Category Archives: Curriculum Connection

What does Communicative Language Teaching look like at Hamlin?

Communicative Language Teaching or el Enfoque Comunicativo is a language teaching methodology that emphasizes the importance of building meaningful communication through the use of highly contextualized, authentic scenarios that parallel a language learner’s everyday life experiences. (Richards, 2009)

If you are a first grader at Hamlin enjoying recess, your communication with peers might be filled with a simple hand game like Bubble Gum, Bubble Gum In a Dish, or as you see in this short clip, a Spanish version of this traditional game.

While Communicative Language Teaching gained momentum in the early 1970s, traditional perspectives of a language classroom experience still permeate our thinking today. Our own recollection of past language classroom experiences might include a language teacher who positioned herself at the locus of the class and created a highly controlled learning environment where students mimicked textbook sentences, memorized dialogues, or filled in cloze paragraphs with the present tense verb conjugations. Accuracy reigned as the desired outcome for all language learners.

With the CLT model, errors are seen as opportunities for growth. Perfectionism stands as the most dangerous obstacle to fluency and one’s own creative production of personalized language.

“You need to make 10.4 million errors before you are fluent. How many have you added to your total today?”
-Kirsten Gustavson, current SS teacher and past French Teacher

We would never expect a toddler just learning to speak to produce a seven word long sentence, employing all the proper pronouns and all verbs in their correct irregular past tense forms. Yet when we hear a young 3-year-old child ask, “Us take the bus?” there is no doubt that she has successfully communicated. Errors like this show that a learner is willing to take a risk, to experiment and to explore what she knows about the language. This in-between language is defined as Interlingua (Selinker,1972). The process of reaching advanced proficiency or level 3 takes an estimated 600 hours of class-time and the practice involves making plenty of mistakes along the road! (Foreign Service Institute)

Let’s compare two lessons, both involving teaching the language function of how to buy a gift at a store.

Example A
Students listen to an audio recording of a textbook dialogue between a saleswoman and a client. Once completed, they answer comprehension questions about vocabulary and grammar from the dialogue. For homework, they memorize the dialogue and present to the class the following day.

Example B from 8th grade Honors Spanish Class at Hamlin:
Students first discuss strategies for how to barter in an open-air market. They list both what the salesperson might say as well as what the buyer will say. Before they take on the role of either salesperson or client, they receive a list of goods-the salesperson has suggested prices and the client does not. He only has a fixed budget. The objective is not the perfect recreation of a memorized script, but rather an improvisation of a negotiation between the two individuals in this highly contextualized and exciting real life setting.

In this information gap exercise, it becomes necessary to communicate no matter what to achieve the goal of making the largest profit or spending the least amount of money, depending on which character you are acting out. Students are forced to try what they know, experiment with the language and focus on a meaningful, relevant interpersonal exchange. Undoubtedly, errors will abound. Yet this highly energized practice of the language increases the student’s motivation, confidence and ability to speak with fluency. Grammar presents itself in the form of making comparisons, using descriptive adjectives, superlatives, and of course a necessary review of numbers to discuss cost of items. Feedback on errors is saved until the end of the exercise when the teacher then shares what she has heard during the bartering exchanges.

Real world, authentic communication is at the heart of each lesson. In addition to information gap exercises like the one above, other classic CLT examples include pair interviews, draw-what-I-say activities, home or neighborhood tours, find-someone-who surveys and a plethora of role-plays.

Here is a link to a short video called “¿Quién soy?” or Who am I? In this clip of a student role-playing a farmer, the language function being practiced is how to describe a person of a specific profession.

Look at the following three examples with the common goal of building cultural competency.

Example A: students write a research report on a Latin American country and present findings to the class via a PowerPoint slide show

Example B Folletos: 7th grade Hamlin students create their own Youth Travel program that focuses on being a traveler, not a tourist. They design a brochure for a customized summer trip to a Spanish-speaking country, explaining activities, points of cultural interest, how they will spend their budget, community service projects and destination highlights.

iBook example #1: click photo to download full book

Example C Entrevistas: 8th grade Honors students at Hamlin interview native speakers about their home country, their transitions to the US and the challenges they faced. They synthesize all material into an iBook Author presentation, including photos and sound bytes from live interviews.

This interview project offers students the opportunity to stretch their language learning outside the walls of the classroom in an authentic, meaningful way. They see the need to learn Spanish in order to communicate with communities beyond just their classmates. More and more, we are urging our students to explore new communities, but also see their own community with a fresh perspective.

Ultimately, at Hamlin we strive to create authentic learning environments where our girls grow into confident and comfortable language learners who have the tools necessary to engage with the world.

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

At 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