Ratios, Proportions, Chocolate Milk, and Hummingbird Feeders

Photo Courtesy of Krissy Venosdale

I am kind of an unconventional math teacher... I want my students to find other ways to solve problems that do not involve blindly following rules that I give them, oh I don't give them rules.  I spend an abundance of time asking them to problem solve and use critical thinking to solve problems.  They also have to show proof of understanding and share their processes, thinking, etc...

Over four years ago when I was in the classroom as a middle school math teacher one of my favorite activities was Dan Meyer's Nana's Chocolate Milk - 3 - Act Math  activity (love these problems and there is a plethora of them).  I love this activity because it it gives students an opportunity to solve ratio problems using proportional reasoning and problem solving without following a rule.  They can find "their" way to solve the problem using what they know.  It provides opportunities for math talks that create a community of mathematicians and "lead learners" rather than blind rule followers (obviously I have issues with step by step).  And on some days students have to embrace their "Ishness" - Here is a past post on that - CLICK HERE

Now back to Nana's Chocolate Milk and what it has to do with Hummingbird Feeders...

Ironically, I had a recipe mess up moment when I was making the potion we put into our hummingbird feeders.  I mistakenly used the 1/3 cup instead of the 1/4 cup.  So, of course I turned it into a proportional reasoning problem for my 7th and 8th grade students as a warm up problem for the day after we did the Nana's Chocolate Milk problem.  It was a bit more challenging, but the students
worked in groups and made meaning of the problem in ways that made sense to them instead of blindly following a rule I gave them.

I'm looking forward to later in the year when the students will start creating their own 3-Act math activities to share with their classmates and the world!

Here is the link to the slide deck I used to introduce the problem to my students: CLICK HERE.  Please Steal, Copy, etc... and use it with your students and/or create your own.

If You Hopped Like a Frog - Fractions

The next few weeks I will be co-teaching a third grade fractions unit with one of the teachers I "coach".  Actually, I think she is now my coach.  I have created this document: click here as a Multi-Media Text Set.  Our goal is to create some enrichment lessons that will provide meaningful and connected activities that also integrate technology in a meaningful way.

I will be blogging about each activity in the coming days/weeks to give some insight to my thinking and possible implementation of these activites.

One of the activities is "If You Hopped Like a Frog" based on the book by David Schwartz one of my all time favorite authors who integrates mathematics into children's books.  The activity helps students start thinking about proportionality.  This activity is a cooperative Google Slide presentation where students will use Google Search to research the proportions in the book.

If You Hopped Like A Frog - David Schwartz -

YouTube Video of the Book - Click Here

• This is a proportional reasoning and Google Search Activity Using Google Slides.
• You will need to go over search methods
• You will need to teach students how to find images that are for non-commercial use

Group Google Slide Deck Template - Click Here

Here is the Instructions Slide:

Here is the Example Slide:

I'll be doing this with my third grade classes in the coming weeks and will let you know how it goes and share any modifications/revisions.

Homework in a Standards Based Learning Environment

Yesterday I was sucked into a discussion about homework on Twitter.  My colleague John Walkup likes to challenge my thinking on things which I appreciate because it makes me reflect on my practice.  In doing so, I found that I could no longer participate on twitter because I needed more characters.  So here is a brief explanation of how homework went in my middle school math classroom:

• When the students entered my classroom, there was an activity for them to complete.  (If the students are engaged, I can touch base with all of them).
• The "warm up" is based on THE ONE problem they had for homework the night before and is strategically chosen for it's learning value for all students.
• I ENCOURAGED the students to copy, cheat, and steal ideas from their group members as they communicate and collaborate and get their minds on math.
• As they worked, I "checked homework" by going to each group and checking in with EACH student. 
• If a student did not have their work, their book, their notebook or other materials, I made eye contact and ask them why (with empathy).  I had a coding system so I could keep track of each student's work patterns and level of understanding and look for work behavior patterns.  
• I also made sure that I smiled genuinely at each student and acknowledged their successes or understood their anxiety, frustrations, and/or confusions.
• This formative check I did with EACH student in EACH class EVERYDAY also enabled me to make sure the students knew I was there to challenge and support their learning in a respectful collaborative environment.
• I allowed for 5-10 minutes at the beginning of class to accomplish this task and build relationships.  It was the most valuable time of the day for establishing a foundation for trust and risk taking in a middle school math class.

