Box Plots and Spreadsheets

One of my classes has been exploring box plots and data landmarks lately. Earlier in the year the class created histograms and found data landmarks on line plots. Box plots was not as easy as a transition as anticipated. There were a few roadblocks as students analyzed and created their own box plots while determining Q1 and Q3. Some students picked up on the concept quickly while others took more time. To help reinforce the concept I thought about bringing in a spreadsheet activity. I have been using spreadsheets quite a bit this year and it has been another medium in which students can experience statistics.

Students were first asked to create a question that they would be asking the class. The numbers could range between 1-51. I gave students free rein on what questions to ask and held my breath.. Here were a couple of the survey questions:

  • What is your favorite number between 1-51?
  • How many hours of sleep do you get per night?
  • On a scale of 1-50, what do you rate a cheese burger?
  • How many movies have you watched this year?
  • On a scales of 1-50, how well do you like dogs?
  • How many digits of pi can you recite?

Once students created questions they went around and surveyed everyone in the class. I gave each student a roster list so they could check-off who answered This took a good chuck on time – 10-15 minutes. Once the data was collected students grabbed a Chromebook and copied a spreadsheet that I had pre-populated.

Students took the data from the survey collection sheet and transferred it to column A. The data landmarks in row three were placeholders and awaiting formulas. Students then entered the minimum, median, maximum and mean formulas. They were familiar with those formulas as we explored them earlier in the year. I discussed with the class about quartiles and we put together a formulas for Q1 and Q3. We made predictions of what the vertical box plot might look like before finalizing. Students then entered the formulas for the quartiles and analyzed the box plot to see if it matched the data.

It was interesting to hear the conversations that students had as they compared the data to the box plot. The class had a discussion about interquartile range and variability. It was time well spent. From there, students shared their spreadsheets with me and I took a closer look to see how the data matched and if the correct formulas were in the appropriate places. Students seemed to grasp the concept fairly well. Feel free to use a copy of the spreadsheet by clicking here.

During the next day the class reviewed box plots and the spreadsheets that were created earlier. Students then complete the Desmos task Two Truths and a Lie. This is one of my favorite tasks for students to discuss box plots and use math vocabulary while doing so.

The spreadsheet and Desmos task took about 2-3 days to complete. The class took a unit assessment on Friday and I will be checking out how they did over the weekend. I put these two activities in a digital folder for next year.

End of the Year Survey Data

At some point during the last week of the school year I generally have my classes take a survey.  The survey is designed to provide feedback and to reflect on learning experiences that have occurred throughout the year.  The survey is composed of questions about the class in particular, favorite memories, different learning experiences, and feedback on how I’m perceived. For the past few years the classes and I review the survey data together before the students write their final reflections. For this post I took out the learning experience pieces and am focusing in on teacher perception.

Survey Directions:

Screen Shot 2014-06-09 at 6.41.22 PM

I read through the directions with the class and answered a few clarifying questions.  Students weren’t required to submit their name.  Students took about 20 – 30 minutes to complete the survey.  I averaged the classes together and the results are below.


I’ll be showing the class the chart above tomorrow.  Before doing that, I’m going ask the students what they think are the top 3.  In the past I usually compile the list into the “top 3” and then the class discusses the results and implications on how these categories impact learning in the classroom.  This is always a rich discussion that evolves into an understanding that feeling safe and respected in a classroom often encourages academic risk taking. Here are the top 3 we will be discussing tomorrow:

  • The teacher is fair to all students in the classroom – 1.154 / 10
  • The teacher uses technology to teach the class – 1.179 / 10
  • The teacher shows that she/he really loves to teach and learn – 1.359 / 10

I’ll then show the bottom 3:

  • The teacher gives choices to complete an assignment – 5.39 / 10
  • The teacher allows opportunities for students to reflect on their learning – 3.256 / 10
  • The teacher gives assignments that connect to the real world – 2.821 / 10

During this time the class will be tackling questions about what’s important in a typical classroom.  The class discussions during this time are so important.  This type of reflective thinking is purposefully planned to encourage students to take part in understanding how their environment and mindset plays a pivotal role in the learning process.

