Early Algebra

I’ve been in a number of junior classrooms lately looking at how we use pattern rules for growing patterns. Visual representations can significantly help with this, and the transition to an algebraic representation.

There’s usually a disconnect between how we use pattern rules in late primary / early junior, and the transition to algebraic representations later on.

Consider this number sequence:    5, 7, 9, …

In grade 3 we tend to accept “Start with 5 and add 2 each time”

But the algebraic representation is 3 + 2n

The difference is that algebraically, we add something to each stage including the first stage.

I’ve always thought about the idea that we seem to change the idea of the pattern rule over the grades without being explicit about it to the students.  So should we just start with the pattern rule that correlates to the algebraic representation?  In words, should it be something more like “Start at 1, and add 2 to every term (including the first one)”?

This is easier for students to see pictorially or with manipulatives.

Visually

IMG_2142

 

In words

Start with 3 and add 2 each time

 

 

Algebraically

3 + 2n

Number Sequence

5, 7, 9, …

To test this out I visited a grade 4 class who had been exploring growing patterns (but not visually).

When asked to draw their own pattern for Start with 1 and add 2 each time, most drew pattern similar to alg2
But a couple drew alg1

Over the course of a 20 minute discussion and students defending their point of view, the entire class decided the second representation actually depicted the given pattern rule better.

 

 

How is Your Literacy Block Working for You? Try the Daily 5!

How is your literacy block working for your students and you? Mini-lessons, small guided groups and conferring all sound wonderful but where do I find the time while keeping the others doing meaningful work? My answer was and is “The Daily Five”.PicCollage

This framework, developed by educator/authors Gail Boushey and Joan Moser, provides structure to your literacy time and gives students choice, building independence while being productive and engaged in authentic reading and writing.

The Daily Five is a research based framework that allows teachers to structure their program using the components that are meaningful in their own classrooms. Students are taught to build stamina at the following options: Read to Self, Work on Writing, Read to Someone, Listen to Reading and Word Work. Students have control over the order of the options and in some, the task to be completed. This choice gives the students a sense of independence and ownership for their learning. It gives the teacher a chance to individualize learning goals with students at their just right levels.
The authors encourage teachers to make the framework their own but provide insight on what has worked for them in their easy to read book and website, “thedailycafe.com”.
My literacy block usually follows the following format:
10 minute Mini-lesson (accuracy skill)
15-20 minute Rotation – students choose from the 5 options, I run a guided reading group or confer with individual students
10 minute Mini-lesson (comprehension skill)
15-20 minute Rotation – see above
10 minute Mini-lesson (vocabulary/word work)
15-20 minute Rotation – see above
5 minute Sharing
25 minute Writers’ workshop (my choice – not part of The Daily Five)

My students get the choice of two or three rotations most days and must have chosen each of the five options at least once throughout the week.
I have used this framework with success in grades one, two and three and my students would highly recommend it. When students ask if they can “do a daily rotation” during indoor recess, you know it is working!

Submitted by Pauline B., Teacher in AMDSB

Negotiating Learning Within the Science Curriculum

Drain and Creek Inquiry – Grade 2 Understanding Earth and Space Systems –
Air and Water in the Environment

There is a myth that inquiry based learning is fully emergent, driven wholly by student interest. This leads some educators to abandon inquiry based learning as a teaching and learning strategy due to the pressures of meeting and reporting on the topics and expectations outlined in the curriculum documents. We wanted to debunk that myth by planning for an inquiry that fit within the curriculum topics and expectations, but was still driven by student interest within the bounds of the curriculum. Before starting the inquiry, we met to read through the curriculum. We wanted to be sure that the experiences were anchored in the fundamental concepts and big ideas, the curriculum overall and specific expectations, and the scientific skill continua in the front matter of the curriculum.