I found that formatively assessing my students, providing a safe environment to make mistakes, learning from failure and building relationships were the driving forces behind all that happened in OUR math classes.  

Oh and by the way, when students were able to let go of their math anxiety by "copying" or "cheating" or "stealing" from a classmate a few things resulted:

• their math anxiety decreased
• their confidence increased
• they took risks and began trying difficult problems on their own
• they asked more questions and sought help and support 
• they increased their scores on unit assessments (which they could NOT "copy" or "cheat" or "steal" on.

Meaningful learning for all is my goal.

Building Balloon Cars - Ambiguity and Cognitive Dissonance

NOTE: These beginning paragraphs are the "Background" to the what and why I do this activity with my students, you can skip to the lesson link below if you are short on time and want a fun and challenging activity to do with your students the last weeks of school.

 from: Krissy Venosdale: Venspired.com                                                                     

Way back in the summer of 1995, I attended a summer institute on integrating technology into the classroom.  I received a computer with a dedicated phone line for internet access, a stipend, and two weeks of STEM (not called that back then) activities.  There was a cohort of 25 Idaho teachers who would build what we now call a professional learning network.  The expectation was that we would use our computer and dedicated phone line to collaborate and stick together as a group since we taught in different areas of the state.  One of our first activities (and the only one I remember) was experimenting with rubber band cars leading to the building of balloon cars.  It took the entire first week to test the cars, collect data, make observations, and then transfer what we learned to build our own balloon powered car.  Of course we were working in collaborative teams and using the computers to organize data, graph data, and make notes (much more clunky than using Google Docs/Drive).

The University of Idaho science professors who were leading our group used ambiguity to force us out of our comfort zones.  There were no guidelines, just guiding questions.  When they introduced the rubber band cars they handed them out, dumped a pile of rubber bands on each table and we sat in silence for a few minutes thinking and waiting to be told what to do.  As the seconds ticked away, our looks became more perplexed as we continued to wait for instructions.  Finally the professors broke the silence and said "Get to work".  "What are we supposed to do?" one brave student asked.  They answered with two simple and profound words, "Be scientists!"  They gave us the ultimate statement of ambiguity to send us on our thinking way long before #geniushour and #20%time existed.  After continuing to sit with dumbfounded looks on our faces, (we were all very obedient science teachers/students who wait for instructions and procedures) the professors realized they needed to gently nudge us forward.

They began by asking us a question, "What is a scientist and what do scientists do?"  Make a list in your groups, you have 2 minutes to brainstorm.  For the first time that morning the room was a buzz with chatter.  After the brainstorm session, we shared and made a collective list to help us remember our role as active, thinking, tinkering, and information seeking scientists.  The next guiding question the professors asked was, "What are you going to do with the rubber band cars in front of you?"  Again they sent our groups into a brainstorm session and the room was once again a buzz.  We shared with the whole group after 2 minutes and wrote the collective list on the board.  The professors asked one last question, "How many of you have enough information to get started?" All of our hands went up and we spent the rest of the day and the next two days "playing" with rubber band cars in the halls of the science building.  At the end of the three days, we had rubber band car races down the halls.  We used the data and knowledge we gained from tinkering and experimenting with them to find the combination of tweaks that resulted in the fastest car and the farthest car.

Day four began with the professors dumping piles of materials down in front of us and challenging us to use only those materials to build a balloon powered car that would be the fastest and/or the farthest.  We experimented for a day and at the end of day 5 we had balloon car races in the halls of the science building.  The ambiguity and cognitive dissonance was at times extremely frustrating, but it lead to a strong commitment to the process and a willingness to persevere and get it figured out.  And, way back then, we could not Google It.

So, the next school year in my middle school science classes in Twin Falls, Idaho, we played with the rubber band cars and then built balloon cars.  And from that time, the project became a yearly staple in my classroom.  Before I share the lesson plan, I want to share some interesting observations I have noted as my classes have completed the exploration over the years:

• High achieving students struggle with this process because of the ambiguity - they don't do "play and figure it out" well
• You will be surprised and inspired by what your students create.
• Be prepared to provide questions to guide struggling groups so that they do not give up
• Remind everyone that this learning experience is about the process and that there is no failure 
• Figure out ways to give the students hints without telling them what to do

Here is a very basic outline of the lesson and supplies you will need: 

Balloon Car Lesson Ideas Click Here

I will be going into third grade classrooms this week to have them build balloon cars and I will add pictures here.  You can use the links and information below to have your students explore NASA's Balloon Car Challenge.  I would do this part with middle school students.

