The “greater” the visual the “less” kids struggle: Teaching greater and less then to your kindergartner. Ideas from an Expert

Author: Erin Vosseller, Kindergarten teacher, Summit School of Ahwatukee
Published in the Ahwatukee Foothills News, October 2016
Picture by Summit staff, Micki McIntyre

Most of us grew up memorizing math facts and definitions of terms. This short term memory trick may work for test success, but does little for understanding and applying math to solve real problems.

Can you recall trying to remember which way the greater than/less than symbol should be placed?  Would it have helped if you first designed your own large alligator mouth to place between real objects?

kindergarten-math_greater-than-less-than-sized-for-websiteChildren excel when math is taught through concrete, sensory experiences. The younger the child, the more important it is to provide hands-on, visual tools to create a deep understanding of concepts. This especially true when it comes to numbers and math symbols.  Children may be able to count very high, but does the number 58 really mean anything to them?

When introducing greater than and less than symbols, kindergartners need to have already built a strong understanding of more and less. My kindergartners do a lot of work with manipulatives when learning this and other math concepts. This helps them build a visual memory of numbers so that they can find patterns and see the relationships that numbers have to each other.

There are many things we do at Summit School of Ahwatukee to help children understand symbols and other abstract ideas. A fan favorite in my class is turning greater than and less than into a very hungry alligator, which would rather eat more, something that children can relate to. Our alligators always open their mouth towards the larger group of objects or larger numbers.

Children who are still working on building a visual understanding of numeric values can use objects or drawings to represent numbers. To create a visual, put items on two sides of a table, or in two boxes, or create spaces with tape for your objects. Many stores have inexpensive buckets of cubes or animals, or you can use Lego bricks, pennies, or other favorite things you have at home.

Ask your child to look at the items and ask which they think has more, from a visual perspective. Next have them count by touching each piece to confirm their prediction. Now place the alligator mouth so he can happily eat the most! Don’t forget to have your child make an equal sign on a card to use as well.

Use sticky notes, cards, or dry erase boards for your child to write the number next to each group.  This helps create a mental picture of the number and what it represents. Another idea is to use balance scales.  Students can weigh groups of objects to help them see more, less and equal while putting the correct symbol in the middle.

Making an alligators is fun, and kids can use it to model and talk about numbers in different ways. The alligator is a visual reminder to them about what the symbol means and they soon move on to using the symbol itself.

As children are ready to progress, use larger numbers or even expressions, such as 3 +2 on one side with 5 – 1 on the other.

It is also very important for children to talk through their thinking, explaining the strategies they use.   Take turns with your child reading the expression he or she made, and ask them to teach you how to determine which is greater or less and why. Explaining their thought process takes understanding to a deeper level.

In our kindergarten classroom, we ask students look at each other’s work, listen to each other describe the strategies they used, and begin to analyze someone else’s approach to see if they make sense.  Learning is enhanced when math is a team sport!  It should be a noisy process as children think out loud, ask questions, and listen to and talk with each other.

They should read the expressions they write, testing them to see if they make sense.  With the alligator project, one child might say, “10 is less than 12” while showing classmates the visual he or she created.  We teach children to listen carefully and either agree or disagree respectfully and explain why, combining a successful social skill with mathematical reasoning.

Seeing + touching + listening + explaining = visualizing and understanding! Why is this important? Think about your job.  How often does your boss ask you what 28 + 52 equals? Isn’t it more likely that you are asked to analyze a problem, and find a solution that can be communicated and implemented? Let’s prepare our children for more than test grades. Let’s help them prepare to be successful in life.

Erin Vosseller enjoys using her 18 years of experience to teach kindergarten at Summit School of Ahwatukee. She holds a bachelors of arts in Elementary Education from the University of Arizona, an Early Childhood Endorsement, a full SEI endorsement, and is CLIP (Collaborative Literacy Intervention Project) certified.  She also volunteers as an Assistant Director of Arizona Camp Sunrise and Sidekicks, a camp for children with cancer and their siblings, sponsored by the Southwest Kids’ Cancer Foundation.

Summit Alum hailed by NASA for winning design

kyle-corretteFormer Summit Student Kyle Corrette creates a 3-D model featured on NASA’s website, as his design was selected as the teen winner of the “Future Engineers 3-D Printing Star TrekReplicator Challenge.

