when I begin teaching. While writing, I realized it would be nice to have a go-to graphic for teaching constructive feedback during peer reviews and discussions. I’ve used the Passive/Active Positive/Negative system I learned from Dave Levin from KIPP Public Charter Schools in a previous lesson plan. I assume I’ll be needing it again for another.

So I created a graphic!

Constructive Feedback

I think it’s simple, and kinda cute. I figure whenever I need to teach my students what kind of feedback I expect from them, I can print it out on cardstock so they can hold onto it for the remainder of the year.

Feel free to use it for your own purpose! All pictures were taken from free clipart sites.

Bring Your Beef through the Door

In my MOOC “What Future for Education?” an interviewed expert disputed the concept of “leaving your beef at the door.” This phrase encourages students to keep emotional baggage and responses out of the classroom. This idea is perpetrated in my education program, with the reasoning that baggage and inter-student beef hinders learning in the classroom. The interviewee brought up the point that we can’t expect students (especially those in the pre-teen and teen years) to be able to remove themselves of their emotions. While everyone can agree that we don’t want students bickering during a lesson, it’s kind of silly to think of emotions like a jacket or scarf one can just take off when it becomes inconvenient.

Emotions and moods shape how students take in information. Naturally, we want students in the most receptive state possible. Without expecting them to leave their day’s events at the door, is there a way to help students enter the classroom in a better mindset? Can I do an activity at the beginning of class that will (truly) give students a break from their lives or from drama? Often people think stretching or doing a “fun” group activity can bond others or start the day fresh, when in actuality this activity only helps those already in a good frame of mind. How do I guide my future students in preparing themselves to learn without disregarding their feelings and baggage in the process? What do I do when a student comes into my classroom crying after receiving bad news or breaking off a relationship during passing period?

What High School Is

This week’s assignment for my MOOC, “How to Teach Us” is to create a ‘dream day’, consisting of a schedule or narrative that explains how I would like to plan my day. Part of it will vary due to the school-wide schedule, but I’ve based it on my ideal. Please give feedback in the comment section.

My Schedule
High School
Student Day Length: 5 1/2 hours

  • 9am– School buses begin to arrive
    • I open classroom for students who need tutoring and prepare my room for the lessons ahead.
  • 9:30– School day begins
    • Students arrive for their first period.
  • 10:25– Passing period
  • 10:30– Second period
    • This subject is the same as the first. (I may try different methods of teaching this lesson to see which works best.)
  • 11:25– Lunch period
    • My class is open while I eat for students who want tutoring. I use this time as a prep period.
  • 12pm– Third period
    • Students arrive for a new subject.
  • 12:55– Passing period
  • 1pm– Fourth period
    • This subject is the same as the previous. (I may try different methods of teaching this lesson to see which works best.)
  • 1:55– Passing period
  • 2pm– Fifth period
    • Students arrive for an honor’s class.
  • 2:55– School day ends
    • I open classroom for students who need tutoring. I use this time as a prep period to collect paperwork and tools for the next day.
  • 3:30– I go home

Class schedule:

  • 0 min.– Bell rings. Students may collect supplies and ask questions before sitting down.
  • 2 min.– Students should be sitting and working on the entry task.
  • 5 min.– Go over entry task as a class.
  • 10 min.– Merge from entry work into related lesson.
  • 17 min.– Brain break. (This is a 30-second opportunity for students to move their bodies, which increases blood-flow and glucose to the brain.)
  • 30 min.– Brain break. Transition to next section.
  • Work time. Students may use this to work on their daily assignment, unit homework, or other class work.
  • 53 min.– Students are allowed to begin packing and preparing to change classes. (This gives them time to mentally prepare for the change– something important for those with agoraphobia or sensory disorders– and some extra time to walk so they can use the facilities between classes.)
  • 55 min.– Bell rings. Class is dismissed.

Homework Plan

Hello, again!

I’ve been auditing a second MOOC, How to Teach Us, from the Coursera platform. This week, one of the readings was a chapter from Fires in the Mind entitled “Is Homework Deliberate Practice?” This chapter covered how many teachers approach assigning and assessing homework in secondary grades, and included quotes from interviewed students. While reading this chapter, I started cementing my ideas (which have previously been vague, but purposeful) of how I wanted to assign homework in my classroom.

