Data Science

 At PSESD, a hub for teacher training and information in the Seattle area, a group of teachers congregated and talked all things math. We chatted about making a difference in academic outcomes (and ultimately life outcomes) through mathematical instruction. We discussed equity through a math lens, and we learned about new learning outcomes that are headed for classrooms. 

I am so excited for the newest strand of mathematical standards in Washington State.  The creators are people after my own heart.  We are going to be diving into the world of Data and Statistics, which is necessary and interesting as so much of our world is surrounded and revolves around these mathematical principals.  Charts and tables litter the media and we need to have citizens be able to read and understand these ideas with a critical eye.  What makes a graph biased?  What makes is believable?  I want my students to be honest skeptics and think deeply about the world around them.  

As a biology major, much of my undergraduate program consisted of creating science experiments, exploring results, collecting data, and searching for meaning in the natural world.  Now I get to bring some of this type of thinking to my students. 

This week, my 5th graders started an assignment called "Dear Data" that I learned from the PSESD training.  We are discussing statistical questions.  We will create some statistical questions, gather the data to answer our questions, and then we are going to represent our learning in an artform or a graph. 

The students have already jumped into the process and I am busy creating lesson plans to go with the new strand of data learning.  I have heard the slow reveal graphs also go along with this learning, so I am planning on finding some of those online.  We will discuss what the graph is saying and apply it to our thinking as we make our way through this unit. 

The Role Vocabulary Plays in Math

 One idea/question that I have been wrestling with lately is "What is the role of literacy in mathematical understanding?"  I have noticed that my gifted students are very adept at processing equations and showing ideas with numbers.  I have seen a lot of growth and understanding in their flexibility to solve problems in multiple ways and assess which ways are most efficient. 

 However, there seems to be difficulty around multi-step and multi-part math stories and interpreting these stories in order to make sense of them mathematically.  With this knowledge, I will be focusing on vocabulary usage and understanding in the classroom.  I am creating more vocabulary games, where students need to explain their thinking using vocabulary words in order to make it to the next level.

For example, with Ms. Cairelli's second grade class, my students analyzed a picture and looked to find the math in it.  I placed up a chart of math vocabulary for students to reference in case they needed to scaffolds and supports.  Students looked at the image and told me what they noticed and each time the student used a mathematical term, I gave the class a point.  Ultimately, the class achieved more than the goal of ten points.    

Here is the image I used: 

I listened as students found addends, patterns, arrays, multiplication problems, sums, and discussed results in detail with their classmates.  It was fun and a great way for students to use the vocabulary that we hear in mathematics every day. 

If you are interested in finding more images like this one, you can find them here: Creative Advanced Math

Visual Images Revisited

 My fourth grade students have been hard at work analyzing images, predicting patterns and then finding algebraic equations to predict future figures in the patterns.  They have collaborated well, showed their thinking mathematically, and now I am pushing them to express their ideas in ordered pairs on a coordinate plane.

Students first created a pattern with ordered pairs.  Then I asked them to build the pattern with cubes and blocks and manipulatives in the classroom.  It was fascinating to watch my students think through the process and have to logically and visually represent the growth of the cubes.  Some students found creating the patterns difficult, while others wrestled with how to show the pattern visually.  

It was so interesting watching my students take their learning to the next level.  Here are some images of the patterns they created. 

The final lesson was analyzing a partner's pattern, turning it into an algebraic expression and graphing it on the coordinate plane.  We had a lot of fun with this one! 

Choral Counting and How to Differentiate It

 One of the most successful math discourse routines that I have used this year comes from Turrou, Kazemi, and Franke out of the University of Washington.  It is called Choral Counting, but it is much more than a class counting out loud together.  Students do chant and count together, but they discover patterns in numbers, understand the number system, identify why patterns occur and discuss with partners. 

When I introduced this routine to my fourth graders early on in the school year, we started by counting by 9's as this is a skill most students have mastered.  As we counted by 9's, I created an array of the numbers.  

We paused after about three rows of counting by 9's and I asked my students.  What do you notice?  Do you see any patterns?  

"I see that it increases by 45 when you go down a column!" cried one student.  

"That's because there are five numbers is a row and they are each worth 9," replied another. 

I asked the students to turn to a partner and chat.  "What are you noticing and wondering?"

The class erupted into discourse.  Students saw the ones digits decreasing across the rows, and the ones digit alternating as you move down a column.  Some students noticed that if you add the numbers in the digits together, you get 9 again and again. 

I circled the patterns with various colors as the students chatted and shared their mathematical thinking.   This is differentiated because all students can notice something, but other students can take the learning deeper by discovering relationships and explaining why those relationships exist within this structure.

