I am on spring break this week and have had the wonderful opportunity to relax a bit and take some time to reflect on my classroom. I've been reviewing student achievement data, evaluating their progress toward goals, and making plans for the remainder of the school year. As part of this process, I have also spent some time looking over my students' portfolios. Each child's portfolio is divided into four domains (social/emotional, physical, cognitive, and language) and contains artifacts (work samples, pictures, and notes) that demonstrate their development in that domain. I use the materials in each child's portfolios as a way to assess their progress and determine individualized goals. I also share the portfolios with families during parent-teacher conferences, and send them home with students at the end of the year.
I absolutely love looking back through my students' portfolios! Not only is it an authentic way to gauge their progress, but it also reminds me of just how much they have learned in school. I'll walk you through some pieces of Julia's writing as an example.
August, 2008. Julia drew this self-portrait on the first day of school. She added some details such as feet and hair, but neglected to add arms and a nose. Julia spent several minutes laboring over her first name; several of the letters were crowded, but they were all legible (her name has since been removed for privacy purposes).
November, 2008. Julia was very interested in the presidential election this year! We talked about what elections were, learned a bit about each candidate, and then held a mock election in our classroom. Julia wrote this piece the day after the election. She included many more details than in her August portrait, and also demonstrated an understanding of perspective – she explained to me that she drew Barack Obama significantly larger than John McCain because he had won. Julia writes letter strings for each word in her sentence, but does not yet associate specific letters with the sounds that she hears in words.
December, 2008. Julia wrote this piece completely independently. She demonstrated an increasing attention to detail by using a different color crayon to make the snow, and she drew simple figures to represent herself and her mother. Julia devoted the majority of her paper to writing, which displays an increased understanding that she can use writing to convey her ideas. She still uses letter strings and does not associate letter shapes with the sounds in words.
January, 2009. In January, Julia began using inventive spelling to write unfamiliar words. I helped her “stretch out” the words to hear all of the sounds, and she wrote what she heard. She knew how to read the word “is” and was able to recall that knowledge for her writing. Julia's ability to correctly identify all the sounds – including the vowel – in “big” was a tremendous accomplishment.
March, 2009. Prior to writing this piece, Julia found a picture of Barack Obama with his arms folded across his desk and announced that it looked like he was “hugging himself.” From there, she decided to draw a picture of the entire Obama family hugging themselves. She was careful to draw their arms wrapped around their bodies, and drew a line for the desk under each of them. Julia was extremely interested in writing about her story; she spent over 20 minutes writing Barack Obama’s name and sounding out the rest of the words in her sentence. I sat with her the whole time, but did not give her any assistance with stretching out the words or identifying letter sounds (as a side note, when she was stretching out “hugging,” she pronounced it “hucking”, hence the “HC” that she wrote). Julia started to lose patience by the last few words in the sentence, but overall did a wonderful job and was extremely proud of her work.
Julia has worked hard on her writing this year and has made tremendous progress. For the last two months of school, Julia will focus on writing a beginning, middle, and ending sound for each word, as well as continuing to learn and use sight words in her writing. We will continue to add work to her portfolio to document and celebrate her progress!
As a pre-k teacher, I've always been a little bit thankful that my students don't take high stakes tests. I know that my students learn a tremendous amount of information in school, but I also know that a formal assessment is not always the best way to measure what they know. I rely heavily on observational assessment to track my students' progress and guide my instruction. My observational assessments are mostly in the form of daily anecdotal notes -- I write down brief, objective accounts of what my students do and then at the end of the day I reflect on my notes, correlate them with my standards, write "next steps" for individual children and/or my whole class, and use all of this information to inform my instruction for the upcoming days and weeks. This process takes time, but I've found that it really helps me provide differentiated instruction that is tailored to the needs of each of my students.