NASA Balloon Car Results

Pictures of NASA Balloon Cars

• Pick 8 of the cars, write their name, distance and time.  Then calculate the rate of each one (SPEED).

Have a great end of your school year!

How I Taught my Middle School Math Students to Blog

I posted this information last summer, however, it was embedded into a post that had other parts and pieces.  I am thinking it would be a good idea to post it individually so here it is.  This is not only how I start student blogging but also how I begin the exploration of student passions that will transfer to connecting their lives to mathematics and the start of #geniushour

Unit Overview:

It is my goal in the 2013-2014 school year to have monthly writing assignments that will become blog posts for each student in my math classes.  Each writing assignment will be tied to the 7th grade Common Core writing standards and the 7th grade Common Core math standards.  Since we start school August 20, our first assignment will need to be completed by the end of September.  

At the beginning of the year I like to build a classroom community of learners.  To do this successfully, we need to learn about each other and build a supportive environment filled with passion, empathy, and understanding.  This will enable us to create a collaborative classroom environment (either online or face to face).  The students will work together in a variety of ways, with a variety of people, and will look for commonalities rather than differences.  With this in mind our first writing assignment will be a “Passion Paper” which will address the Narrative Essay Standards:

Writing Standard 7.0:

The student will write grade-appropriate narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences (W.7.3):

• Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally

and logically (W.7.3a)

• Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters (W.7.3b)

• Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another (W.7.3c)

• Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events (W.7.3d)

• Provide a conclusion that follows from and reflects on the narrated experiences or events (W.7.3e)

Activities:

• The students will create a heart map that will require thoughtful reflection on the things and people that are important to their lives.  They can create digital or hand made heart maps and we will post them around the room for inspiration and so that the students do not forget their hearts.  Heart Mapping and Inspiration Station Questions/Ponderings
• I will introduce online discussions through Schoology by having students share what is important to their hearts and practice commenting (to at least 3 others) appropriately to each other by 1. writing a relation 2. asking a question 3. making a prediction 4. commenting appropriately
• The students will create a “dot” that represents their mark on this world.  This activity is based on the book “The Dot” by Peter Reynolds.  Link to International Dot Day Again those can be digital creations or hand made
• The students will use Schoology to explain their inspiration for their dots and comment on at least 3 other’s explanations.
• All of these activities will lead to the writing of their 3 paragraph passion paper.

Passion Paper:

Based on the Common Core Standards for writing a Narrative, I will provide instruction and practice in all of the areas:

• Interesting lead or begin by grabbing the reader
• organization of events/paper
• varied techniques: dialogue, pacing, description (showing not telling), development of characters, experiences, events
• use of transitions and varied language to make writing interesting and varied
• how to write a conclusion

Formative Assessments:

I have found that the best way for students to consider and revise their writing is to provide opportunities for them to “revise” someone else’s writing.  So my formative assessments will be on Schoology.  I will post a paragraph and ask the students to “revise” the writing keeping in mind the standards we are working towards.

Formative Assessment #1: Writing an Interesting Lead

• I will provide three different leads and ask the students to “vote” on Socratic for the one they like the most.  I will evaluate their votes and note which students are struggling and need more instruction and/or support.
• Then I will have the the three leads posted on Schoology and have the students critique and then revise using the standard rubric as a guide.  The students will see what others have posted and then discuss with each other.  I will provide guidance and questions.  I will evaluate the revisions and base my instruction on their understanding of what makes a strong lead (introduction) to their writing.

Formative Assessment #2: Using transitions effectively:

• I will provide three different writing samples with transitions and ask the students to “vote” on Socratic for the one they like the most.  I will evaluate their votes and note which students are struggling and need more instruction and/or support.
• Then I will have the transition examples posted on Schoology and have students critique and then revise using the standard rubric as a guide.  The students will see what others have posted and then discuss with each other.  I will provide guidance and questions.  I will evaluate the revisions and base my instruction on their understanding of what makes a strong lead (introduction) to their writing.