My takeaways

I think teachers can be extremely critical of their own practice.  I tend to focus more on the areas of improvement, but I think it’s important to share this data with the students as one way to model a growth-mindset.  I was surprised to see that reflecting on learning scored lower than others. By low, I just mean it wasn’t rated as highly as others. This year I’ve utilized student reflection sheets, but only really using them after assessments.  I feel like I need to merge more opportunities for students to reflect throughout a math unit of study, not just at the end.  I’m also willing to explore different avenues to reflect.  Instead of using the same sheet, possibly using multiple forms of reflection may help.  This is something I’m going to work on over the summer and have in place for next school year.

Also, what’s interesting is that as grade levels progress from lower elementary to upper elementary, assignments connecting to the real world decrease.  I’m not totally surprised as there’s a large emphasis on algebraic equations for my upper elementary classes.  The algebra concepts and practices are often disconnected from practical use. Again, I’d like to find a way to change this perception.

I’m excited to see that students feel safe and feel like I’m fair in the classroom.  The environment and having positive rapport with students can go a long way in having students exceed their own expectations.  Also, even though it wasn’t in the top 3, I’m proud to see that students feel that they can use technology to demonstrate their learning.  This has been a huge emphasis this year with my student content creation theme.

Overall, using student survey data can be a valuable experience.  The transparency that it provides can encourage students to take additional risks.  Looking towards next year, I might want to give a similar survey earlier in the year and then closer to the end.  That way we can look at the growth of the class.  Regardless, I feel like the moments we have to reflect on our learning experiences and survey data are well spent.  This time can can help revisit learning experiences and offer an opportunity to cement an authentic enjoyment in understanding mathematics.


Low-Risk Formative Assessments – Kahoot

Using Kahoot as a Formative Assessment Tool
Using Kahoot as a Formative Assessment Tool

Over the past few weeks I’ve focused in on using low-risk formative assessments in the classroom.  I continue to find that these types of assessments bring out the best in students. I want my students to feel comfortable enough in class to take an educated guess without negative judgement.  Moreover, I want my students to be able to use the formative assessment and teacher feedback to improve their mathematical understanding.

In the past I would give my students a paper exit card.  A typical exit card would have a few questions on a half-sheet of paper.  The questions would relate to the concepts covered in class.  I’d gather up the sheets and write feedback on the pieces for students to read during the next class. I also found that some students weren’t willing to take a risk to showcase their skills.  They might leave a question blank or put a question mark in the blank space.  I wanted to find a way to increase the willingness of the students to take a risk.

I came across the website after following a Tweet by Matt.  I explored it a bit further and found it to be very similar to Socrative.  I enjoyed using Socrative with my classes and thought that Kahoot had some potential to be used for formative assessment purposes.

After creating a teacher account I decided to browse lessons on the site. I was surprised as there were over 160 thousand quizzes in the lesson bank. Many of the lessons were shorter quizzes, but I found some to use with my math classes. The students used the iPads in the class to go to and enter the PIN. Many of the students had no problem with this.  As long as their device had an Internet browser, students could use a tablet, computer or phone to access the quiz.  Once the students all joined the quiz I started it from my computer.  The questions popped up on the whiteboard for students to see.  You can add your own pictures to the quiz.  I found this to be helpful as I took pictures of the classroom and imported them into the quiz.

Screen Shot 2014-05-15 at 8.07.26 PM
As seen on the whiteboard

Students are able to see the whiteboard and read the question.  Students answer questions on their device. Their device looks like the image below.

