Class-generated Quizzes

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One of my classes explored multiplication, factors, multiples and arrays in December. Students solved problems involving using different multiplication strategies and we thoroughly discussed how arrays can be arranged using the rows and columns as factors.  A unit assessment is scheduled for January so students were given a task before break.  Students were asked to create a problem involving multiplication. They had to write out the problem, provide three close but incorrect answers, and one correct answer.  Students could use dice or a random number generator to create the problem.  Most opted to create an original problem.

Students picked problems involving arrays, while others decided to add to the challenge and have students identify factors and distinguish between the product and factors.  Other students created square array problems.  I found that in the creation process many students had to erase their model and start over.  They had to be clear and I reiterated that everyone in the class would need to be able to clearly distinguish the rows, columns and total of an array.  Students realized that the array had to be in the form of a rectangle or square and some used a ruler for precision purposes.  Yay!  Others didn’t. I collected all of the potential questions and answers and brought them home over winter break.  I didn’t look at them again for another two weeks.  I

Yesterday evening I took pictures of the drawings with my iPad and inserted each question into a quiz.  It didn’t take as long as I originally thought to put all the questions and pictures into the quiz.  Feel free to access the actual quiz here.

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Today I paired students up and they took the class quiz.  Students were stoked to see their question on the quiz and the excitement was contagious.   It took the students around 15-20 minutes to complete the quiz and the class reviewed each question together.  The author of each question revealed themselves as we went through the questions and drawings.  Students gave feedback on the questions and I was impressed with how close the incorrect answers were to the actual solutions.   They wanted to make sure the students actually read the questions carefully.  Good call!

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In the future I’d like to add more topics to the quiz.  Adding variety will also give students more options to review the topics discussed in class.  I feel like this idea has legs and I might use it again later in the year.

Self-Reported Grades

The first trimester grading period ended about a week ago.  Soon, students will receive their report card grades and teacher comments.  The majority of teachers in my school have been carefully crafting the right words to be placed on the report card.  These comments often communicate how the students are learning compared to the standard, possible struggles, and next steps to improve their learning journey.  The report cards are usually sent home via backpack and most students gravitate towards the letter grade that is at the top of the report card.  My school isn’t standards-based so that letter grade is often a place of emphasis. The rest of the report cards components come secondary.  I’ve noticed this trend for years.  This year I’m changing up this process to help students understand and reflect on their own learning before they receive their actual report cards.  I decided to create an activity based on Hattie’s self-reported grades influencer.

In preparation for this activity I filled out each report card with comments that I thought were appropriate.  These comments mentioned the scope and sequence of math skills explored during the trimester.  They also communicated what students could bolster during the second trimester. I left the actual grade portion of the report card blank.  I also left the MS, LS, AC and NI blank.  These were for students to fill out.

I gave each student their partially filled out report card and student file.  The student file contains all of the unit assessments for the first trimester.  Students were also asked to use their math reflection journal during this activity.  This tended to help empower the students as they were given all the tools needed to fill out their own report card.  Before students started to assess themselves I decided to review what the MS, LS, AC and NI meant.

screen-shot-2016-11-13-at-7-21-40-amThis took the most time, but I feel like it was worthwhile as students were connecting how particular math skills fit within certain learning goals. They started to analyze their unit assessments, journal and reflection sheets to determine whether they mastered the skill or not.

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After students filled out their report card I met with them 1:1 for about five minutes.  We had a productive conversation regarding where the student assessed themselves.  Sometimes the students were right on point, while other times they were very critical of their own performance.  The process of reviewing their own performance brought a new meaning to the actual report card.  Some students also asked questions about the comments and asked that certain items to be taken out or added.

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When the report cards come out I find the students have a few different reactions.  Some students shove the report card into their backpack while others critically analyze their results in preparation to answer questions from their parents. In an instant, the amount of effort and time spent in crafting the right words can easily be ignored or highlighted.  I’m thinking that this activity will help students to start to see their report in a different light.  Self-assessing takes time, but this is an activity that I plan on using during the second and third trimesters.