One thing that stood out was the idea that, in order to be deliberate practice, each homework assignment should fall into one of four categories known as ‘The four Rs’:

  1. Readies students for new learning (more complex concept/step)
  2. Repetitive in knowledge and application of skills
  3. Reviews previously learned material (such as practicing instrument exercises to improve the playing of a musical piece)
  4. Revises work or understanding (such as editing a paper)

Another point made was giving students an opportunity to complete work at school. Some students don’t have time or help at home of they get stuck. I will make sure to have tutoring time available during my prep, lunch, or after school each day. I will also encourage my school to have a study time available throughout the week.

The final thing that guided my plan was how students believe their teachers see homework. Many see it as a one-size-fits-all assessment. I’ve tried to cater to that by basing the final homework assignment for the lesson on what was missed in the first unit homework assignment. I can do this by having sets of questions (or worksheets) created before the unit for areas in which I foresee struggling, or using software to help find problem areas en masse (The Learning Company computer games were excellent at catering to the child’s level of understanding). A second concern the interviewed students voiced was that they believed teachers didn’t use or really looked at the assignments that were assigned. I would make it obvious that I go over and make notes and consider altering lesson plans based on what I am reviewing.

My Plan

I’ve tried to weed out the issues as I went, and did an overall review to add specifics after I first wrote it all down. But if you see something you think I’ve missed, please comment! This plan is for my future high school math classroom, which may include more at-risk students than the average classroom.

Daily Assignments

  • Formal, formative
  • Graded on completion (based on a holistic rubric– partial credit available)
  • Expected work time: 20 min.
  • Time available during class

This will be a short set of questions (less than ten) that are directly related to the material covered that day. These will be pre-created, but may be altered if necessary. When assessing my students work, I will look over and mark which parts were wrong (and what the correct steps would be), then make note of concepts they are struggling with. I will note class-wide trends for review during class time. When completing these, students should:

  • Do it! Partial credit keeps their grades up, and seeing their work helps me find gaps in understanding or if they are ready for more.
  • Show their work. Having that window into their process gives me better insight into where things may be going wrong in my lessons.
  • Work out the problems they struggle with to the best of their abilities. I don’t know where students get stuck if they don’t attempt the question.
  • Make note at the end of the assignment of points where they notice they struggle. This would also be an opportunity to note when too little time was spent on a concept during the lesson.

Unit Homework

  • Formal, formative
  • Graded on correctness (based on an answer key)
  • Expected work time: 45 min.
  • No work time given in class

This will be a long set of problems assigned at the beginning of the unit. These problems will be a mix of elements from each lesson, as well as questions that ‘put it all together’. Students are to complete this as they feel competent in each area. This will be collected at the end of the unit, giving students time to seek help and find time in their schedules. This will be an opportunity for students to practice time-management and academic honesty. The motivation to complete this with their own work is intrinsic, as the final assignment will be based on what they need practice in and will rely on them understanding each concept fully, without outside help.

Final Homework Assignment

  • Formal, summative
  • Graded on correctness (based on an answer key or analytic rubric)
  • Expected work time: 30-60 min. (varies for each student/activity)
  • No work time given in class

This will be a follow-up assignment based on what each student needed from the Unit Homework. Assignment activities will vary. Students may be given a problem set, worksheet, or BINGO card (containing multiple projects that fulfill one or more concepts). Activity purposes will be determined by assigning each student to one of four categories:

  1. Students who understand everything will receive deeper questions or require deeper thinking in their projects/application.
  2. Students who misunderstand one or two things will receive problems/projects based on improving, practicing, and applying that specific element.
  3. Students who misunderstand multiple things will receive problems dealing with specific base concepts, then combined and applied concepts in questions/projects .
  4. Students who understand little will (hopefully) have been given intervention as the unit went on. This will be built upon in this assignment by giving them questions and explanations dealing in base knowledge and practice. Reviewing past lessons and subjects will occur if necessary. Altered assessment will be considered for final testing.

That’s it! Let me know what you think!

What Future for Education?

I’ve started auditing the MOOC “What Future for Education?” on the Coursera platform. It’s common to think of the future of educating and school in terms of what we have available and what we value today. This course admits that extrapolating what the future will hold has failed multiple times in the past (in everything from past teaching techniques to sci-fi films of the last century).

I hope this course will open my mind to techniques and tools that I haven’t considered, as well as bring up philosophical questions concerning teaching and schools that I haven’t been exposed to in my bachelor program.