From student device
From student device

Students receive a certain amount of “Kahoots” for answering the questions in a certain time period.  I’m a fan of rewarding quality over speed in math so I give students the maximum time allotted.  This can be changed when creating questions.   Students pick an answer and at the end of the countdown the correct answer is revealed.  During this time I can stop the class to check the answer choices that were made.

Reviewing student choices
Reviewing student choices

This can be a great time to clear up student misconceptions as you can see all the responses without names.  I’ve had lengthy math discussions after completing this activity with students. I felt the conversations were rich and gave insight to student understanding.  When finished I opted to download a report for later perusal.  The report gives all the student response and how long each student took to respond to the answers.  Both of these are valuable to me as I can use the student responses to group students and differentiate instruction going forward.

Note:  I’ll still be using general exit cards in class, but I’m finding a variety of tools useful in collecting data and providing feedback to students. I’m finding that diversifying formative assessment measures has its benefits.  It also gives students a variety of options to showcase mathematical understanding.


Student Data and Balance

Data and Balance
Data and Balance

Teachers in K-12 often use student data on a regular basis.  Student achievement data can be used to qualify students for reading, gifted, remedial, enrichment, acceleration, differentiation, and a variety of other services.  Recently, standardized testing data has been the forefront of educational trends and in the news.  Implementing a  balanced approach when looking at student data can keep stakeholders (educators and administrators) grounded in an understanding that the numbers behind the tests may give light to areas of strengths/needs.

Data isn’t evil

Assessing a student’s understanding of a specific concept isn’t necessarily a bad thing.  In fact, over the past few years I’ve grown to appreciate and utilize student achievement data more and more.  Whether the data is from a standardized test or not, the data can be helpful if used correctly. Moving data beyond just a number can benefit teachers and students.  Data can help teachers ask better questions and provide opportunities to reflect on how students learn best. Involving students in analyzing their own data can encourage student goal setting and ownership.

Having conversations with students about their data is powerful.

Have the conversation


I’m definitely not an advocate for having additional standardized tests, although some seem more useful than others.  I find that assessments that give detailed feedback (e.g. areas that need strengthening, %ile compared to the norm, strength areas, next instructional steps, etc.) are more frequently used by teachers, compared to assessments the give little feedback.  Obviously, there isn’t a perfect test available for school purchase.  The assessments that a school uses should give detailed feedback that can be immediately used.

Do you hear a lot of negative talk in regard to standardized assessments?  Having a conversation about an assessment’s effectiveness in informing instruction may be needed. Instead of trash talking the assessments in general, educators and administrators should find assessments that work for them.  PLC teams should emphasize the importance of using formative assessments regularly.  I’ve found that teacher created formative assessments are some of the best ways to find areas that need strengthening and to identify differentiation opportunities.  The purpose of giving the assessments should be communicated to all stakeholders.  When teachers understand why the tests are given, (not just for VAM reasons), they may start to value the benefits of assessing students using a variety of tools (such as Common Core performance assessments).

Balance is needed

With teaching and in life, balance is needed.  Teaching is a profession that can be stressfull.  It has many teachers thinking right now, how many days till Spring Break??   Balancing assessments with instruction takes skill and patience.  Standardized tests are often at the forefront of school administrator’s minds.  One test shouldn’t be used to determine if success, or enough growth has been made to call that school year/class/school successful. Take a breath and look at assessments from a macro lens. A combination of formative, informal, formal, review checkpoints, activators, performance  (insert your assessment here), and even standardized assessments have their place in a school and can be beneficial to a certain extent.  The value of the data often depends on how it’s utilized.

Picture Credit: DigitalArt

“Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won’t come in.” Isaac Asimov

Overemphasizing Standardized Test Data and Possible Solutions

Standardized Tests and Formative Assessments
Assessment Data

Assessment Data …. If you’re within listening distance of a classroom you’ve probably heard the words.  The words can hold positive as well as negative connotations. Two different types of data are often used in the classroom – summative and formative.  I think this picture helps show the difference between the two.  If used appropriately, formative assessment data (exit card, common assessment, observation, journal, data binder, etc.) can be used to improve student learning.  Many teachers that I’ve met through Twitter utilize formative or local assessments to maximize student learning. I believe that it’s possible to use student achievement data to identify specific strengths/concerns as well as assist teachers in developing interventions (remediation/enrichment) for students.