Pick Three

Over the past few years I’ve transformed how I give quizzes.  The format and what I expect from students has also changed.  I’m finding that students are expected to explain their reasoning more frequently.  They’re also asked to showcase multiple strategies when solving complex math problems.  This shift has caused my own formative quizzes to change.  It’s also led to some great discussions with my teaching team as we design assignments.

I give quizzes throughout each math unit.  These “review checkpoints” are used to assess where each student is in relation to a particular math standard.  The checkpoints indicate whether students are meeting the standard and if they need additional support or enrichment.  Students also understand that they can make a second attempt if needed.  One things that I’ve done differently this year is to give more choice with these quizzes.  The objective is still the same, but students have an opportunity to have a choice in what problems or response to to complete.

So what does this look like?  In the past I’d give students a worksheet or half-sheet and have them complete it as a quiz.  This year I’ve expanded student choice with my quiz format.  Students are still given a sheet, but I give them a few options.  I tell the students that they can pick 3 out of the 10 problems to complete.  At the beginning of the year students weren’t exactly sure what do with that directive.  They first started to look for the easiest problems that they could find.  I feel like their attitudes have changed over the school year.  Now, students look at each problem and pick a problem that they feel comfortable addressing.  I feel like this is due in part partially because students are aware that they can retake the quiz.  That aspect loosens up some anxiety and helps some students approach more challenging problem.  I’ve also noticed that students have performed better using this technique.

Ideally, I’d like to offer more student choice in the classroom when it comes to being able to show mastery.  I feel like this is one small step in moving towards that goal.

Student Empowerment and Learn Like a Pirate

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Over the past few weeks I had the opportunity to read Paul Solarz’s book, Learn Like a Pirate. Through his book, Paul takes readers on a field trip into his own classroom. His experience as a classroom teacher is insightful and I feel as though many educators can relate to this book. As I read through the book I found moments of personal affirmation and times where I questioned on how to better my own practice. One of the main themes in the book revolves around the need to empower students to collaborate, lead and succeed in the classroom.

As I read through the book I started to examine my own practice. Ideally, I’ve always thought that students learn best when they’re are invested in their own learning. When invested, students often feel empowered and that sometimes produces results beyond expectations. Throughout my experience I’ve found that putting that into practice consistently can be a challenging task and needs to be built from day one. Giving students responsibility can change how they view their role in the classroom. I find that as students take on more responsibility they start to monitor their own actions in relation to the expectation.

As this school year comes to a close I’m reflecting on how to incorporate more student empowerment opportunities in my school and classroom.  These opportunities happen on a daily basis and I feel as though they’re some components that need to be cemented first before student empowerment can take shape.  Creating a classroom community from the beginning of the school year helps students feel comfortable in voicing their opinions. Along with a classroom community, I believe other management components need to be implemented strategically for empowerment to begin.  Each classroom is different, but I believe the component below will assist in building a foundation to help students become more responsible for their learning.  The list below indicates a few items that I’d like to address for the next school year.

Increase clarity and consistent expectations

Missed expectations cause roadblocks and disappointments for teachers and students alike. I believe that the majority of missed expectations results from unclear or miscommunication. Clearly communicating expectations and allowing opportunities to model them improves understanding, and in-turn, establishes a clear goal for students. At the beginning of the year my class uses a flow chart and the expectations are clearly evident. Although the class might not always follow the flow chart, a quick reminder of the procedure helps keep the class on track. Being consistent with expectations also reinforces the need for students to take on the responsibility to meet the expectation.

Student choice

Giving students a choice in how they show mastery can be powerful. Beyond showing mastery, I feel like projects involving choice-elements enable students to become more intrinsically motivated to complete tasks. Choice doesn’t necessarily have to be limited to academics. Students can build processes that help the classroom run more smoothly. Next year I’d like to give students additional time to reflect more on their progress and create individual goals. Periodically checking in on those goals can lead students to create additional goals and the productive cycle continues.