Formative Assessment #3: Showing vs. Telling

• I will provide three different writing samples with showing and/or telling and ask the students to “vote” on Socratic for the one they like the most.  I will evaluate their votes and note which students are struggling and need more instruction and/or support.
• Then I will have three samples of showing and/or telling posted on Schoology and have the students critique and then revise using the standard rubric as a guide.  The students will see what others have posted and then discuss with each other.  I will provide guidance and questions.  I will evaluate the revisions and base my instruction on their understanding of what makes a strong lead (introduction) to their writing.

Formative Assessment #4: Putting It All Together:

• Using a Google Form I will have students write examples of an effective lead, varying transitions, and showing instead of telling.
• This will enable me to evaluate each individual student and know where he/she is in his/her understanding of the important components of a narrative essay.
• I will use the results of this formative assessment to group students and provide instruction as needed.

Summative Assessment:

Common Core Narrative Essay Rubrics K-8

After their Passion Papers are in final draft form with all revisions and editing done, the students will turn them into a word cloud and then into a paper blog (see example below) and then they will become the first blog post of the school year for each student using either Blogger or Kidblogs.

Fluency Does Not Equal Speed

As an educator with 23 years in the classroom I used to give math timed tests to build automaticity in the basic facts.  After attending many math projects and teaching middle school math the past 10 years I learned that problem-solving, critical thinking and explaining are the foundation for student fluency in mathematics.  I also know that the CCSS (Common Core State Standards) specifically cite "timed fluency" in the third grade standards.  As I deal with this issue personally with my 8 year old son and as an educator who wants teachers to re-visit their practices around timed tests, I have drafted this letter.

Dear Second (or Third, or any grade) Teacher,

I understand that you are working hard to prepare your students for future learning in mathematics.  I also know that you would not want to discourage your students or make them want to quit learning.  That being said I would like to ask you to look at your timed test practices.  I understand you are trying to build fact fluency in your students, however, fluency does not equal speed.  There are many more foundational skills that need to be developed to support fluency.  I also acknowledge that the timed tests are a small part of your math program.

A wise person once told me that if you want to complain about something be sure to offer alternatives or ideas for changing course or forging a new path.  So here are some ideas or alternate ways of giving/using timed tests to build automaticity.

First of all, I would like to request that you actively involve the students rather than continue to have them be passive participants.  By passive participants I mean they take the test, hand it in, it is corrected then given back to them with a score.  As passive participants, the students can pass off their performance or lack there of easily and the poor performers can justify giving up - "I can't do this, the teacher just proved it" might be one such justification.  I am suggesting that you involve the students in every step and make the timed tests a learning experience rather than an assessment.  So, I hope you are. Let me share some ideas in how you can do this:

When the students take the test, set the timer to stopwatch instead of counting down and project the timer so all the students can see it.  When the student finishes they record their finish time.  Just like an athlete (it is Olympics time), you can remind them that they are racing against themselves rather than each other.  Their goal is to decrease their individual time rather than competing against other students.  This is the first step in actively involving students in the process.  Have them graph their times and see their growth each time they test.  It is also a great way for you to track individual growth.  You and the students will be focusing on increments of improvement and perhaps the students will see the need to practice rather than giving up or feeling stupid

After the students are done and have recorded their time, correct the test together or have the students correct their tests with an answer key (if they are all on different tests).  Then discuss (or provide reflection questions) successful strategies students use, patterns in the problems that the miss of find difficult, ideas for improving, etc...  You can also ask the students "How are you thinking about these problems?" and "What are your shortcuts?" which will allow the students to learn from each other.  This will actively involve the students by having them share successes and struggles with the intent of promoting improvement and having the students take responsibility for where they are in their learning.

You can also have a "Timed Test Station" where students go and complete the process of setting the timer to count up, take the test, record their time, and then correct the test.  Then the discussion with the teacher or a parent volunteer needs to take place so the student reflects on where they are.  If you want growth and improvement the students have to know where they are and see their growth (or lack there of).  Then they can set goals for improvement.  Because they are a part of every step of the process, they cannot pass off the responsibility to anyone but themselves.

My last request would be to set a "reasonable" time for the students to achieve.  Perhaps it is 100 in 10 minutes.  You may be thinking that is not a rigorous level of performance.  I would argue that it allows for the diversity of your class.  Since the students are recording their times as they finish, the one who want to be the "fastest" can still aspire to that level.  The ones who have struggled or are considered "slow" have an attainable goal that allows for success rather than failure and giving up.

