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oUR LATEST NEWS:  RIMTA has LOTS to offer for 2024

*Learning Access and Equity in Math Teaching Virtual Series - FREE and open to anyone! - next session is March 13 so register today!

* Building Elementary Numeracy and Fluency: Addition and Subtraction with Ann Elise Record - workshop series held at Winman Middles School in Warwick - you've only missed one session. Registration is available until March 6 (next session is March 7)!


"Seeing Every Learner" Keynote Kyndall Brown - Saturday, March 23, 2024 at East Providence High School -REGISTER NOW!   .


Student of the Year: Lexi, Mt. St. Charles Academy

Rookie Teacher of the Year: Chelsea O'Connor, Samuel Slater Middle School

Teacher of the Year: Nicholas Horne, Burrillville High School

Amedeo DeRobbio Award: Vivian LaFerla

Thanks to all those who attended or supported the RIMTA Spring Conference with Mike Steele

RIMTA BLOG - Check out the latest news, lessons and resources from RIMTA (Our Blog will replace our newsletter).

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  • 18 Nov 2019 9:46 AM | Gina Kilday (Administrator)

    Have you ever met someone and you immediately knew you needed this person to be part of your professional life? Well, I have. I was truly fortunate to have met a Master Teacher, whom I now refer to as my mentor, at the New Cubed Conference at Sienna College at the beginning of July, 2019. I was mesmerized as soon as he started talking about his teaching and was in awe of his ideas for middle school math. Even though I have been a middle school teacher for the past thirty-one years, my hope when I attend a conference is to get one new idea that I am able to use immediately in the classroom. I not only learned one idea, I learned a whole new way to get students excited and to truly enjoy math class. This article references one of these great ideas that was shared with me. I hope you enjoy it as much as I did. Please let me know if you try his lesson and how it went.

    After fifteen years as a banker, Eric O’Brien enjoyed his role as an elementary school teacher in Bellmore, Long Island. Eric used his love of mathematics to enhance lessons in number theory, computation, algebraic reasoning, geometric reasoning and problem solving techniques. He employs keen observation skills to introduce integers to primary students and to solidify computational skills with 3rd through 8th graders. He has been heard asking 4th and 5th Graders to hand him their fears before guiding them into an exploration of algebraic techniques and wields hammers with 5th and 6th graders as they construct geoboards and guides them toward a journey into geometric reasoning. After solidifying sixth graders’ understanding of algebra, Eric has no fear in guiding students on an investigation of Pascal’s triangle and introduction into the calculus. He includes a host of light-hearted tales as he shares his love of mathematical history with his students.

    The foundation of Eric’s ventures into mathematics include a solid investigation into computation. While other educators are pleased when their students can retain a foundation of 100 basic math facts, Eric pushes his students to find methods to mentally calculate over 10,000 basic and maybe not so basic facts. Eric’s students don’t break a sweat when explaining that 360 has 24 factors, that thirty-one perfect squares are less than 1000 or that is a relation between the measure of the arc of a circle and corresponding inscribed angle.

    Lesson One: Double, Double, Doubling as a Multiplication Tool for Struggling Middle School Students

    I have spent many of my years working with middle school students. Often students have entered my classroom, fearing that they will be working with “that math guy.” I ask what that statement means and children often admit their fear of mathematics. I ask them why they feel that way and many admit they have struggled with math for the first five years of their learning careers.

    Asking learners to put their fears squarely in my hands, I tell them I will hold firmly to their fears and I will give them back if they’d like. “May I begin?”, I ask students,gaining some trust from the worriers.

    “Let’s play a game called the Doubling Game,” I tell my learners. “If we make a mistake, we’ll start over again.” I ask the students to take a deep breath and exhale. The students find themselves to relax simply by engaging in that behavior.

    “One, Double,” I say. The students usually give me a resounding “Two.” I look around, showing I am impressed. Again I say “Double.” The kids shout “Four” and I smile.

