Our Collaborative Inquiry:
Promoting a Mathematical Mindset in Kindergarten Through the Development of Students' Vocabulary During Free, Focused and Guided Exploration
Collaborative Inquiry Partners
Northwood P.S. EL-K Teams:
Sunitta Mistry- Early Childhood Educator (ECE)
Cheryl Vallance- Full Day Kindergarten (FDK) Teacher
Rosie Sohal- Early Childhood Educator (ECE)
Susan Huys- Full Day Kindergarten (FDK) Teacher
Sandra Fobert- Student Work Study Teacher (SWST)
The Kindergarten Continuum
The 'AHA Moment that Sparked Our Collaborative Inquiry
1) As educators we know that it is important for students to communicate their mathematical thinking as it assists students in consolidating their mathematical understanding. In order to communicate this thinking, though, students require a foundation of mathematical vocabulary.
2) The FDK teacher, the ECE and the SWST are not the only ones in the classroom with knowledge. The students bring a great variety of experiences and a vast amount of knowledge. They are 'experts' about what they already know and are capable of teaching what they know to their peers.
"42% of children's play involves mathematical thinking." Doug Clements
The Big Ideas Driving Our Collaborative Inquiry
1) The mathematical process of Communication is one of the actions through which students acquire and apply mathematical knowledge and skills.
2) When students communicate their mathematical thinking they are involved in reflecting upon, clarifying, expanding and deepening their mathematical understanding.
Our Learning Goals
1) to encourage students to see themselves as Mathematicians/Math Experts as they investigate their world through free, focused and guided exploration
2) to build students' mathematical vocabulary naturally in order to provide them with a foundation from which to communicate their mathematical thinking orally
Original Theory of Action
If students are presented with multiple opportunities to communicate their mathematical thinking in a variety of ways (e.g., orally and visually), then students will be more successful in transferring these skills to independent practice.
We found that our original Theory of Action was too broad and was not specifically capturing the essence of our collaborative inquiry, so we decided to revise it to make it more specific in order to more accurately reflect our collaborative inquiry.
REVISED Theory of Action
Original Success Criteria
1) Students use the student-generated Math word wall to reinforce their own vocabulary learning and to teach others.
2) Increased use of mathematical vocabulary by students is observed during free, focused and guided exploration opportunities.
As our collaborative inquiry unfolded, we found that our original Success Criteria was not truly measuring what we wanted it to. As such, we decided to revise it in order that it measure what our collaborative inquiry was focusing upon.
REVISED Success Criteria
1) Students demonstrate an interest in generating Math vocabulary for the Math word wall/ class Math book.
2) The Math word wall/ class Math book is assisting the development of student understanding of the Math vocabulary generated.
3) The Math word wall/ class Math book is assisting the development of student confidence in themselves as Mathematicians/Math Experts.
Resources Used to Inform Our Collaborative Inquiry
Our Collaborative Inquiry Process
Math Learning Embedded in Free Exploration
"Children choose materials, activities and events based on curiosities and interests. Through exploration children have the opportunity to do, see, feel, taste, touch, put together, take apart, wonder, discover, invent, accomplish and communicate all that they experience." (Mathematics Learning in a Play-Based Environment: A Reflective Guide for Kindergarten Educators, page 8)
Math Learning Embedded in Focused Exploration (Co-Construction of Learning)
Math Learning Embedded in Guided Exploration (Educator Initiated)
Classroom Math Word Walls
Student 'Math Experts' Classroom Books
Students began to ask if they could take their Math Expert photos home to share with their families. While we wanted to honour their requests, we did not want to remove the classroom book from the classroom and, thereby, limit regular student access to it. It was from this that the idea of creating a Student Math Expert Book for the purposes of sharing with their families was born.
Student 'Math Experts' Home Books
Classroom teachers informed their students' families about our collaborative inquiry through newsletters. Prior to the Student Math Expert Book being sent home, families were informed through a newsletter to expect the book. One student in each class took the book home nightly. Families were asked to review and discuss the Student Math Expert Book with their children. They were also encouraged to participate in a family scavenger hunt where they were asked to explore their homes together and identify what Math words they could find.
Some of the Student 'Math Experts' Photos
Collaborative Inquiry Key Learnings for Educators (FDK Teachers, ECEs and SWST)
The educators have learned that:
* Math is everywhere.
* Students often take materials in directions that we had not thought of.
(i.e. We anticipate something and the students often take their learning in a different direction, thinking outside the box. Taking their learning in a direction that is meaningful to them and bringing their learning forward, on their own.)
* Our perception of the learning environment can be very different than the students' perception.
* Photos are highly meaningful to the students, especially when they are in them. The fact that they are seeing themselves as Mathematicians/Math Experts is building their confidence as Math learners.
* The Math word wall is encouraging communication between students.
* Updating parents about the Math vocabulary collaborative inquiry through newsletters, e-mail and/or Pic Collages might encourage parents to become involved in questioning their children about their developing Math vocabulary and might encourage the development of further Math vocabulary at home.
* We are recognizing the importance of Math – the collaborative inquiry has brought Math to the forefront of our consciousness.
* Where we used to begin with a literacy activity and pull Math out of it, we are now often beginning with a Math activity and literacy is coming from it.
* We are seeing learners standing out in Math learning that are not necessarily strong in other curriculum areas.
* Students are gaining a better understanding of the Math vocabulary through the guided and focused exploration opportunities offered.
* It is important to honour all student responses and to ask probing questions to assist us in fully understanding their answers.
* Students are encouraging one another and have become more aware that all students are Math Experts and have something to offer.
* The classroom has become even more student-directed. Students are taking more of the lead in their own learning.
* It is critically important for educators to stand back, observe and really listen.
* All students' oral communication skills have benefitted from our collaborative inquiry. Our ELL students' oral communication skills have been even more greatly impacted.
* The beginning of a mathematical community of learners is evident.
* The beginning of a growth mindset in Math has been established.
* When the FDK teacher and the ECE (the EL-K Team) work together as a true team, the 'power of co' is transformational for student learning.
Collaborative Inquiry Key Learnings for Students
The students have learned that:
* There are 'Math' words and they can use these Math words to talk about/explain what
they know/created.
* Everyone is able to be a 'Math Expert' (a Math learner).
* Students are able to learn from and teach one another.
* Math is everywhere/all around them.
* Math is fun.
Our collaborative inquiry has broadened all students' exposure to Math vocabulary. This has led to students feeling empowered to use and to share the Math vocabulary that they have learned which, in turn, has increased student confidence in themselves as Mathematicians.
Student J Taking Pictures of Math Experts in the Classroom
Student J: (to the SWST) "I'm using my camera to take Math Expert pictures."
(He overheard the ECE using a Math word)
Student J: "Hey! You just used a Math word! I'm gonna take your picture."
ECE: "What do you mean?"
Student J: "You said 'size'. It's a Math word!"
ECE: "What does 'size' mean?
Student J: "Like it can be big or small. Smile!"
(He takes a picture of the ECE and continues to move around the class looking for other Math Experts.)
Possible Directions for Further Inquiry
* Build an increased written connection into the collaborative inquiry for those students who are able (i.e., written communication in Math).
* Engage in this same collaborative inquiry across other curriculum areas.
Contact Information
Sandra Fobert M.Ed., OCT
Student Work Study Teacher
Peel District School Board
Email: sandra.fobert@peelsb.com
Location: Brampton, Ontario Canada
Twitter: @SandraFobert