At times the word is also associated with standardized test scores and accountability. Those words combined might make a few teachers cringe and organizers protest. A school district’s standardized test scores may make news headlines and influence school improvement plans.  The emphasis on standardized testing has caused teachers to allocate more time for test prep.  Some districts begin the test prep process in January, or before, when the test actually occurs in March. That test prep time takes away time from many non-test related subject areas.

I’ve been told that the Common Core will change the standardized testing landscape. I can’t predict the future, but I believe standardized test scores will continue to dominate local and national headlines. It’s been well documented that there’s an overemphasis on standardized test scores in public schools in America.  The emphasis on test scores impacts teacher instruction and will soon influence teacher evaluations.  Is this a good thing?

I’m not advocating for or against standardized assessments, but I believe formative assessments should drive academic differentiation decisions in the classroom. Even though the overemphasis on standardized test scores seems to be the norm, I’m optimistic. Why?  Many influential education leaders are starting to notice the impact of standardized testing on students, teachers, communities, and administrators.  The leaders below are speaking out on the impacts of standardized testing.  Feel free to follow the courageous people below.

  • Joshua Star @mcpssuper is the superintendent of MCPS, a large, diverse, and high performing district in Maryland. He has concerns over the validity of standardized tests and has asked for a moratorium on standardized testing.
  • Diane Ravitch @dianeravitch, is Research Professor of Education at New York University, wrote a blog post about the inequalities of standardized testing here.
  • Larry Ferlazzo @larryferlazzo, an ESL teacher in California, wrote a blog post comparing the difference between being data-informed and data-driven.

Student Data – Beyond the Scores

Image by:  Adamr

At times, I think that the term “data” produces negative feelings from some educators.  Why?  Well … sometimes  the term is negatively associated with teacher accountability.  It’s also one of those buzz words that seems overused at times.   As an educator, information/data can be an important tool in my tool belt as I utilize it to inform and individualize instruction.  I’m surprised to find that the general public seems to view student data as just scores from standardized tests.  I don’t think that data can be limited to standardized assessment results.

Below,  I’m going to create a data collection list for educators.  I’m not going to include yearly state assessment data, such as MSA in my list.  I’ve found that standardized tests that are given once a year give little to no direction in informing instruction.  I remember a colleague once categorizing state assessments as autopsy reports.   They may be helpful in analyzing school data for school improvement goals, but for the individual teacher, they seem less than stellar.

Data Collection Tools –>

Survey Results – Collecting survey data can be one way to get to know your students on a personal level.  Developing rapport with students is key in helping them reach their potential.

Technology – Students can use iPads or computer activities to work on skills that need strengthening.  In the past I’ve used SplashMath to individualize instruction for specific students. For example, a student might receive only problems associated with place value for a certain time period.  I will get a report on a weekly basis on which problems were missed or correct.  This data can be emailed and utilized to inform further instruction. This feedback can immediately be put to good use.

Guided Groups – Guided math/reading groups can be a great way to collect data on individual students.  I’ve seen teachers travel around the room with a clipboard and collect student data in that manner.

Projects – Student projects can be utilized to collect student data.  Student work samples can also be used to develop a portfolio for each student.  Using a camera, educators can also take digital pictures to review and use during parent teacher conferences.

Journaling – Students write in journals about their skills and overall performance in the classroom.  I believe journals can be used in all classes.  I’ve had success utilizing journals in math classes.  When appropriate questions are asked, teachers can glean data regarding feelings about particular concepts that need revisiting.