I understand that timed tests may be mandated in your school/grade level/district, but please consider being brave enough to try a new approach and start a new dialogue with your PLC.  With your team of educators you can explore new ways of building fluency and automaticity in your students.

Marilyn Burns stated in 1989: "Speed with arithmetic skills has little to do with mathematical power."

I am including some resources and research for you to review and consider:

Can We Please Consider the Evidence? The Ways in Which Assessment Policies and Practices Create Math Anxiety in Young Children.

Math Solutions: Faster Isn't Smarter

GOOD NEWS: MISSILEERS ARE CHEATING TOO.

I have one final request:  Please do not tell me my thoughtful, problem solving son is "behind" in math because he is one of the slowest at the timed tests.  Instead, sit down and have a conversation with him at least once a week and ask him to explain his thinking and problem solving processes.  Find out how he thinks about numbers and how he takes them apart and puts them back together.  Ask him what strategies work for him and which do not.  Fluency is more than automaticity or speed or memorization.

Thanks for your consideration,
Sincerely,
Kristen Beck - Mom and Educator

My #geniushour, Making Math/Science Connections

I have a confession, my #geniushour project is looking for resources that connect mathematics and science to real life situations.  Here is my most recent find:

I found this picture in HGTV Magazine's October/November issue. It is exactly the type of thing I am always on the lookout for, you see I am obsessed with finding pictures, videos, and articles that connect math to any type of real life situation that my students might relate to. Often, the connection is not necessarily something that is of great interest to the students personally. However, they are used to me bringing something of this sort into class, telling a personal story, and then asking them what math they see and/or can explore. This picture provides a great proportional reasoning experience for students. I prompt them to come up with mathematical explorations and record as they share ideas. We use the Standards of Mathematical Practice (SMP) in the Common Core state standards as our guide. For this activity, I might pick SMP 1 - Make sense of problems and persevere in solving them. 

As a curriculum coordinator, I will take this picture, the SMP of focus and then search the grade level standards to make this accessible to all grade levels K-8. Then, I will share with the teachers and hope that a few will experiment with their classes and explore. I am working to find a balance in providing Common Core experiences with the right amount of scaffolding for the teachers. Building capacity is something I was skilled at doing with students in the classroom. I find it more difficult to do with teachers, but I am loving the challenge of being one of the instructional leaders of a school district, not just the instructional leader of a classroom.

I am in the process of collecting close reading resources for the teachers in my school district. It is in the beginning or infancy stages so be patient as I work to organize and tweak what I find.

The resources shared on this page will be periodically edited and revised and updated, they are the beginning of my effort to collect and compile.

Beck’s Close Read Process:

• I keep my eyes and ears open at all times for current articles, news stories, student discussions and likes or dislikes
• I search resources like:
• NPR
• Newspapers
• Local Television
• ESPN - other sports
• Anything that will relate to the students
• I will do a search on a topic I know is of interest for the students
• As I am picking items for Close Reads, I search for information that can be used in a mathematical or scientific nature
• As we read and work to find the main idea, details, meanings of technical words and other vocabulary, we also formulate mathematical/scientific questions using the data in the article.
• We work with the text for the entire week, in class and as homework in both a mathematical/scientific way and in a Common Core ELA way.
• I am particularly interested in looking for proportional reasoning items since it is an area of struggle and foundational for connecting mathematics and science to real life experiences.

What's The Connection? How to Integrate Mathematics, Common Core Standards, Real Life Experiences, and the Content Areas 09/20/13 Global Education STEM Webinar

Close Read Resources (this will be added to continually)

Beck's Close Read Process (this will be revised periodically)

Be the Teacher You Wish You Had in School

The other day while reading a blog post from one of my favorite educational bloggers: Bill Ferriter, The Tempered Radical I came across the following tweet:

This statement George (another one of my favorite bloggers/tweeters) shares struck a chord with me as a classroom teacher of 22 years.  When I started my teaching career, I gave myself 5 - 8 years in the classroom before moving up into some sort of administrative position.  However, what I realized is that my place is with the students, they are the ones I cannot wait to see every morning and think about during the evenings and weekends.  I tell my friends stories about my students and tears fill my eyes (I am a major sap head!).  Everything I do in my classroom is with thoughts of my students.  What I realized is that as a teacher, I stay in the classroom because I am determined to "create an environment I wanted as a student."