I believe firmly that assessments of any kind should be used to guide instruction at all grade levels. When teachers feel comfortable with their assessments and they are an accurate measure of students' abilities, they can be an invaluable tool in the classroom. However, when assessment is structured inappropriately or administered in an unfamiliar manner, it can yield inaccurate results. For this reason, I worry tremendously about relying on standardized tests in early childhood classrooms. They are not the most accurate way to gather data about what a pre-k, kindergarten, or even early elementary student knows, and inaccurate data is not helpful to the teacher. Because I feel so passionately about this issue, I was a bit skeptical when I read the New York Times article explaining New York City's new yearlong pilot program to administer standardized tests to children in kindergarten through second grade. I laud the city for recognizing, and seeking to quantify, the hard work that goes into early childhood classrooms, but I question their methods. Is standardized testing really the best way to go about that? Wouldn't it be better to give early childhood teachers -- who teach not only math and literacy, but also social skills, problem solving, creative thinking, emotional regulation, approaches to learning, and more -- a more holistic option for assessment? I read recently in the Atlanta Journal-Constitution blog, Get Schooled, that Georgia seems to be grappling with this same issue. I will be curious to read more about how their new assessment initiative, GKIDS (Georgia Kindergarten Inventory of Developing Skills), works for students and teachers.
Don't get me wrong, formal assessments can -- and arguably should -- be one component of an assessment plan in pre-k through second grade classrooms. I complete a brief formal assessment with each of my students once a month and more comprehensive assessment once a quarter, simply to gauge their progress on more formal academic skills. This data is invaluable as I plan my small groups and figure out new ways to teach material that my students are finding challenging. But I do not consider these assessments in isolation; I take my anecdotal notes, as well as my students' portfolios, into account when I am analyzing the data from these assessments. Together, I feel like all three sources of information give me a holistic view of where my students are and where they should be going next. I worry that if a district moves to gauge the success of its early childhood programs purely through standardized tests, that they will fail to see so much of the progress made by these young students.
Recently, Inside Pre-K co-blogger Karissa wrote about how quickly summer vacation is approaching for her and her students. By the time this article is posted, her community-based center will officially be on vacation.
However, my pre-k classroom, embedded within a public school system, follows the regular K-12 school calendar. Summer fun won't come until our last day of class, this year it falls on June 5th. And we've got quite a ways to go and myriad of assessments to complete before we get there. For this reason, many teachers in my district refer to the final six to nine weeks of school as “crunch time.”
During our final weeks together, I have to assess each student one-on-one in a multitude of areas. Here’s a breakdown of our testing:
CIRCLE testing on palm pilot: Assesses 7 areas of phonemic awareness, all letters -- uppercase and lowercase, letter sounds, vocabulary, nine concepts of print, and writing assessment. Each question must be administered one-on-one.
PMI- Primary Math Inventory: 3 pages of math assessment that must be administered one-on-one. Questions can only be asked one at a time to each student (for example, if you start with student A and ask question number 1, then you have to move to student B and ask question 1, when you get to the last student you can then move to question number 2).
DRA- Diagnostic Reading Assessment: Students reading levels are assessed, this test is also administered one-on-one. The more the student knows, the longer the test takes.
Report card testing: Each child must also be assessed on report card skills not covered in the aforementioned tests, such as oral counting, name writing, color identification, number recognition etc. All of this testing is also done one-on-one.
Now you’re probably wondering when I have time to teach if I’m doing all this one-on-one testing. The answer is, I don’t! It’s just not physically possible to do all the required testing and teach a classroom of 22 four year olds simultaneously.
Add that to the mix of numerous paperwork deadlines, meetings, registering pre-k students for next year, not to mention the Cinco de Mayo celebrations, class pictures, Mother’s Day, and end-of-year celebrations that come with the territory. It’s no wonder that teacher appreciation days come during the first week of May. It's a bribe so we will make it through until the end of the year!
Karissa also wrote about her concerns regarding her student’s lengthy summer vacation. We’re fortunate that in our district all ELL (English Language Learner) pre-k students are eligible to attend a free summer school program where they will continue to develop their oral language skills, should their parents agree to enroll them. The program Learning the Language is offered from June 11th – July 11th, Monday through Friday, 7:30 a.m.-1:30 p.m. and includes free bussing and meals.
But unfortunately, not all students qualify for Learning the Language, so I send each of them home with a "summer fun" kit I've devised for them and their parents. It includes:
A letter to parents explaining the content of the kit.
A Map, the address and the phone number to the local library, as well as directions on how to obtain a library card.
A Calendar with dates and times for story hour at the local library as well as dates of special local events such as discount days at the zoo.
A reproducible nursery rhyme booklet, enabling students to practice their nursery rhymes over the summer.
A book list of the top 100 books for preschoolers to check out at the library. Titles include classics such as: The Very Hungry Caterpillar, Goodnight Moon, Brown Bear, Brown Bear What Do You See?, The Rainbow Fish, The Snowy Day, Corduroy, and The Runaway Bunny.
An Activity-a-Day calendar, like this one from Preschool Express. I generally make up my own activities for July and August as they're not published in advance.
A number booklet comprised of 20 sheets of paper stapled together with a number and the words to each of our number songs on each page. The students practice recognizing their numbers by singing the song on each page. The words are so the parents can read and sing along as well.
An alphabet chart- so students can practice singing their letter sound songs or use it when they write.
A Blank booklet so students can “journal” or write about their summer experiences.
One free treat coupon from local ice cream shop. If you ask nicely, most places will give you free treat coupons to give to your students.
One Scholastic book: I use my bonus points and buy each child one book so they will have a book at home to read. Scholastic offers one 95-cent book each month.
Information about our summer daycare program for those students that don’t qualify for our ELL summer program. Our district offers summer daycare for students ages 5 and up at very affordable rates. The program is staffed and run by teachers.
A Brown paper bag with leftover crayons, markers, pencils, construction paper, glue, scissors, etc. so students can create and practice writing during the summer months.
A Pre-addressed postcard so students can send me a postcard if they travel, or just for fun!
(Note to self: Add “make summer fun packets” to already lengthy crunch time to-do list!)
As my children prepare for pre-k graduation and the move to kindergarten, I cannot help but wonder about their futures. Will Karen become a doctor? Will Awana have the chance to choose between being a ballerina or a doctor? Will Aniyah’s behavior regress and threaten her academic progress?
I have worked to introduce school to my class as an exciting and fun place where they can make friends, learn, and be successful. Anecdotal evidence and various forms of assessments suggest that my students have already started to realize their potential and are on the path toward high achievement in school and beyond. Parents’ strong attendance at our class events and interest in enriching their child’s learning over the summer also bode well for my students’ academic prospects.
Yet my students still have many years during which their attitudes toward school, themselves, and their peers could change for the worse. Most of them will continue to live in unsafe neighborhoods and struggling school districts. The research showing that students in inner city schools who have had high-quality pre-k do better than those who have not gives me hope. I know that my instruction in the classroom and the active support of family members during this critical stage in children’s development will have life-long benefits. I also believe innovative changes are occurring in the K-12 system, many of them spearheaded by my fellow Teach For America alums. But, on an individual level, it is still hard to predict how high each child in my class will build on the pre-k foundation he or she gained this year.
My time in the classroom has been, above all, about providing the kinds of opportunities for my students that they deserve. The playing field is not level, even for three and four year olds. High-quality pre-k teachers alone cannot ensure that a child won’t face educational and societal inequities down the road, but the vibrant and challenging learning environments we provide are the first step toward giving all children an equal chance at success.
The results are in! After nine months of instructing and assessing in various forms, I have comprehensive data on my students’ growth in literacy. How did they do? Each child achieved an average of 80 percent or better on a wide range of literacy assessments!
Because pre-k children often don’t show you everything they know or can do with one type of assessment, I used two types of assessments and incorporated all the objectives from each into my calculations. One type were performance-based assessments that include anecdotes and work samples collected while the children play and interact throughout the day. I supplemented these with standardized assessments administered by me to each child to test skills like letter identification and rhyming words.
Overall, 10 children out of 14 achieved 100 percent on the standardized assessments and 9 achieved 90 percent or higher on the performance-based assessments. I’m especially impressed by the individual gains made by the children, such as:
Awana, who often struggled to move forward in letter identification and listening skills, in the end achieved 85 percent on the standardized assessments and 83 percent on the performance-based assessments.
Tanasia, who started off the year too shy to even come to school the first day, achieved 100 percent mastery on the standardized assessments and 88 percent on the performance-based assessments.
I realize some in the early childhood community are skeptical of the extent to which standardized assessments are developmentally appropriate. I agree that such tests could potentially produce inaccurate results, given the young age of my students. I try to reduce the potential for inaccuracies by identifying the assessments as “fun games to play with the teacher,” which can help the children feel more at ease and less stressed by the experience. I ask students if they would like to play with me, and many times they jump at the chance to spend some one-on-one time with the teacher, especially since they get to press the “easy” button (thanks, Staples) when they finish. I remember Tyrique expressing sadness that he could not play our “game” a second time.
Consistency between the scores given by the two types of assessments suggests that these techniques can help produce more reliable results from the standardized variety. The results also show general consistency between the two kinds of assessments.
Standardized assessments are necessary in my case because the kindergarten teachers who will have my students next year use them and not performance-based assessments. This begs the question, of course, why are kindergarten teachers not using performance-based assessments? I think they should use some combination of the two, at a minimum, to gain a more comprehensive understanding of their students’ strengths and needs.
I am very proud of my students’ growth and know that the combined efforts of Ms. Morrison, Ms. Bimba, each child’s family, and me contributed to their success.
No, I’m not digging out from an anomalous May snowstorm, but I do feel quite overwhelmed by end-of-the-year paperwork. Like other teachers, I have mostly assessments and annual school wide forms to complete this time of year. My pre-k program has additional sets of the former handed down by the district and the state.
The state mandates the use of ELAS, a performance-based assessment system focusing on six language arts/literacy expectations. Normally, I would not voice concerns about ELAS; despite the tedious paperwork involved, it has been very helpful as a tool for targeting the strengths and weaknesses of my students. My concern is this: the collection period for ELAS ends in June, but my support person from the Office of Early Childhood has insisted we hand in the paperwork nearly a month earlier. Why? My guess is because other pre-k sites have been delinquent in handing in paperwork on time in the past.
The problem with this creative revision of the ELAS timetable is threefold:
1. This time of year many pre-k students start to demonstrate remarkable academic progress, especially those who entered pre-k younger than the other students. If we stop collecting anecdotes and work samples from those children in mid-May (to ensure we can finish the paperwork before Memorial Day), we may fail to capture this growth and, thereby, provide the state, our schools, and parents with inaccurate results.
2. We are also responsible for a social skill checklist and the district’s experimental assessment forms (requiring the collection of anecdotes covering over 30 expectations) in the same time frame. Now, I am all for an Amazing Race-style challenge for teachers to balance three assessment systems, simultaneously, while also instructing students. But, if we are really in early childhood for the children and not just to satisfy the sadistic cravings of paperwork hungry bureaucrats, we should think realistically about how our demands on teachers affect their ability to perform in the classroom.
3. I have always handed in paperwork on time along with additional individualized action plans for my students. If the folks at the Office of Early Childhood were as organized and well managed as they should be, they would put additional pressure only on those teachers who need it. In a sense, they should differentiate their approach to employees in the same way that they require teachers to differentiate our approach for the varying needs of our students.
Well, I have to go now…because this paperwork is not going to fill out itself.
"Choice Time" is a critical time for pre-k students to grow academically and socially. During choice time in my classroom, the children can go to any of ten interest areas that provide a wide range of opportunities for learning through hands-on, experiential activities. Each area has labeled materials and books pertinent to that area (e.g., Blocks has books about building and transportation; Dramatic Play has cooking and career books; Art has books of art with famous paintings). These materials help teach how literacy permeates all areas of life.
Here is a glimpse into choice time in Pre-k 114:
Blocks Area – Quite logically, the blocks area contains different types of blocks - wooden and plastic, large and small. In addition, we have worker hats, transportation toys, animal toys, and people figurines. We put illustrated labels on all toys to help make children aware of letters and words and how we use print in a functional way. When this photo was taken David and Samar were trying to construct a tunnel through which the car could pass. I asked them to recall what the tunnel looked like in the book we read. They found the book and discovered they were missing the top part of the tunnel. They also learned about cause and effect when they pushed a car through their construction project too fast and the tall sides fell in.
Dramatic Play – This area includes everything from plastic fruit to a medical kit. The children take on pretend roles ranging from mommies and daddies to doctors and waiters. We expose them to different functions of print by including real maps, menus, recipe books, and bus schedules to support their play. I often engage students with open ended questions that build their vocabulary and target their individual needs. In the "doctor's office," I asked Doctor Tyrique whether he was going to fill out a prescription for my medicine. He responded by grabbing a notepad and writing my name. We worked on listening for the sounds in Pappas and connecting those sound to letters. In the photo, Tyrone is writing a grocery list for his family.