More feedback

I need to beef up this part of my teaching practice. I tend to give feedback, but the form isn’t very diverse. My feedback is usually found in verbal or written form. Since my district requires teachers to use grades, I tend to ask students questions on their graded papers. The questions are designed to have the students reflect on the process of understanding a concept. Next year I’d like to be more specific with my verbal and written feedback.  I haven’t used this much, but feedback can also be from the students. At the end of each school year I give students a survey about their learning experiences.  In the future I’d like to collect feedback from the students on a trimester basis.

The three components above are not the end-all, but I feel as though focusing in on those areas will help build a solid foundation for the remainder of the school year.  My hope is that the foundation will yield dividends that will help students become more successful in and outside of the classroom.

Better Student Reflections


This year I’ve attempted to incorporate more student reflection opportunities in math classes.  This reflection has taken on different forms.  Reflecting on math practices is evident through classroom conversations and through student math journals  I feel as though a heavy dose of student reflection can go a long way in having students build awareness of their strengths and areas that need bolstering.  My focus this year has been geared towards students reflecting on their unit assessments.  I want students to understand that reflecting on past performances and setting goals can help them improve going forward.  I don’t believe all elementary students come to this conclusion all on their own.

At the beginning of the year I analyzed all the different methods to promote student reflection opportunities.  The timing of student reflection matters. My classes generally have approximately 11 unit assessments throughout the year.  Having formal reflection points after the assessments provide a number of checkpoints along the way.  I decided to start by finding/creating student self-reflection templates.

My student reflection sheets have changed over time.  The evolution of what was created can be found below.


Students identified corrected answers and showed reasoning.
Students identified corrected answers and showed reasoning.

At the beginning of the year students were asked to find problems that were incorrect and delve deeper into the reasoning. Students had to seek out why a problem was incorrect and explain how to find a correct solution.  This offered little interaction between the student and teacher, although some students would come up to the teacher to get further clarification on specific concepts.


Positive elements

The above portion was added to the first and helped students focus on positive elements of their performance while still addressing areas of improvement.


Persevere and stay focused component
Persevere and stay focused component

One major area that I thought needed strengthening was in the perseverance department.  The above section was added to help students find strategies that they could use when approaching a complex problem.


Analyzing specific math concepts
Analyzing specific math concepts

Around the third unit assessment I decided to merge a more standards-based grading approach.  I had students identify which problems were associated with certain math strands.  Students then analyzed those results to look at possibly setting a relative math goal.


Written reflection and growth mindset
Written reflection and growth mindset

By this time students were becoming more reflective learners.  I liked what I was seeing and felt like students were benefiting from this reflection opportunity.  I added more pieces that emphasized having a growth mindset – e.g. connecting to achievement.  This was also the first time that I had students and teachers sign-off on the reflection.  I was able to have short discussions with the students about their assessment.


Identifying areas of strength/concerns
Student goal setting piece

Around the fifth unit assessment I added a goal setting part to the reflection sheets.  I haven’t tweaked the reflection sheet much since then  feel the results are positive.  Students are not as infatuated with the letter grade, but more focused on specific concept areas of the test.

I’ve used this sheet for the last few unit assessments.  It’s in a Word format so feel free to edit it and make it your own.  There’ll never be a perfect student reflection sheet but this has worked well for my students.  Moreover, students are able to look back through their math journals and see their own growth over time.

Last week I passed back a graded unit assessment back to a group of fourth grade students.  Each student took a peek at their paper, looked over their problems and grabbed their math journals.  Students found a comfy place in the room to reflect on their results and set goals for the next unit.  After students finished the reflection they brought the sheet up to me to discuss the reflection and next steps.  We both signed-off on the reflection and the students move on to another activity.