Collaborative Work – Students often show dynamic strengths when working with a partner or group.  This type of information can be documented by the educator.  A self-reflection piece may also be helpful.

Unit Assessments – Unit assessments are not only meant to be graded and recorded.  Unit assessments can also be analyzed by students.  Students can check what questions were missed and set goals for their learning.

Exit Cards – Exit cards are generally given at the end of a lesson.  These cards are quick and informative.  Teachers can collect the exit cards and even have the students analyze the results.  Students can determine strengths/concerns and document them in a journal.

Student Data Binders – Students can place homework, tests, and projects in an individual data binder.  This binder should be a transparent way for teachers, parents, and students to review data to view strengths/concerns.

Standardized Assessment Data – The type of data that I’m talking about for this category relates to assessments that are given more than once per year.  An example could be the NWEA MAP assessment.  This assessment data can be used to find strengths/concerns and individualize instruction for students.

Utilizing Student Survey Results

 Image by: S. Miles

I’m currently preparing for next school year.   Part of my preparation includes the creation of a student survey.  After reading a post from @TerryFErickson I decided to create a survey (similar to this) for my current students.

I’m planning on using the survey data to make changes for next school year.   I’ve always valued student feedback via plus/delta charts, but this survey is intended to be utilized for next school year.   In order to best meet the needs of my students next year, I wanted to give my current students an opportunity to express their opinions regarding motivation.  I believe that motivation is often affected by the classroom climate.  The process I used for this survey activity is below.

1.)  Students complete the survey.  Here is the beginning of the survey:

2.)  After students complete the survey, I complied the results and displayed the data from different classes. (Click to enlarge)

3.) The class reviewed the data.

Based on this survey, the top three things that motivate my students are:

  • The teacher shows she/he cares about you and the other students in the class
  • The teacher shows that she/he really loves to teach and learn
  • The teacher uses technology when teaching

This activity took two class sessions to complete.  After a rich classroom discussion about the data, students concluded that the main factor that helps motivate them to learn is the teacher.

Students That Own Their Learning

Image by:  Jscreationzs

After working on a math world problem for approximately five minutes I hear ….

“I don’t get this”

“I’m confused”

“I’m lost”

“I don’t know what to do”

I believe every educator has heard one or more of the above statements while teaching.  These statements don’t really help a student succeed in any class.  This type of student feedback is important, but the words themselves seem discouraging. When words like the above are communicated, I feel as though the classroom instruction isn’t meeting the students’ needs or students aren’t utilizing math problem solving strategies.  This post is going to focus on math problem solving strategies.

Image by:  I. Images

Teaching new math concepts often requires building on students’ background knowledge.  When students experience a challenging math problem, they generally have two options.  Students can become frustrated and quit or they can find a solution.  A discussion regarding this particular situation took place in the past after their was a major struggle with one particular math word problem.  As a class we had a brainstorming session.  The students came up with some ideas of how to overcome mathematical struggles.  We called these strategies the math tool belt.

During this discussion, the students began to recognize that the teacher will not solve all of their problems.   I pointed out that giving an answer without support isn’t learning.  In fact, I pointed out that I will help, guide, and assist, but they are responsible for completing the problem.  Making mistakes and having “I don’t know” moments are part of the learning process.  Having students reflect on their learning through journal writing may also benefit the student.  I feel that students should “own” or take responsibility for their own learning as @pammoran, @mthorton78, and @irasocol indicate.