    Again I shout “Double,” awaiting their reply. While many students shout “ Eight”, a few shout “Six”, followed by “Oops!” There is laughter in the air.

    I explain that it is fine to make a mistake. Asking the guilty party why he or she said “Oops”, the students say they were thinking they were counting by twos and had to remember they were doubling, two different processes.

    I wanted to let students know a few things. First of all, it’s ok to make mistakes. My room is filled with experimentation. Mistakes will happen when students are learning. Secondly, teachers should anticipate that mistakes are going to happen and when they do, we acknowledge without punishment and return to work.

    “Let’s get back to work,” I recommend. “One. Double” The children shout, “Two,”

    And after a short wait, I say, “Double” The children answer, “Four.” Again I wait, allowing students to learn that true learning comes through chanting and cadence. Tension builds before I say, “Double” and the children shout, “Eight!”

    I look at the child who mistakenly replied, “Six” the first time. A little nervousness appears on his or her face before we continue. I reassure the class that some of their replies will require some thinking, before I say, “Double” again. After a short delay, children say, “Sixteen.” A few others join in.

    Whether middle schoolers know it or not, adding eight plus eight mentally takes more effort than two plus two or four plus four. Their learning will sometimes indeed take a moment. We teachers have to learn the importance of students’ wait time. That wait time will soon rear its head again.

    With my next “Double,” many students will not know how to double sixteen. The positions of the 6 and the 1, meaning one ten, are reversed. I have to say, “When we say ‘sixteen’, we mean 10 and 6. Double 10, double 6, and add them.”

    When students double 10 and double six, there is another level of cognition they must encounter. Doubling 10 gets them twenty, and doubling six gets them twelve. I like to say 10 and 2. By doubling sixteen, students’ minds have a lot of processing to complete to answer “Thirty-two.”

    But after some thought process, the students do answer “Thirty-two.” Happy that  my students have succeeded, I say, “Let’s start again!” Having struggled to get the solutions, we begin again, the students usually flying through the five responses.

    “One. Double”, I confidently say. “Two,” they respond.

    “Double,” I say. “Four!”

    “Double,” I say, “Eight!”

    “Double,” I repeat, “Sixteen!”

    “Double,” I smile, “Thirty-two!”, they are surprised.

    “Double,” I say confidently, watching their eyes roll in their heads. “Sixty-four!”, many of them say. The rest repeat 64. Of course it is. They doubled 30, they doubled two. No carrying. They just say the number.

    “Let’s repeat the process,” I recommend. Usually there are no complaints. The students, new to sixth grade, have successfully doubled right through 64.

    “All right! We will continue beyond 64 tomorrow. Great job, everyone! Would any of you like your fears back?”

    My students always squealed, ecstatic that they had accomplished so much. No pain! Their struggles were met with only my assurances that they would succeed in the process. And no one wanted their fears back.

    Oh, by the way, the next day, we get past 1,000. When I assure them that that means they have gotten past 2 to the power of 10, we sneak right into a discussion of exponents. And we talk about their accomplishments. I ask them why they were so scared before our first lesson. They say they never knew math could be so fun.

  • 06 Nov 2019 10:44 AM | Gina Kilday (Administrator)

    by Sara Donaldson, Ed.D., Wheaton College, Norton, MA

    In their series of articles about rules that expire, Karp, Bush, and Dougherty (2014, 2015, 2017) discuss the negative impact many provided hints and short-cuts have on students’ future mathematics success and confidence. Many of these “rules” do not hold true as students move into more complex topics (e.g.; just adding a zero to the end of a number when multiplying by ten no longer works when you are working with decimals). And even when the “rules” do hold true, students’ reliance on them does not support their understanding of the patterns and structures that make math work and that help them develop the sense making and reasoning needed for long term success.