This process of math reflection seems to help my students.  It does take up around 30-45 minutes or so, but I feel like it’s time well spent.

How do you use student reflection in the math classroom?


Student Shape Books


Last week I introduced one second grade class to Christopher’s Which Shape Doesn’t Belong book.  After hearing about its success on Twitter I decided to use it with one of my classrooms. After downloading the pdf I displayed the images in front of the class and asked the students to think of which shape didn’t belong. Just about everyone in the class raised their hands. Students overwhelmingly decided that the unfilled shape didn’t belong. Students were ready for the next page of shapes when I saw a hand raise from the back of the classroom. That particular student said that wasn’t the only answer. Quite a bit of the class raised their eyebrows and their voices in saying that the unfilled shape was the answer. The student raising his hand said that the triangle doesn’t belong because it only has three vertices. Other students started to raise their hands with additional solutions. Through this process students started to find more solutions.  The student input became contagious. I would sum up what happened during the next 10 minutes here. Words like vertex, diagonal, side, symmetry, and angles were starting to be part of our class conversation.  I also was able to identify misconceptions and ask questions to think about their responses.  This led to more student responses and questions.  This conversation wasn’t planned but I felt like it was worth the time and fit in perfectly with my geometry unit.  I was going to move to the second page of the book when our class ran out of time.

So the next day the class started the day off with page two of the book. Again, students found different solutions and the class continued the conversation. After a brief amount of time I introduced a shape book activity.

Click for pdf
Click for pdf book

For this activity students were asked to create a personal shape book similar to Christopher’s book. In addition to creating a which shape book, students were asked to include particular shapes in their book.


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Students were given guidance on the first page. I explained the directions, what was expected for the assignment and answered a few questions. I included a formative assessment on the last page of the booklet.  Students worked diligently in creating the initial parts of their books for the rest of the class. Most of the time was spent on the reasoning pages.  The gallery below will show some of our progress from last week.


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I’m planning on having students share their books with the class next week.


Classrooms that Encourage Risk-Taking Strategies


Creating a Classroom Environment
Encouraging Risk-Taking in the Classroom

A positive classroom environment often plays a pivotal role in student learning.  Fostering a classroom climate that promotes the learning community can reap benefits for all stakeholders involved.  Feeling a sense of belonging to an organization can increase participation and build confidence.  Primary and elementary grades often spend a good part of the first few days of school focused on creating a classroom community. Building that classroom community can take many forms.  Joy Kirr’s Livebinder provides many classroom community building activities that I found helpful.  A focus on team building, sharing and reflection can all aid in building a productive learning environment that will set a strong foundation for the school year.

This isn’t necessarily easy as there’s always curriculum to cover, but setting aside time to create a classroom climate is worthwhile.  Once established and continually reinforced, it can be a driving force in which students take academic risks in the classroom.  Whether its student council, clubs, art class, or whatever, that sense of belonging often enables students to participate at higher levels as they feel that their voice is truly valued. When I speak of risk, I think of the term in a positive way.  The risks that I’m speaking of often help students move beyond taking a stagnant stance with their education.  Student risk can take many forms in the classroom.

Taking a risk could mean that students:

  • Answer/ask questions more often
  • Are more open to feedback given by peers and teachers
  • Are able to collaborate with others
  • Show perseverance when approaching challenging tasks
  • Take more ownership of their learning
  • Able to explain their mathematical thinking in more detail
  • Take pride in their work more often
  • Reflect on their performance and set goals
  • Rise above their own personal expectations
  • Start to develop leadership skills

For some students a risk is to raise their hand in class. For others, students might engage in mathematical conversations with their peers or use feedback as a learning tool.  Another student might want to take what was introduced in class and start an enrichment project.  Personal risk is truly determined by the student. To make sure that students take academic risks they need to feel as though their community supports them.  Modeling how to approach risk-taking in the classroom is important.  Sharing personal stories and continually reinforcing that making mistakes is part of the learning process can help create opportunities for students to take risks on their own. Teachers can start by creating low-risk opportunities in the classroom (See Reed’s post for examples).  These tasks can be powerful and foster a positive classroom climate in the process.