Long-term retention infrequently occurs when students are required to just regurgitate what the teacher says.  Here are some of the math problem solving strategies we decided to use when confronting a complicated math word problem:

  • Read the problem and underline important numbers or information.
  • Cross out information that isn’t needed
  • Create a visual model (chart, graph, or table)
  • Indicate what operations will be needed
  • Restate in your own words what the question is asking
  • Work backwards – keeping the end in mind
  • Write steps needed to solve the problem
  • Guess and check
  • Look for a pattern
  • Estimate and use logical reasoning to solve
  • Use manipulatives to solve (students can just grab them off the shelf and use as needed)
  • Use a formula
  • Work in collaborative groups to brainstorm what steps can be taken to solve the problem
  • Use a ratio / proportion to solve the problem
  • Ask the teacher for help
In an effort to foster resilient and responsible citizens, I ask the students what problem solving tool they used before they ask me for help.  This also reminds the students that they should be utilizing the tool immediately in the learning process.  I believe that students need to understand that their effort (not mine) leads to individual achievement.  Creating a classroom environment that encourages learning through engaging and relevant instruction is vital, but I feel as though students need to “own the classroom and their learning.”  When students are stumped or are struggling with a math problem, they need to have the tool belt readily available to power through the obstacle.  Giving opportunities to utilize the tool belt gives students positive experiences of overcoming obstacles and builds confidence. Students become owners of their learning and they find that their learning experiences are primarily controlled by how they react to the problem.  Overcoming obstacles will develop confidence so that the next time they encounter a complicated problem they will reach for the tool belt and be successful.

 Additional Resources:

Exit Cards and Formative Assessments

Image by:  Nattavut

This particular post stems from the above tweet.

Most educators understand that formative assessments can be a valuable tool in teaching and learning.  I’ve found that formative assessments play a pivotal role in my instruction as an educator.  Specifically, I’ve found that exit cards can be a powerful tool in analyzing student learning.  If you’re unfamiliar with the idea of using exit cards as a formative assessment tool, click here.  Below, I’ll give you a brief overview on why and how I use exit cards in the classroom setting.


It’s not required, but I feel as though exit cards  give me an opportunity to quickly assess students’ understanding of the objectives taught for a particular lesson.


In my experience exit cards work well near the end of a lesson.   During that time, the students fill out a small half sheet of paper that includes 1-3 questions related to the objectives taught during a specific lesson.

The questions may be multiple choice, but they generally include some type of written response that demonstrates an understanding of the objectives.

I don’t grade the exit cards (A or B …) instead I put a check on exit cards that show understanding and a subtraction sign that reminds the student and teacher that extra support may be needed.  The exit cards are placed in each student’s portfolio and can be utilized during parent/teacher conferences.  Periodically, I may conference with a student to review their exit cards and set goals based on the conversation.

Students are also given an opportunity to review the exit card slips before an assessment and may even journal about their academic growth in my class.

How often?

I may give exit cards once or twice per week or more frequently as needed.

Next steps?

The exit cards can be utilized to engage students in self-reflection activities (journaling or individual student conferences).  The exit cards can also be reviewed in class to give examples of correct answers.  I’m also planning on using exit cards beyond math and incorporate them into other content areas.

Here is one resource that may be beneficial in communicating what makes a “good” exit card with question and response examples.  I was also thinking that exit cards could be created and shared with a team of teachers and discussed during grade level meetings.

Student Growth Mindset

Image by:  S. Miles

Students that have an intrinsic drive to learn often retain information and are able to apply their learning in practical situations.  When students develop a growth mindset, they become much more goal oriented, which is a valuable skill to learn at a young age.  When students take responsibility for their own learning and understand the pivotal role that they play, a growth mind set begins to set in.  How do we as educators promote a growth mindset?  I have provided a list of activities that can be used to inspire students to become more responsible for their own learning in order to nurture a growth mindset.

1.)  Students communicate how they feel about their learning …

  • Students  become more aware of how metacognition plays a role in learning
  • Students review their latest assignment/test and reflect on their performance
  • Students complete a plus/delta chart on their weekly performance
  • Students analyze classroom achievement data and set goals based on the results
2.)  What happens after reflecting via journaling is vital …                    

  • Students monitor their progress to ensure that they are making steady progress towards their goal
3.)  Next …
  • Look at specific areas of concern for continuous improvement

What do you do to encourage student responsibility in the classroom?

%d bloggers like this: