Category Archives: Curriculum Connection

SAMR Model: Excellence in Teaching with Technology

Effective teaching with technology relies on a teacher’s understanding of available technology tools and applications. In order to promote teaching excellence with technology, Hamlin has adopted the SAMR paradigm as the criteria to critically assess instructional technology choices. SAMR stands for substitution, augmentation, modification and redefinition. This reflective framework promotes deep understanding of technology and the intended learning outcomes for students. Specific and intentional planning of outcomes comes first followed by the selection of the type or mode of technology that supports the outcomes. Technology may be used at any point in the teaching and learning cycle. Teachers can substitute, augment, modify or redefine their work with regards to assessment, delivery of instruction or student work. The following post authored by Liz Beck with support from the Technology and Innovation team highlights our professional development workshop and commitment to effective instruction with technology.

This post was originally posted to pubs.hamlin.org:

What does infinity have to do with the SAMR model? It’s all about mindfulness in the classroom.

When the Tech Team first landed on the SAMR model, it resonated with us. We had already launched 1:1 iPad and laptop initiatives, but searched for common language to discuss our ed tech vision. SAMR seemed like a perfect fit!

Except for one thing. We don’t view the integration and use of technology in the classroom as hierarchical. We view iPads, laptops, apps, 3D printers, etc., as tools. Just as you wouldn’t choose a jigsaw to hang a painting, you wouldn’t choose Microsoft Word as a programming app. There is a time and place for each tool and the key is to know how to choose the best tool and why it’s the best tool for the task at hand.

Since it’s creation by Dr. Ruben R. Puentedura, the SAMR model has been discussed alongside various images, like flow charts, ladders and scales. Another popular SAMR metaphor is attributed to a 2013 blog post by Tim Holt as well Jonathan Brubaker’s subsequent post, comparing each SAMR category to various types of coffee.

SAMR_InfinityAs you move through our presentation you will notice a new image created by the Hamlin Tech Team, where the infinity symbol is used to describe the flow as teachers mindfully select technology and its uses within the classroom. This is also meant to symbolize our decision not to weigh one SAMR category over another, but rather to raise teacher awareness and the capacity to make informed technological choices in the classroom. For example, Word (substitution phase) can make perfect sense for some projects and be the right tool for the task, whereas a blog (modification or redefinition) may be the right choice for other tasks.

Guiding teachers to discover new technology, be mindful of the pedagogical reasons for selecting one tool over another, as well as creating a safe space for openness, risk taking, and creative thinking, are more important to our team than striving for redefinition above all other categories.

We hope you enjoy our take on the SAMR model, originally presented to Hamlin faculty on May 12, 2014.

Teaching Number Sense by Gillis Kallem

At Hamlin, we develop number sense through a series of mini lessons called Number Talks or Problem Strings. These lessons last no more than 15 minutes and can be taught as a whole class or in small groups. During a number talk, a “string” of number problems are presented one at a time. A string is a collection of related problems designed to guide students to construct big ideas about numbers and devise their own strategies. The number string gives students a chance to notice patterns and practice mental computation strategies. Over time, number talks help to elicit efficient and reliable strategies.

During a number talk, girls are asked to solve a problem using mental math. When they have an answer, they place a thumbs up on their chest so as not to disturb others who might still be working. While a quick student is waiting with her thumb up, she is encouraged to solve the problem in a different way. For each additional way she finds, she can raise another finger. When enough thumbs are up, the teacher calls on a student to share her answer. The teacher will call on other students to collect different answers.  All answers are accepted and written on the board regardless of accuracy.

Next, the teacher asks for a student to defend an answer by sharing her strategy. While the student shares, the teacher represents the student’s strategies on the whiteboard using open number lines, arrays, ratio tables or pure numbers. The teacher facilitates a conversation about the meaning the girls are generating from the problem.After several different strategies have been recorded, the teacher will present the next problem and repeat the process. At some point in the number talk, a student will share a highly efficient strategy. Through the facilitated discussion, other students will take note of it and with teacher encouragement, the whole class will be asked to give this strategy a try for the next problem in the string.