How do you create a classroom that encourages risk-taking?



Reflections from Digital Leadership

Digital Leadership Takeaways
Digital Leadership Takeaways

About a month ago I started to read Digital Leadership by Eric Sheninger.  His book is full of leadership strategies that are applicable at any school level.  Specifically, he speaks of how to integrate technology in schools and the reasoning to do so.  While reading I took out of my highlighter and it was busy as they’re many gems in the book.   I thought the topics on the role of technology in the classroom and student content creation opportunities were especially intriguing. I’ve outlined my takeaways and reflections below.

1.  Combining pedagogically experienced educators with technology-savvy students can be beneficial

Students often come into the classroom with an average to above average understanding of how to use technology.  Their understanding of technology can benefit a classroom and the learning experiences within.  I like the concept of being able to combine background knowledge of technology-savvy students and pedagogically experienced educators.  Weaving instructionally sound teachers and technology can reap dividends.  Both parties bring an understanding to the table.  Merging both can can turn technology into a tool for learning.

2. Students need to be aware that technology tools are for learning  

I believe that students are aware of the capabilities of the devices that they use, although understanding how they can be used for learning is another story.  I think this is where it’s essential for pedagogically experienced educators to seek avenues to combine  the capabilities of the device with learning opportunities. The transition from a perceived consuming/gaming device to a learning device may take time.  Due to corporate marketing and education success stories, I believe that transition is taking place in the field of education.  Naming them as learning devices also reinforces the concept that technology in schools can contribute to the learning process.  Regardless of the device, the opportunities for learning exist.  Educators and students can benefit from revealing this possibility.

 3.  Students’ learning experiences become more meaningful when they use real-world tools to show conceptual mastery

It’s becoming clear that technology devices can be utilized to showcase conceptual mastery. This year my students created online tutorials and various projects to demonstrate their learning of mathematical concepts.  Based on my end-of-year survey, students found the content creation projects meaningful.  Seeing that they were published online and available for comments provided opportunities to showcase their projects for an authentic audience.  To be honest, not all projects were optimal and I’m going to make changes for next year, but I was encouraged to see students use real-world tools to demonstrate learning.

4.  The aim is that students move towards creating an actual product.  They need opportunities to show what they’ve learned in a variety of forms

Students in many classes are expected to show mastery of particular concepts through worksheets, usually categorized as unit assessments.  Many times this is mandatory, in the form of district summative testing or state-wide standardized assessments.  Students should be afforded the opportunity to showcase their learning beyond worksheets. Technology devices and apps offer presentation tools that didn’t exist before.  These student content creation tools also give students opportunities to infuse their projects with voice and creativity. This aspect brings student ownership and an opportunity to extend their learning beyond the requirements.  I’ve found that student content creation can showcase learning while providing a lead to engage students in their own curiosity regarding a particular concept. With flexibility and clear expectations, this  type of product can show learning and at the same time be a publishing opportunity for students.

photo credit: Jamais Cascio via photopin cc

Using Badges in the Elementary Classroom


During the last #msmathchat the topic of digital badges was brought to the forefront.  The idea of badges in the classroom has always interested me.  I was first exposed to the idea of using badges in the classroom by @mrmatera last summer at a Downer’s Grove PD event. Michael used a form of a digital badge/achievement token while integrating gamification in his own classroom.   His idea spurred on a brainstorming session with another colleague which resulted in the creation of badges for my own classroom.

Looking back, this past year was the first year I decided to use a form of badges within my classroom.  Back in September I decided to research a few different options for using badges.  After much review I decided to use the badge philosophy without a digital component.  Even though there are many digital badge sites, I wanted to start small and simple and using paper badges seemed like the right move.  I decided to create a simple badge template.  The one below is for the app Prezi.

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The  badges were going to be used to show milestones or proficient use of certain skills.   One larger theme in my classroom revolved around the idea of student content creation.  My students were using a variety of apps to showcase their learning through digital means. Since students were using content creation apps, the badges would show proficient use of specific apps.  I found some blank Avery mailing labels around the house and created a simple badge template and then imported it into Word.

Flowboard Badge Label
Flowboard Badge Label
Label Template
Label Template

The title of the class was on the top and the name of the app was on this inside of the logo. Students received a badge when they successfully created a math product with a particular app.  Students decided to put the labels/badges on their personal folders. Individual student folders started to fill up with badges as the year progressed.


Student folder w/badges
Student folder w/badges

Not only were the students proud of their accomplishments in creating mathematical content, but they were able to reflect back on all their badges and growth since the beginning of the school year.  It was encouraging to hear how excited the students were to receive a badge once they finished their project successfully.  Even more powerful was the reflection component that the students recognized as they wrote their final reflections at the end of the school year.  I’m still brainstorming how this idea could transfer to mathematical concepts without turning this into student competition.  Regardless, I’m looking at using a form of a digital badge next year, but using labels is my first step in that journey.


How do you use badges in the classroom?


Student Choice in the Classroom


I continue to find that student choice is important.  Giving students a choice in the classroom is a shift from some classroom models, but this change that can make a large difference.  My journey with student choice began many years back.  During my first year of teaching I started to ease into giving students options in completing specific problems on assignments.  Students were able to pick 5 out of the 20 problems on a particular page.  From there I started to give students choices in what assignments to complete.  I limited the option to two assignments and then progressed from there.  As I gave students choices they became more engaged and took more ownership.  I took this as a sign to continue. From once a month, to twice a month, to once a week, I gradually was giving up some my control to allow opportunities for students to choose their assignments.  Students started to ask for additional choices as the year continued.

For the next few years I taught a different grade level.  Another colleague and I started to use student choice for a math presentation assignment.   We gave a list of concepts to students and they created a presentation on one of the topics with a Power Point presentation.  The assignment was a success and we decided to use a similar strategy the following year.

A big shift happened when I started to give students choices in how the classroom was setup.  I remember the class had a discussing on how the learning environment plays a pivotal role in the learning process.  After the discussion students offered feedback on how our classroom could be improved to optimize learning.  Students decided on how to group the desks, move the classroom library, and modify the arrival/dismissal process.  Each change was agreed upon keeping in mind that the change helped create a better learning experience. Students started to take initiative, take risks and offer solutions.  Students that were less enthusiastic about student choice with their academics took full advantage and offered their opinion on classroom design.  Students created floor plans on where the desks should be placed and how table groups should be created.  The learning spaces were changed every few months depending on the feedback I received from the students.

This year my students created digital math projects.  Students are self-selecting topics within units and creating presentations to showcase their learning.  The tool was standard but the topic choice varied.  Some students created presentations on algebraic expressions, while others showed examples of how to use the order of operations.  Rubrics were created for each presentation.  For the first few presentations I created and gave the rubric to the students.  Eventually the students became part of the rubric creation process.

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As the year progressed the quality of the projects increased.  Students began to independently research their chosen topics.  Students started to use different research tools to find information about specific mathematical concepts.  Various Internet sites, student reference books, math journals, and manipulatives were all used to research math topics to create a presentation.  Students were also starting to use apps simultaneously to create final products.

Importing picture into presentation
Importing pictures into a presentation

As my classes enter the last few weeks of school our final content creation project is in its early stages.  Last week I gave students a choice on what tool to use and what concept to cover within the unit.  I was encouraged as all the tools that have been introduced this year will be used by the students.

Tool Selection
Tool Selection

Next Steps:  Eventually I would like to incorporate some type of math genius hour.  I’m still brainstorming ideas on how to use this for next school year.


How do you offer student choice in the classroom?


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