My current views about education are a bit scattershot, but overall I have a few resounding beliefs:

  • Technology in education should be used primarily to teach standards and skills in the respective class or subject. A secondary goal may be to expose students to that tool. Technology shouldn’t be brought into a school unless the primary goal is served, as education is often lost when classes are forced to use objects that are “cool” and “fun”, but hinder learning.
  • Schooling should be teacher guided, but student-centered. At the moment, I believe school is student-guided (students are supposed to know what part of a lesson they don’t understand, then ask the right questions to get there without being given the base knowledge to do this), but teacher-centered (teachers decide what levels students should be studying, whether or not that student is above or below that point).
  • Students need to be given a reason to be in school that is useful to them. Many students have other responsibilities (young siblings or their own child to care for, work or parents’ bills to help pay, etc.) and education should offer those students skills that will help them in their alternative lives.

Future posts will follow my path in this class, where I touch on these topics as they are brought up in the lectures.



Adjustable Timelines

With all of the fuss about world education ranks and standardized testing these days, many seem to have forgotten the point of assessments– to assess learning. Testing is meant to tell how much the student has been able to absorb, process, and explain what they were taught. The ideal concept is that the teacher and student would get more out of the feedback than the government.

Unfortunately, there are many teachers who see a poor average grade in a unit and use it as a chance to lecture the students for not working hard enough. Some will think, “Well, I guess that section was too hard to grasp. Let’s move on to something else.” There is a race to cover as much as possible before the end of the year (or before the state testing) comes along, and there is no time to emphasize a single section when you school’s funding (and possibly your job) is on the line.

One of the reasons I love the new Common Core (I have many; feel free to ask for more!) is that a lot of that pressure is taken away. In the Montana CC Mathematics Standards, secondary objectives are to be taught over the course of four years, rather than by the end of each year, as the former “benchmarks” were. Students learn at their own pace. Within this, they will learn different concepts at different rates. Your class may fly through the Pythagorean Theorem, then get stuck on the rest of the Trig Identities. Teachers need to me aware of this. We need to plan to change our plans to accommodate our learners.

This last Monday, when my professor went over the class syllabus, he gave us a timeline for when we would cover each concept. The class objectives were on the board, along with how long he predicted each to take. But then he said, “We may spend more, if you guys need it.” The schedule was tentative. This should become more common, as public education (hopefully) improves in the near future. We no longer need industrial workers. We have machines and robots for that, now. What our society needs now is workers who can adapt to difficult situations, alter their strategy when necessary, and self-evaluate their methods. To create those future citizens, we need teachers with those skills. Set plans are safe. Schedules and deadlines let us know what is expected of us. But sometimes, our future students will expect a little fluidity as well.

Inventing Problems

I’m sure many of you have been annoyed by the story problems in math classes. They are often boring, worded funny, and require a large suspension of disbelief. You may ask yourself what kind of idiot would write questions like those.

Well, I would.

In my Probability class, one of the projects assigned was to come up with unique questions that would need to be solved using the methods we were learning in class. We didn’t do that well. Now, I don’t mean to insult my classmates. Our questions were clever and fun to think about. However, they fell short when we were asked to solve each others. They became as mundane and silly as the work we had done our of textbooks in previous math classes.

In Jo Boaler’s class, she mentioned a different approach to assigning larger problems. In most American classroom, Mathematics is taught as a subject, rather than a tool. Teachers search for a circumstance applicable to their current curriculum, rather than providing problems and giving the students tools and resources to solve it how they see fit. The questions my class and I came up with were synthesized with answers and a process already chosen. We had worked backward to get the problem, which made them straightforward and fake.

Jo spoke of a school that taught Mathematics as a tool. Instead of giving their students a procedure out of thin air and asking cookie cutter question that didn’t really apply to life outside the classroom, teachers would assign a project, then make a number of tools available for their class. These tools would include what the teachers would think would be of use, such as protractors and straight edges, along with random ones that were unlikely to be necessary. Students would have to think critically about how to go about solving the problem. Some students would even use the ‘unnecessary’ items to problem solve in a new, unconventional way. The students had to choose the procedure, rather than being force-fed one to plug-and-chug throughout the class period. When groups came to the teachers with questions, they would be led in the right direction, or given a concept or procedure useful for how the group decided to overcome their current hurdle. Students would understand why and how the procedure they had just learned worked and how it could be applied to real-world situations. The groups would even share what they learned with others. (I mentioned in an earlier entry how explaining to peers solidifies understanding of the material.) Mathematics was no longer a thing to be memorized and regurgitated, but something to experience first-hand and apply.

Inventing problems with specific information in mind does have a place in the classroom, though. By creating our own, personal questions in my stats class, we were deepening our understanding of how the procedures worked as well as where we could use them in our own lives. It gave us a chance to be creative and invent the most complicated (yet solvable) problem we could.