I have created graphic organizers to help me with these patterns.  If you are interested in checking them out, you can click here: Choral Counting.  

Below is a picture of me circling relationships for a first grade pattern. I did this under the document camera. 

The Limitations of Testing

 Let's face it.  Students today have to undergo a lot more testing than we did as children.  There is i-ready testing, COGAT testing, TTCT testing, SBA testing, Benchmark Assessments, fluency assessments and end of unit assessments to name a few.  There is so much data being compiled for our little ones, that it is staggering.

This data can paint a picture, but it does not paint the full picture.  In i-ready math,  we assess for accuracy and the right answer.  We don't assess the process so we are going to find children who are good and efficient at getting the correct answer, but they might not understand why an algorithm works, how to communicate their knowledge to other people, draw models, or use vocabulary correctly.  

I am finding that my students can solve equations really well but need work on the math practice standards.  For example, one of my first grade students has memorized her multiplication times tables but has no idea what multiplication is.  I have another young student who knows how to add three digit numbers with other three digit numbers but doesn't understand what it means when you are placing a one in the tens digit or hundreds digit when adding.  The understanding of place value underneath the process is missing.

It is really important for our students to go deeper with the math and understand why algorithms work, rather than just memorizing how they work. Therefore, the students can learn to think logically, reason critically, and problem solve rather than memorizing.  With the advent of AI, the need to calculate is limited.  But the important skill of working with people, reasoning logically, and explaining thinking is more crucial than ever.  

It is important for teachers and parents to ask, "When my student is faced with an unknown problem, can they work through it without giving up and really problem solve? Or are they just coping what a teacher showed them a minute prior?"

We need to give students challenging problems that push their thinking so they have to learn something new.  We have to allow students to fail and try again so they have work ethics when they are older.  They have to talk about their thinking and reasoning and that is the opportunity I hope to bring to my students in SAGE and PEP this year. 

The Start of the 2025 School Year

 The sun is still shining and small people dressed in their best march across the blacktop toward a year of new beginnings, new friendships, and new learnings.  Some students are excited, others are anxious or worried about the days ahead, but one thing is certain, school has resumed. 

My class starts on September 8th, since I am a specialist and the students must learn the procedures, rules, and routines in their homerooms first.  I am anxiously waiting for my kids to walk into the door.  I want to hear stories about their summers, see their smiles, and connect with them again for a new school year. Some students will meet me for the first time, as I have new first graders, third graders, and others who have joined the Science Tech. program.  

We will do some work together in a whole class setting and other work in a small group setting this year.  We will work on growth mindset, collaboration, communication, creativity and focus as we explore the world of mathematical thinking, the intersection of science and math, coding and book clubs.  

Busy days are ahead as I meet my students and I will invite parents to an optional curriculum night later on in the month. Stay posted to learn about upcoming dates as I greet new students and welcome back old friends. 

The Year Comes to a Close

 The boxes are packed up, the containers are closed, the kids are saying good-bye and goals have been reflected on.  The stars that once hung on the ceiling are down in a pile on the desks, waiting to be moved to the portable on Monday.  We are switching classrooms at Creekside Elementary and a new year awaits. 

Teaching is so cyclical and we are at the close of another year. I will luckily get to see most of my students again in the fall with smiles on their faces, sharpened pencils, and new school supplies.  We will go through routines again, catch up about summer trips, and begin another learning year and journey together after "Meet Your Teacher."

In teaching there is an open and a close.  You can compare data in test scores and data on exit tickets from the beginning of the year to the end of the year.  Did the students grow in their understanding of geometry?  Do they know how to do algebra?  

But in the bigger scheme of things, a lot of social-emotional learning is also happening.  Did the student learn how to make a friend and keep a friend?  Did the student learn how to laugh until their belly ached, write poetry, express their feelings or persist when life got hard?  How do you measure friendship and compassion?  These are important growth areas for children as well, and are arguably just as important (if not more important) than geometric equations on a test. 

I hope when the students look back at this year of SAGE and PEP, they will remember the year they collaborated to make a Rube Goldberg machines, got really into books, made a new friend, learned how to code a microchip or code a game on scratch. I hope they learned to have deep book discussions and work with others to create plays and puppet shows.   

Some of my special 5th graders are leaving this year, and of those, I have taught some since they were second graders pretending to be foxes on the regular. I remember teaching others how to read the word "tiger" and now they are moving onward to middle school.  

My role is a unique one in the school.  I get my kids year after year (as long as they don't move) and I am able to really see how they grow, learn and change.  It is a gift.  I don't have them as long during the day or week, but I get them over years of their elementary school life. I am lucky to have such a role and get to work with funny, quirky, fun and thoughtful kids.  I hope they have a great summer.