Kyle’s brainchild was one of 405 submissions from 30 states. His design was selected by a panel of judges from NASA, the American Society of Mechanical Engineers Foundation and Made In Space, Inc.

Kyle’s success was also featured in Popular Science

In 2016, Kyle was named as semifinalist for a National Merit Scholarship. Finalist will be selected later this year.

When asked about his experiences at Summit, Kyle shared this: “One of Summit’s strengths is the ability to bring out the best within its students; kids can develop their logic skills in Mrs. Yocum’s science classes, while also cultivating their creativity as part of Chris Dorsey’s band. The school environment is geared towards building a stronger all-around person, so that no matter what discipline a student chooses to pursue, they have the ability to utilize more than one intellectual strength in their endeavors – something which I would say is absolutely necessary to be successful.

The faculty also highlights each student’s individual talents, aiding their self-confidence and personal growth. In the last few weeks, I’ve had the pleasure to meet and converse with astronauts, NASA engineers, leaders of nationwide STEM organizations, highly accomplished people within the media, and the CEO of Makerbot, one of today’s most prominent tech companies. If Summit hadn’t helped me to gain the self-assurance needed to be a competitor within this challenge, I would never have had these amazing experiences. In the future, I plan to continue to progress within the engineering field, and be a part of meaningful projects within the technological world. Everyone has to start somewhere- Summit was an excellent place to begin.”  Kyle attended Summit from Kindergarten through 7th grade

Summit alum Ben Fitch chosen to intern for U.S. Senator

ben-fitchSummit proudly shares the success of alumni Ben Fitch (class of 2009), who was chosen to serve as an intern for U.S. Senator Bill Nelson, in Washington D.C.

Ben is a rising senior at the George Washington University pursuing a Bachelors of Science in Economics with a minor in Statistics.

In 2016, Ben was selected for the Atlantic 10 All Academic Team for the second consecutive year.  He currently maintains a 3.87 GPA and expects to graduate Summa Cum Laude in May of 2017.

Ben has long believed that renewable energy and increased efficiency provide an unique economic opportunity at every level of the private sector. His passion is renewable energy, which he has explored through his undergraduate career with a number of environmental, energy, and developmental economics courses.

Ben is also working as a research assistant on a global oil market project, conducting long-term economic analysis of international oil markets under the direction of Professor Frederick Joutz. Responsibilities include data preparation and analysis through programs Excel and E Views, as well as drafting reports.

During the 2015-2016 school year, Ben served as the Varsity Men’s Swimming and Diving Team Captain. Under his leadership, the program broke nine records and was nominated for community service team of the year. Ben was awarded the Men’s Community Service Athlete of the Year Award. This was particularly significant because the George Washington University Athletic Department won the NCAA Division 1 community service national competition.

Ben was also recently elected to the executive board of the Student Athlete Advisory Committee (SAAC) and is serving as the community service chairman. He is designing and executing a strategic plan for community service for every varsity team.

Forward Together: from Head of School, Mark Bistricky

This week the faculty had opportunity to dig more deeply into our goal of equipping our students with both the content knowledge and the 21st century skills they will need for the future.  What are 21st century skills?  They start from a foundation of robust content knowledge.  Building on this base, students are challenged to develop their skills in the areas of creativity and innovation, critical thinking, communication and collaboration.  We call these the 4C’s, and they will be our emphasis this year.  21st century skills also include themes such as global awareness and economic/business/entrepreneurial literacy.  Information, media and technological skills are additional critical components, as are life skills such as initiative, adaptability, cross-cultural skills, productivity and leadership.  Many of these themes are already integrated into Summit’s curriculum, and our goal is to accentuate and expand their emphasis from Preschool through 8th Grade.

You may be wondering how a 21st century classroom looks differently than those we remember from our own days in school.  Here are a few examples:  teachers are learning facilitators, asking challenging questions and assisting students as they work through problems.  Because the learning process is as important as the product, teachers may not provide all the answers, but allow students to push through struggles to find the solutions themselves.  Students often work in teams, applying what they have learned to solving real-world challenges in areas such as the environment, economics, health or global issues.  Students demonstrate learning in a variety of ways– learning portfolios, multidisciplinary projects, and presenting plans and results. Summit’s focus on 21st century education will augment and extend our curriculum content as students develop their ability to apply what they have learned in creative and meaningful ways.