Recognizing the importance of hands on experience, a local creek and drainage system adjacent to the school was selected as the setting for the inquiry. Rather than starting with a teacher initiated lesson, our first provocation was a visit to the creek. The children were paired up as either “explorers’ or ‘photographers’ and had instructions to observe the creek area and take pictures of what they found interesting. They recorded observations in their lab books, which will serve to house their individual theories and observations, and also provide a platform for individual assessment. This information, phrased as “what did you notice” in a subsequent Knowledge Building Circle and question generating process, would indicate for us which direction to go with the learning.
Following the visit to the creek and the Knowledge Building Circle, the students wrote questions they had on sticky notes. Analysis of these questions would inform the next direction of the inquiry.

We sorted the student generated questions into like-piles, and determined there were three directions the students were interested in – which were also confirmed by a reflection on the transcript of the first Knowledge Building Circle.
1. Where does the creek water come from and finding out more information about the creek.
2. What is the plant growth/slime that is on top of the creek?
3. What kinds of living things live in or near the creek? (Plants and animals)

Student generated questions were sorted into like categories, which informed the direction of the inquiry.

Student generated questions were sorted into like categories, which informed the direction of the inquiry.

Reflections on the KBC transcript confirmed the student interests and aligned with the questions they generated.

 

If the KBC had not aligned with the sorting of student generated questions, additional areas of interest would have been added.

If the KBC had not aligned with the sorting of student generated questions, additional areas of interest would have been added.

 

 

 

 

 

 

 

 

 

 

 

 

Each of these student-identified areas then became the focus of expert visitors (Conservation Authority, a tree specialist), hands on investigations (daily creek data collecting, organizing and analyzing, observations, water purification experiment, examination of the slime, creature findings) and strategic background knowledge building and explicit teaching (ex. Videos on water cycle, watersheds, mapping, tracking the drain to the creek to the river to the lake, to the St Lawrence to the Atlantic, success criteria for enlargement diagrams, recording and revising theories in the Lab Book as learning happens). Students were frequently asked “what did you notice “ and “what are your questions and wonderings”, and these responses fed smaller KBCs and investigations.

 

 

 

Students determined what data about the creek they would measure and record, to analyze and draw conclusions about.

Students determined what data about the creek they would measure and record, to analyze and draw conclusions about.

 

Each of these central questions relates to the Overall Expectations and many specific expectations in science, literacy, and numeracy. For example, in order to support both the expectations and the science skill continue, the children determined what they should measure and record, and determined where they wanted to locate the measuring tools. Once the data is collected, they will organize the long-term data into graphs and analyze the trends and patterns that emerge.
Skill Continua – found in the front matter of Ontario Science Curriculum, Grades 1-8
• initiating and planning (e.g., asking questions, clarifying problems, planning procedures)
• performing and recording (e.g., following procedures, accessing information, recording observations and findings)
• analysing and interpreting (e.g., organizing data, reflecting on the effectiveness of actions performed, drawing conclusions)
• communicating (e.g., using appropriate vocabulary, communicating findings in a variety of ways)

Through this inquiry example, we tried to highlight that inquiry based learning can be student driven and negotiated within the context of the Ontario Curriculum. Each step is carefully considered, constantly revisited, and layered with connections to the curriculum. Student driven questions and observations feed the KBCs and the hands on experiences as they relate to the context.

Submitted by Allison Plumsteel, Grade 2 and Jodi Regier, Primary Coordinator

For further information on Environmental Inquiry and Knowledge Building Circles, please visit www.naturalcuriosity.ca and http://program.yourschools.ca/early-learning/the-inquiry-process-in-kindergarten/knowledge-building/
For further information on beginning an inquiry through provocations, pleased visit:
http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_inquirybased.pdf
“Moving students beyond initial curiosity to a path of regular inquiry is one of the great challenges of inquiry-based learning. In this process, educators play an important role. Teachers model how to contribute and extend ideas, how to question and how to carry out an investigation of one’s ideas or theories. They play the role of “provocateur,” finding creative ways to introduce students to ideas and to subject matter that is of interest to them and offers “inquiry potential” or promise in terms of opportunities for students to engage in sustained inquiry of their own.”