So, what am I doing in my class that I wished my teachers had done with me?  In the spirit of the common core and the inspiration I get from Dan Meyer's 3 Act Math, I have been working to change how my students learn math.

First, on Monday's our district has articulation time from 2:15 - 3:45 so the students have shortened periods and go home at 1:56 instead of 3:10.  I am using Mondays to introduce a "3 Act Math" type of activity that I then also use as the basis for my homework for the week.  I make sure the activity I pick is either related to our current pre-algebra content standards or will act as a preview for upcoming standards.  Here is an example of one of the activities we recently did and how this past week I referenced back to the activity as I introduced ratios and proportions.

Nana's Chocolate Milk (link to Dan Meyer's activity complete with video etc...)

Monday - I usually begin each of these activities with a story about myself and/or my family:
"During vacation, Skyler and I visited my parents in Oregon.  My mom, Nana, loves chocolate milk and Skyler loves to make it for her... I then show the video of what happened.

Nana's formula is one cup of milk to 4 scoops of chocolate, however, the video shows one cup of milk and 5 scoops of chocolate.

I ask the students to share some "math questions" they have and they all come up with
How can we fix Nana's chocolate milk?

After letting them fumble for a few minutes, and noticing that most of them are just doubling the "recipe" I stop them and throw a tidbit in "Oh, I forgot to tell you guys that when you fix the mixture, you can only add milk, you cannot add any more chocolate.  This really forces the students to think and work together.  

This takes the better part of the half hour we have together.  Pairs that are stuck are encouraged to walk around the room and "steal" ideas.  I cruise around and only ask questions to help them get unstuck.  By the end of the period, all of the pairs/groups have a solution.

Their homework is to write an explanation or illustrate their understanding of the problem/solution.  When they come to class the next day, they work with their partner to "revise" their explanations/illustrations as their warm up.  If a student does not bring anything, they participate in the group discussion and "copy" the groups/pairs end products.  (I do not penalize students for not completing homework - that is a completely different blog post.)

The rest of the week during class we worked on the standards in our unit of study, however, the homework all week was a  problem that related to Nana's Chocolate Milk: Nana's Eggs (the sequel to Nana's Chocolate Milk), Papa's Iced Tea.  Again, I have the students work on explanations and illustrations at home and bring something to revise the next day in class.

By the way, we did get a different solution than Dan's Solution Video - we added 1/4 cup of milk instead of a 1/2 cup, we must have thought about it a different way!  That is what I love about these activities is that they are open to the questions that the students ask.

This is one way in which I work to create a math class I would have loved as a student.  Problem-solving working to write explanations of my thinking, illustrating my math work and collaborating with other students in class.  Discussing, getting stuck, feeling frustration, persevering, learning from others, all things I rarely had the chance to do as a math student.

This past week when we started our ratio and proportions unit, I started by reminding the students about Nana's Chocolate milk and used that problem to create a concrete reference to define ration and proportion. The students loved it!

Grading Irony

This past week, as I graded the first chapter assessment in my pre-algebra classes, I had a realization.  The last page was filled with problems on mean, median, mode and the best measure of central tendency (I will remind you soon about these) using a set of "test scores" from a social science class.  Some form of these questions have been on the chapter test for the past 6 years and I am embarrassed to say that I failed to see the negative impacts of averaging grades that were explicitly pointed out on these assessment questions.  Part of my ignorance can be attributed to the fact that I have been using a 4, 3, 2, 1, 0 grading system that equalizes the A to F grading range.  I learned many years ago that a 100 point grading range can be devastating to a student's grade.  But it took my student teacher and her discussions with students to really hit the point home.

The test scores that were given in the data set were:

92, 82, 88, 90, 82, 0, 98, 100

mean: 79
median: 89 (the middle number after putting the data in order from smallest to largest)
mode: 82 (the number that occurs the most)
mean (without the outlier): 90.3
outlier: 0

The mean or average of this data is 79 which is a C+ in most grade book programs.  When you look at this data, do you think the mean is an accurate evaluation of this student?  If we look carefully, there are four scores 90 or above, three scores in the 80's and then that ZERO.  Wow, can you believe the impact that one little zero has on the other scores when using the mean to calculate the grade?  What about the other measures?   Now it is story time...