On behalf of the Summit staff, we are grateful to be able to serve your children and partner with you in helping them reach their full potential.

Mark Bistricky, M.Ed.
Head of School

Always moving “Forward Together” – Head of School update

The new school year is just a few days away, and we have been busily preparing for the students’ return.  The past week of teacher professional development and team building has us all energized and ready for an extraordinary school year.  Our theme for the year, Forward Together, will keep us focused on deepening relationships with our students, peers, and families as we continue to build momentum for Summit’s future.

I am very pleased to share the enhancements Summit has made in the past few months.

To continue fortifying our math program, we created two Math Coordinator roles.  Molly Danforth (2nd grade teacher), and Ashley Burbach (4th grade teacher), will be our Math Coordinators for Kindergarten – 2nd and 3rd – 5th grades respectively.  In these roles, Ms. Danforth and Ms. Burbach will provide leadership and coordination to bolster our math program’s rigor, comprehensiveness and enrichment, to meet student learning needs.

Completing the “Fund the Future” projects has been a priority for us this summer. Additional curriculum materials were added, and three campus improvement projects finished, with one more in the works that will be completed very soon.

Hands-on learning in Science has always been a curricular strength at Summit, and with the new FOSS Science kits, Elementary and Middle School Science classes will reach even higher levels of innovative thinking.

In preschool and kindergarten, innovative OSMO technology and iPads will now be augmenting our curriculum. OSMO actively engages students in physics, numeracy, literacy, coding and spatial skills, using brain-based interactive games.

The security improvement project is now complete. This included installing a magnetic secured entry system on the main lobby doors, removing a wall section that obstructed visibility to the side entry door, installing a new door to the nurse’s station to allow for greater visibility and access, and rebuilding the reception desk to improve its security and functionality. These enhancements will make the lobby a more secure entry point.  The secured entry system will be in full use later this fall, restricting entry to the front lobby, and requiring visitors to be buzzed in.

We also made major progress on Phase 1 of the playground improvement projects.

On the elementary / middle school playground, we installed new rubber mulch throughout the playground area, and are nearing the final installation of three shade structures over the playground and bleachers, as well as installing a mister system in these areas.  To provide safe playing surfaces for our students, we re-sodded the field, removed the gravel from around the grass area, and removed the boulders behind the basketball court.

The preschool playground also offers even more to our youngest learners. The fencing around the bike storage was removed, and pavers added near the sidewalk, significantly increasing the area for children to ride bikes and wagons and enjoy.

Thank you once again to our parents and supporters for your generous contributions that enable us to improve the Summit experience for all our students!

I’m looking forward to seeing you at Back to School Night!

Go Sabre Cats!

Mark Bistricky Head of SchoolWarm Regards,
Mark Bistricky
Head of School
Summit School of Ahwatukee

IOWA Assessment Testing Results: Summit School of Ahwatukee Students Score High Nationally

IOWA Assessment Testing Results

Student achievement results are an important way for parents to compare schools and make choices for their child.  We are frequently asked if we have standardized test results to provide evidence that Summit School of Ahwatukee provides a high quality academic program.

We are proud to share summaries of our standardized assessment scores as evidence of Summit students’ high achievement in science, mathematics, reading, and writing.

From 2006-2014, Summit grades 3-8 participated in state-wide AIMS testing and these data consistently indicated 90% to 100% of our students met or exceeded state standards in reading, language arts, mathematics, and science (science was tested only in grades 4 and 8).  In 2015 the AIMS test was discontinued by the State of Arizona.

Beginning with spring of 2015, Summit elected to use the Iowa Assessments  as  it is a well-established, nationally norm-referenced test that measures student learning in alignment with the College and Career Ready Standards, which served as the foundation for our more rigorous Summit Standards.

We proudly share our students’  2015 results for all subtests and composites within the domains of English language arts/reading and mathematics, as they are exceptional.

1) Where does Summit School stand in comparison with other schools nationally?

In every subject and grade level tested, Summit’s performance ranks at or near the top among the national distribution of schools. This can be gauged by examining the national percentile ranks of Summit’s average student standard scores among all schools’ averages in the national norming sample for the Iowa Assessments. These school-normed national percentile ranks are provided by grade and subject, and indicate Summit’s relative standing in a national distribution of schools. For example, all grades at Summit had a national percentile rank of 99 on the English Language Arts (ELA) Total. This means that in all grade levels tested, Summit students collectively performed better in ELA than those in 99 percent of schools. Similarly, on the Math Total scores, Summit students in grades 3-5 and grades 7-8 performed better, on average, than those in 99 percent of schools, and Summit 6th graders performed better than those in 95 percent of schools.

National Percentile Ranks of Summit’s Average Standard Scores among Schools Nationally

Iowa Assessments Administered in Spring 2015

Grade Reading Written Expression Conventions of Writing Vocabulary ELA Total Mathematics Computation Math Total Core Composite
Grade 3 99 96 99 99 99 99 99 99 99
Grade 4 99 99 99 99 99 99 97 99 99
Grade 5 95 98 99 94 99 99 97 99 99
Grade 6 91 96 99 89 99 95 98 95 97
Grade 7 94 99 99 98 99 99 98 99 99
Grade 8 93 97 99 90 99 99 99 99 99

2) How does a typical Summit School student perform in comparison with other students nationally?

A typical Summit student standard score is the average student standard score among Summit students in the named grade level and subject; this average score provides a reasonable estimate of students’ collective performance. The student-normed national percentile ranks shown in the table below indicate where the average Summit student’s score in a particular grade and subject is located in the national distribution of student scores. Nationally, the typical, or average, score for a grade level and subject is the scale score that corresponds to the 50th percentile of the national distribution of student scores. The table below shows that a typical Summit student ranks very well in comparison with the national distribution of students. The average Summit student is at or above the 81st percentile nationally on all ELA, Math, and Core composites.

National Percentile Ranks of Summit’s Average Standard Scores among Students Nationally

Iowa Assessments Administered in Spring 2015

Grade Reading Written Expression Conventions of Writing Vocabulary ELA Total Mathematics Computation Math Total Core Composite
Grade 3 86 81 84 87 87 90 85 90 88
Grade 4 86 84 82 90 92 86 81 87 88
Grade 5 77 80 81 79 87 84 80 85 84
Grade 6 74 79 81 75 85 78 81 81 81
Grade 7 78 82 84 88 90 83 81 85 86
Grade 8 76 79 88 77 88 88 84 89 88

Another way to gauge student performance is to examine grade equivalent scores. Typical Summit students, in all grades and subjects tested, achieve standard scores that are comparable to those of typical students who are several grades higher. Grade equivalent scores are decimal numbers provided by the test publisher that describe a particular standard score’s location on an achievement continuum scaled to reflect the grade level and months at which a typical student earned this same standard score (i.e., the grade level and months at which the same standard score would be at the 50th percentile). For example, the average standard score for Math Total among Summit’s 7th graders corresponds to the Math Total standard score earned by a typical student nationally who is near the end of 11th grade. More specifically, Summit’s reported grade equivalent for Math Total in grade 7 was 11.9, which indicates that the average student in the national sample achieved this scale score when 9 months into 11th grade. All other grade equivalent scores in the table can be interpreted in a similar manner.

Grade Equivalents of Summit’s Average Standard Scores by Grade and Subject

Iowa Assessments Administered in Spring 2015

Grade Reading Written Expression Conventions of Writing Vocabulary ELA Total Mathematics Computation Math Total Core Composite
Grade 3 6.0 5.7 5.5 5.5 5.7 5.7 5.1 5.5 5.5
Grade 4 7.6 8.4 7.1 7.0 7.6 7 6.3 6.8 7.1
Grade 5 7.9 9.4 8.9 7.5 8.6 8.4 7.7 8.2 8.3
Grade 6 9.0 11.1 10.7 8.4 10.0 9.3 9.4 9.3 9.6
Grade 7 11.2 13+ 13+ 11.1 13+ 12.2 11.6 11.9 12.6
Grade 8 13+ 13+ 13+ 11.4 13+ 13+ 13+ 13+ 13+

As we all know, test scores are only one part of the equation supporting the academic excellence at Summit School of Ahwatukee. Summit is a unique, affordable, and high performing private school with data to prove it!