Number talks while short offer clear and direct instruction for developing computational fluency that reach far beyond the use of standard algorithms. They make use of breaking numbers apart, making friendly numbers, adjusting numbers, and doubling and halving to name a few strategies.  They work to develop deep understanding of numbers, cultivate relational thinking and support creative yet highly efficient pathways for solving problems mentally.

Examples of number strings

First Grade – Making Tens

7 + 3 =

7 + 5 + 3=

3 + 6 + 7 =

Second Grade – Doubles and Near Doubles

30 + 30 =

29 + 29 =

29 + 31 =

Third Grade – Making Landmark or Friendly Numbers

37 + 69 =

79 + 26 =

89 +28 =

99 + 19 =

Fourth Grade– Doubling and Halving

35 x 8 =

70 x 4 =

140 x 2 =

Fifth Grade – Doubling and Halving to remove the fraction

2 ½ x 28 =

5 x 14 =

10 x 7 =

 

 

First Comes Number Sense by Gillis Kallem

number-icon-setAt Hamlin, we want to cultivate a rich math experience, which includes a vibrant mathematical adventure into the world of numbers and reasoning, problem solving, and creativity, as well as real-life applications. At the foundation of this important work is number sense. In its most general definition, number sense is the ability to intuitively work with numbers. It reflects an understanding of numbers, their magnitude, and relationships. As educators, we expand the meaning of number sense to include a well-organized concept of numbers that allows a person to solve mathematical problems accurately and efficiently in a variety of ways that are not bound by traditional algorithms. (Bobis 1996)

Number sense involves the understanding that numbers are flexible. For example, a number is malleable like a ball of clay. You can change its shape – make it long and skinny, or short and fat—or you can break it apart into smaller pieces and in the end roll it back to its original ball. The same is true for any number. Take 28, it can be seen as 2 groups of 14, 4 groups of 7, or as 20 + 8 or 10+18 or almost 30. Take your pick. Having this ability to see 28 or any number in its many forms allows the user to think freely and creatively when asked to solve problems involving operations with numbers.

When we are presented with a problem such as 131 – 28 in which we might be tempted to write it out in the standard algorithm, then regroup/borrow/cross out numbers and so on, we can instead think about the many forms that any number can take and find one that makes sense for solving this problem in our heads:

Think of 28 as 20 + 1 + 7.
We can first think: 131 – 20 = 111
Then, 111 – 1 = 110,
Finally, 110 – 7 = 103.
In this method, we break apart the subtrahend.

Or we can think that 28 is almost 30 by adding 2 more.
We can change the problem: 131 – 30 = 101
Then we add back 2:101 + 2 = 103.
In this method, we adjust the subtrahend to make a friendly number or a round number, and then add back what we added to the subtrahend.

Or we can play even further!
Change both numbers by adding 2 to each.
Thus, 131- 28 becomes 133 – 30 = 103.
In this method, we adjust both sides, keeping the distance the same but making the numbers easier to work with. This method is known as constant distance.

What about 28 x 5? How would we efficiently and accurately solve this mentally?
One way might be to think of 28 as 20 + 8
Then, 20 x 5 = 100 and 8 x 5 = 40
Combine, 100 + 40 = 140.
This makes use of the distributive property of multiplication.

Another way might be to think of 28 as 30.
Then, 30 x 5 = 150.
Now, subtract two groups of 5: 150 – 10 = 140.
Again, this is using a friendly number and then adjusting afterwards.

Or you could think of the problem in an entirely different way!
Turn 28 x 5 into 14 x 10 = 140.
This is a clever method called doubling and halving.
Various classroom activities and lessons in Grades K-5 at Hamlin support the development of number sense and flexible thinking.  Additionally, our assessments measure the girls’ learning of robust number sense. Building computational fluency is a core skill that fluid and flexible number sense girds for long-term success in mathematics.

In my next Curriculum Connection, I will highlight the specific classroom practice of Number Talks/Number Strings as it relates to number sense.

Gillis Kallem
K-5 Mathematics Specialist