As we went over this assessment question in class, an amazing thing happened.  Before discussing this question, I asked students which measure of central tendency was the best for "grading".  Overwhelmingly my students voted for mean.  I asked them why and they stated that the mean had been used in every one of their classes from fourth grade until now.  After the informal poll and the discussion, I posted the last page of their chapters 1 and 2 assessment.   I asked the students to get their phones or a calculator out and find the mean of the data since on the test they only had to describe/define how to calculate the mean of a set of data.  As each student saw the result appear on the screen of whatever device they were using there was a collective sigh of disbelief.  They were absolutely shocked at the result.  When they saw that the mean was 79, they began formulating arguments and questions as did I.

My first question was: Do you still think the mean is the best measure of what this student knows?  My next question was: Is there a measure that you would rather have your teacher use?  My last question was what are you wondering?
Here are some of my student responses to the data and my questions:

First, overwhelmingly, the students felt that the mean was the worst measure to use with this data.  They argued that the student obviously understood the material and that he/she had one bad day which had a huge impact on his/her overall grade (something that could be proven by using standards based grading).   If they had to choose, they preferred that their teacher use the median to "calculate the grade.  The interesting part came when we discussed the things my students were wondering.

They wondered why grades are calculated the way they are.  They wondered how grading can be more informative and meaningful.  The most insightful question came when a student asked, "Mrs. Beck, why didn't the teacher ask the student what happened or have a talk with the student to get to the bottom of the zero."  Many of the students stated that if this had happened to them, they would feel defeated.  And because we are in a middle school and there is no consequence for failing, they would no longer put much effort into a class that pays more attention to the one bad grade instead of acknowledging the many outstanding grades.  This question and discussion opened the door for a new look at the standards based grading system I use with these students.

I shared this problem and the discussion with the teachers at my school.  I am the lone wolf of standards based grading and this was not about converting others.  It was about awareness and having my colleagues consider the effects of their grading system on student learning and motivation.  Unfortunately, the message fell upon deaf ears.  I shared this information with the teachers because I promised my students I would.  I am sharing on this blog because I know there are many folks out there that will think about this and consider it.

Needless to say, my students have a new appreciation of standards based grading.  I will be sharing more about all of this soon.  I ask that you pause and consider your grading and what it actually measures.  Then join the #sbar group on twitter to join the journey to make grading more meaningful to all!

Standards Based Grading: The Foundation for Learning in my Classroom

The other morning I got up early to journal before my first PAID day back to school.  I emphasize the word paid because if any of you are like me, I had already spent a handful of unpaid days in my classroom knowing I would need the extra time to get myself ready for a new school year.  Before I wrote, I closed my eyes to visualize how I wanted our (students and educator(s)) classroom to look:

When I close my eyes and picture walking into my classroom, I see students busy or should I say INTENT on being mathematicians.  Some are working in pairs, others individually.  I am sitting at a table with a small group providing instruction or intervention or enrichment.  There are students on the computers, sitting on the floor, working with tools, writing, sharing, creating and they are all engaged, self-directed, and self-monitoring so that I can focus on working with my small group.  Everyone is involved in meaningful math activities all with the same goal of proving their understanding of the math standards.   The students are focused on the standards individually rather than everyone doing the same thing at the same time.  It is calming for me to think about my classroom operating the way and also daunting - it takes a lot of work, preparation, and foundation building to have a middle school classroom that actually works this way!  I've always had this vision and when I taught elementary students, I took the needed time to establish this vision.  So, this year, I am going to do the work to create a classroom that is as close to my vision as possible.

The foundation for building a classroom environment described above is Standards Based Grading.  I will be using what I learned from reading the book: The Daily 5 which is a book about elementary literacy.  The reason I bought and read the book is because they go through and describe exactly how to create a classroom of self-directed, self-monitoring students who are focused on learning.  The authors describe some "Core Foundations" one of which is "Creating a Sense of Urgency".  They also state that
"Purpose + Choice = Motivation".  As I thought of these two ideas, I realized that the driving force for my classroom would be my use of Standards Based Grading.

So, as I begin my second year of working to implement standards based grading and having it drive my vision, I decided to re-visit an invaluable resource that I found November 2011:

Educational Leadership:Effective Grading Practices

For those of you interested in implementing standards based grading or changing your grading practices to support student leaning and achievement, you need to read these articles!