Thank you for continuing to send your children to, or for considering attending  Summit School of Ahwatukee!

Summit School of Ahwatukee Preschool offers eight – $6,000 scholarships

Summit School of Ahwatukee is proud to partner with Quality First, First Things First, and the United Way. Through these programs we can offer eight children a $6,000 scholarship to join our NAEYC, nationally accredited preschool for the 2016-17 school year.

Preschool scholarships are for Summit’s academic school year, August 3, 2016 through May 17th, 2017, for a five day program. Hours are 8am – 3:15pm.

The scholarships are based on family income, with limits set by the state. Qualifying families are responsible to pay the tuition not covered by the scholarship, and the cost of before and after school care, or enrichment classes, if needed.

Learning in Summit’s NAEYC accredited Preschool is fun and enriching. The developmental, experiential, play-based curriculum, utilizes Teaching Strategies Gold objectives for teaching and learning. The curriculum is research-based, developmentally appropriate, and taught by experienced teachers, who nurture cognitive, social and emotional growth. Preschool also includes classes in Art, Spanish, and Music, Tumbling and Library. Preschoolers can range in age from 30 months to 5 years old, but must be fully independent in the bathroom.

Ahwatukee Foothills News voters have named Summit School of Ahwatukee one of the Best Preschools for 8 years in a row! Why? Students gain skills, above and beyond those needed, to thrive in kindergarten. They develop a joy of learning and inquiry.

Summit is a private preschool, elementary and middle school, located in Ahwatukee, on 46th street and Muirwood, just south of Chandler Blvd.

Click here to see if your family qualifies for a scholarship to attend the Best Ahwatukee Preschool_Summit School of Ahwatukee   then click on “Preschool Scholarships through Quality First” or call Summit’s admissions office at 480-403-9506 or to schedule your personal tour.

The importance and success of high quality Science instruction at Summit: Kindergarten – 8th grades

In creating a world-class academic program for 21st Century learners Summit has established a strong reputation for teaching communications, math and science.

  • Communication is the process of expressing our thinking and understanding, including the skills of reading, writing, speaking and listening.
  • Math has been called the language of science and Willis Harman, a noted engineer, social scientist, academic, futurist, writer, and visionary, described Science as “…the cognitive authority of the world.  It’s where we turn for our understanding of reality.”
  • Science is the language of precision and inquiry used around the world.

Science: At Summit we use the Full Option Science System (FOSS) curriculum as the foundation of our teaching.  Science classes are taught in lab settings, beginning in kindergarten and continuing through middle school.  Over the past three years we have been making changes to this core curriculum using ideas from the Next Generation Science Standard (NGSS) which include connections to Science-Technology-Engineering-Math (STEM) practices, crosscutting concepts, disciplinary core ideas, and the Summit Core Standards for English Language Arts and Math.

Science is inherently interesting, and children are natural investigators. Children learn science concepts best by doing science which is why 50% of middle school classes and over 70% of elementary classes focus on experiments; hands-on experiences with objects, organisms, and systems.  Hands-on activities are motivating for students, and they stimulate inquiry, curiosity and collaboration. Students at all grade levels investigate experiment, gather data, organize results, and draw conclusions based on their own actions.

Each year our fourth and eighth graders participate in the AIMS Science tests which are administered to students in public and charter schools across the state.  The AIMS test reports the percentage of students that meet and exceed state standards for science. The table below illustrates that over 90% of Summit students met or exceeded standards for the past six years.

Grade 2010 2011 2012 2013 2014 2015 AVG
4th 100% 100% 98% 91% 92% 97% 96%
8th 96% 100% 100% 100% 100% 93% 98%

We are very proud of our two amazing Science teachers, Andrea Yocum (middle school) and Lori Phillips (kindergarten – grade five), for inspiring our students to learn and love the language of Science.

At Summit we prepare your children for success as the students, workers and citizens of the future.  Thank you for continuing to send your children to Summit School of Ahwatukee.


If Adelle can name an album after her age then Summit is going to re-name January the “Happy 15th Month!”  This month we are celebrating our 15th anniversary!  Décimo quinto cumpleaños feliz!

Summit Parents are Invited! As a way of commemorating this special birthday we would like to invite parents to join our students and staff on Monday, February 1st  at 10:00 a.m. to take a group picture on the play field.  We would like everyone to wear a white-colored top so we can form the number “15.”