    Rule number two of their original 13 Rules That Expire (Karp, Bush, & Dougherty, 2014) article is “Use key words to solve word problems” (p. 21). The authors explain that although key words can be helpful, when students are encouraged to scan problems for key words and numbers instead of first making sense of the overall problem situation, the everyday and multiple meanings of key words can lead to wrong answers and an inability to determine whether an answer makes sense (e.g.; left might indicate subtraction, but it could also just be identifying handedness). One strategy for helping students develop the ability to make sense of problems, instead of relying on short cuts, is to have them practice sorting problems based on the type of operation they would use to solve the problem. This task shifts the focus from solving problems to making sense of problems (as finding the answer is not part of the work) and allows students to determine the characteristics of problems that require adding versus subtracting on their own, thus helping to promote understanding and confidence.

    Here is how I approach this type of lesson:

    Preparation: Gather 10-15 one step word problems with approximately half of them for each operation (e.g.; half addition and half subtraction). You can make up problems, adapt problems from your curricular materials, or simply use problems from your math text or workbook. I try to choose problems with familiar contexts and easy numbers so students can focus on the structure of the problem without being overwhelmed by other details. Depending upon your grade level the problems could involve addition and subtraction of single-digit whole numbers or multiplication and division of fractions, making it easily adaptable for different parts of the curriculum.

    Once you’ve chosen your problems, print them out and cut them apart. Each group or pair of students will need a complete set of problems. I put them into envelopes for easy distribution.


    Step 1: Display two problems (one for each operation). Using a think-pair-share structure, have students determine what operation would be used to solve each problem. Then lead a short discussion around how students made their decisions. If students bring up “key words” as their strategy, push them to talk about what the word means in the problem and what the word indicates is happening in the problem situation.

    Step 2: Explain to students that today they will be working in pairs/small groups to sort problems into two sets based on the operation needed to solve the problem. Emphasize that they will not be solving the problems, just sorting them. I usually encourage students to see each problem as a mini-story and to use what they picture happening in the story to help them determine the operation, just like they work to create a movie in their head to help them understand texts when they are reading.

    Step 3: Group students and distribute the problem sets. I like to have students work with at least one other student on this task so they need to talk through decisions, however you could also start by having students complete the sorting independently before moving to step 4 where they will compare their sort with another student.

    Step 4: Once students have sorted their problems have them work with another pair/group to compare their sorts. For any problems where they disagree on the operation, ask students to discuss their thinking and work to reach consensus. If a group is unable to come to agreement on a problem, ask them to put it aside so we can discuss it as a whole class during the debrief (Step 5).

    Step 5: After groups have had time to talk through their sorts, bring the class together to debrief their thinking, talk through any problems which caused disagreement, and come up with some guidelines for determining the underlying characteristics of problems requiring each operation. With the problems displayed for all to see, have students make “We noticed that…” statements that generalize the patterns found for problems using each operation. For example, “We noticed that for subtraction we were finding the difference between two groups but for addition we were putting groups together.” Recording these generalization statements on anchor charts, along with representative problems, will serve as a good future resource for students that will promote their sense making and reasoning ability, as well as their independent problem solving ability.

    Some groups of students are very adept at generalizing patterns, while others are not. Being prepared with questions such as, “Is that always true?” and “How is that different than in the (opposite operation) problems?” can be helpful. Additionally, pulling out a few problems that have similar structures and asking students, “What do you notice is the same about these problems?” is also a helpful scaffold.

    Extending the lesson. In addition to sorting problems based on inverse operations, students can also sort problems that use the same operation, but which have different underlying structures. Connecting this type of sort to solution strategies helps students develop fluency as they come to recognize entry points for different types of problems and thus are better able to pull forward prior experiences as they tackle unfamiliar problems. The “Mathematics Glossary” of the Common Core State Standards for Mathematics identifies common addition and subtraction problem situations (Table 1) and multiplication and division problem situations (Table 2). Although students are not expected to be able to name these different problem structures, becoming familiar with them and recognizing that each type requires a slightly different approach will empower students and allow them to carry these strategies forward to similarly structured problems using more complex numbers in future years, as this knowledge and understanding will never “expire”, unlike the rules upon which many students currently rely.

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