Here are some highlights:

• Susan M. Brookhart:  "Standards-based grading is based on the principle that grades are not about what students earn; they are about what students learn."
• Thomas Guskey : "No research supports the idea that low grades prompt students to try harder.  More often, low grades prompt students to withdraw from learning."  
• Rick Wormeli:  "Lawyers who finally pass the bar exam on their second or third attempt are not limited to practicing law only on Tuesdays."  
•  Alfie Kohn: "Grades don't prepare students for the "real world"- unless one has in mind a world where interest in learning and quality of thinking are unimportant."
• Robert J. Marzano and Tammy Heflebower: "Demonstrating knowledge gain can be intrinsically motivating to students." and "Teachers should allow students to upgrade their scores from previous grading periods."
• Douglas Fisher, Nancy Frey, and Ian Pumpian: "When practice work is part of the overall grade, students don't take risks, and teachers don't get valuable glimpses into their understanding."
• Carol Ann Tomlinson: "An A that doesn't represent personal struggle and growth is a lie."  

There are other great articles from inspiring educators.  The final quote I want to leave you with is from Susan M. Brookhart: Teachers who are skeptical about standards-based grading need safe honest conversations about their beliefs."  Keep this quote in mind as you take the next step in sharing your successes in using standards-based grading with your colleagues.

I did not mean to be this wordy, however, I felt I needed to share my re-focus process at the beginning of the new school year and this ASCD issue helped me.  If my vision is to work, and my grading is to be motivating, then I need to keep these articles close!  At my school, I am still a salmon swimming upstream against an incredibly strong current, as are some of you out there who are taking on standards based grading in your classrooms.  

Thank you all of the #sbar folks!  You keep me going and fighting the good fight!  There is no way I would have persevered with this one if I did not have your resources and support!  I look forward to a great school year of learning and sharing with all of you!

Let the fun begin...  Happy New School Year!

What is the Purpose of Grades in my Classroom?

My first semester of the new school year will be over in eight days.  I have whole heartedly began my journey into using standards based grading this year.  At the halfway point, I want to share some beliefs, insights, and struggles that I have acquired the past few months.

First, I want to begin with my beliefs on the purpose of grades in my classroom:

• I believe that grades are about what students learn not what they earn ASCD Article by Susan Brookhart
• I believe grades do not motivate or provide incentives for students to do well
• I believe one single grade given on a test with multiple learning standards is not an accurate measure of student knowledge and understanding.
• I believe that students should not be punished for taking longer to learn essential skills or standards
• I believe the students should be asking: "What does advanced look like on this standard?"
• I believe students should get credit for showing thinking and understanding in any way that makes sense to them as long as they can explain their thinking and procedures
• I believe students should get full credit even if they did not learn the standard "on time" 
• I believe that Summative Assessments are also Formative because the students know anything they do not score proficient on, they still have to show proof of understanding.
• I believe any work I assign to my students must be tied to a standard

How has my classroom environment changed based on my beliefs?

• My classroom atmosphere encourages thinking and problem solving rather than rule following because students have to understand the process they are using to solve math problems
• Students work and persevere on problems rather than giving up and waiting  for a fellow classmate or the teacher to give them the answer (#1 rule in my classroom - no one will give an answer, we agree to ask questions to guide thinking and learning).
• The students know that proof of understanding requires deeper knowledge and the ability to explain their process/thinking.  So when they don't understand something, they tell me rather than hiding it
• They do more work to show their understanding
• My students know their strengths and weaknesses and  find relief in the fact that I will work with them to improve and show understanding

I feel like I am in my infancy in the standards based grading journey.  I am experimenting with grade book formats and a variety of resistance from my colleagues, parents, and the students who have become comfortable taking the F.  At this point I feel as though I have made a break through with the kiddos that are used to taking the F.  They have learned that failing is not an option and that they have to prove understanding.  I also love the conversations that occur around standards based grading:

"how is advanced different from proficient on this standard"
"what do I need to do to prove understanding of this standard"
"I don't understand this concept/standard"

I am struggling in a few areas:

• providing timely feedback often is challenging
• my grade book and how it informs students and parents
• strong resistance from my colleagues (hence this post to share with them)
• training middle school students who are entrenched in the "old way" of grading to work to prove understanding

What I know for sure:

• my classes have changed for the better of all students
• I have so much work and growth in this area
• I will use my Twitter PLN and especially #sbar for resources, support and learning

I can't believe my school year is almost half over... YIKES!!