Let’s celebrate fifteen great reasons why your children belong at Summit:

  • Community – Students, teachers and parents who care about education and work together to make Summit strong!
  • Great Teachers – Educators who are passionate about inspiring learners and leaders for life!
  • Preschool – The happiest place on earth where child-centered education and life-long learning begins.
  • Elementary – Grades Kindergarten through five are the “wonder years” of learning to learn.
  • Middle School – Academic rigor, social development, study skills, electives, community service and athletics prepare well-rounded young adults for success in high School, college and beyond.
  • A Rich Variety of Special Curricula – Science, Spanish, Art, Music, Physical Education, Technology, and Library, designed to enhance our comprehensive liberal arts approach to learning.
  • Learning – Critical thinking, creativity, problem solving, collaboration, presentation skills and communication are the 21st century skills that we teach, what  your children need to thrive and what they deserve from their education.
  • Safety – Summit provides the physical, social, emotional, and psychological safety that children need to be confident and unique.
  • Character – Summit’s Character and Respect Education (CARE) program combines character education and positive discipline in order to teach and support the behaviors that create a safe and healthy learning environment, and strengthen social and academic skills and confidence.
  • Leadership – Providing opportunities to cultivate the leader within each child is a priority at Summit.
  • Diversity – Our community values and celebrates our differences.  We need more talented kids and diverse families to join us!
  • Technology –  Teacher and student use of tech tools provides new opportunities for teaching, learning and creating.
  • Affordable – Keeping tuition reasonable, offering scholarship assistance, and Arizona’s prívate School tax credit helps families stay at Summit.  Can you afford not to have your child receive a high quality Summit education?
  • Happiness & Success & High Achievement in every experience, everyday in every classroom.

Thank you to our parents for sending your children to Summit!

Warmest regards,

Patrick O’Brien, Head of School

Summit School of Ahwatukee

Community Invitation to attend an inspiring documentary film “Beyond Measure”: dynamic learning environments that inspire

Summit School of Ahwatukee invites Summit families, friends and the community to experience the inspiring feature-length documentary film “Beyond Measure” on Thursday, January 14th from 6:30 pm – 8:30 pm on the Summit School of Ahwatukee campus.

View a Trailer of Beyond Measure

The event is hosted by the school free of charge, however, registration is required. Click here to reserve a seat.

Six years after 2010’s award-winning movie “Race to Nowhere” rose to national prominence, Reel Link Films brings the inspiring film, “Beyond Measure” which shines a light on tenacious and cutting-edge alternatives to the stifling, high-pressure education system presented in its predecessor film.

Where many past documentaries have dwelled on the education crisis and the policies to blame, “Beyond Measure” follows public schools across the country as they take matters into their own hands, innovating from the inside. By spotlighting success stories, the film shows that it is possible to rise above America’s fixation on achievement tests and build a richer, deeper, more empowering, and student-centered education culture from the ground up. The Summit School of Ahwatukee is very proud to be able to feature this documentary.

“Beyond Measure is a road map for communities looking to put true learning at the forefront of their school experience,” says Timothy Quinn, Former President, Princeton Board of Education. “It demonstrates what students, educators and parents can achieve when they look beyond merely improving upon an outdated model of instruction to creating dynamic learning environments where every student can thrive.”

Notable people featured in the film include Sir Ken Robinson (international education expert and presenter of the most watched TED talk of all time), Linda Darling-Hammond (education advisor for President Obama’s 2008 campaign), and bestselling author Daniel Pink (Drive and A Whole New Mind). The film team includes Oscar-winning editor Jeffrey Friedman (Common Threads) and Executive Producer Lynda Weinman, founder of The film coincides with the release of director Vicki Abeles’ new book, also titled “Beyond Measure”. The book, published by Simon and Schuster, examines cultural and educational symptoms of the academic rat race and suggests steps big and small that readers can take to reclaim their schools and children’s lives. Called America’s “wake-up call” by Maria Shriver and praised by New York Times bestselling author Brigid Schulte as “one of the most important books of the early 21st century,” “Beyond Measure” is now available in book stores.

Reserve your complimentary seats today! Click here to reserve a seat.