Art Area – This area includes a wide range of materials intended to spark the children's creativity and invite constructive and open-ended dialogue between the teacher and student. Rather than tell children exactly what to make, we give them tools such as water color paint, paint markers, hard and soft clay, and collage materials. We provide an example, and then encourage them to express themselves with their tools. The symmetrical paintings shown on the back wall in the photo exemplify this process. I showed students how to paint on one side and make a mirror image on the other side by folding their paper. They then made their own paintings and, in the process, learned about symmetry.
These examples reveal the successful results of learning through play, or what I would deem constructive play. Teachers create interest areas with opportunities for children to explore and grow in various content areas. They then use choice time as a chance to target individual student needs identified through ongoing, performance-based assessments, and analysis. As children explore and discover, teachers can seize teachable moments and move their students forward.
[This entry was contributed by guest blogger Marissa Castro Mikoy, the director of the Universal Pre-Kindergarten Incentive Program at CentroNía, an educational community-based organization in Washington, D.C.]
The birds are chirping, trees are budding, and flowers are blooming -- Happy Spring everyone!
I appreciate the opportunity to fill in for Sophia this week, provide a window into the pre-k program I direct, and read your comments. I thought I'd focus on the activities that make CentroNía's practices unique to the early childhood education field, the importance of high-quality bilingual education, and how our program supports children and families in the transition to kindergarten.
CentroNía is in the heart of a diverse and vibrant neighborhood in Northwest DC. Our classrooms are filled with children of families who speak Amharic, Spanish, English and Vietnamese. To support our children's native language and culture, we engage in a dual language model of instruction in Spanish and English. Every classroom is outfitted with a designated English speaking teacher and a designated Spanish speaking teacher. All learning centers are labeled in Spanish and English print, and passersby in the hall quickly notice the children engaged in conversations with each other in both languages. We aim to provide a safe environment where the children can express themselves in their language of choice while also having the opportunity to speak in the language they are learning.
Research has repeatedly demonstrated that second language acquisition is successful if children are given the opportunity to develop a strong foundation in their native language. (This letter to the editor in The Washington Post sums up why bilingual education, contrary to the assertions of folks like Newt Gingrich, is effective in teaching children English.) We are beginning to look at how to measure second language acquisition by administering the Brigance Screening in both languages through a baseline and post assessment. But we already have many anecdotes showing our children's progess -- here is one.
Four-year-old Diana entered our pre-k program with knowledge of Russian and English. At the beginning, Mom was concerned that Diana might get "confused" learning a third language. My suggestion was to see how the first couple of weeks went and to observe her comfort level in communicating with her classmates. Fast forward nine months and I can tell you that Diana is singing in Spanish, learning to write her name and identify letters in English, and increasing her Russian vocabulary with her family. Her father stopped by my office one day to say, "Marissa, who knew we had a genius on our hands?" I share this story in part to say that, if children are exposed to an additional language in an intentional and research-based model, we would see many more "geniuses" entering kindergarten.
I strongly believe that our success comes from the support and celebration of a family's linguistic and cultural differences. We bring these differences into the center and make them part of the classroom environment. I hope the benefits of supporting English language learners are seen by more and more of our community stakeholders. It is only in this way we will be begin to see a stronger public education system.
Recent debate over Head Start’s National Reporting System got me thinking about the challenges of assessing what three and four year olds know and what they have learned from their pre-k teachers. Early Stories sums up the NRS debate with some great examples.
Not being a Head Start teacher myself, I have never administered the NRS. I am required, however, to use the Brigance screening in the beginning of each school year to identify developmental delays. While some of the sections are helpful (e.g., following two and three step directions; fine motor and gross motor evaluations), many of the questions seem to measure a child’s exposure to certain words and objects rather than development. For example, in one section Brigance asks the child to identify a picture of a tractor. I personally fail to see how the inability of a four year old from the inner city to identify a tractor indicates any sort of delay in her development. The test also requires children to identify several body parts including the jaw and ankle, a stretch for any four year old in my opinion.
I think my ideal pre-k assessment tool would breakdown the four areas of child development (i.e., social/emotional; physical; cognitive; and language) and be able to measure each of those components regardless of a child’s background. Unlike the Brigance screening, such an assessment may have to be partially or entirely performance-based since a child may not reveal the full extent of his problem-solving or language skills in a single one-to-one interaction at the start of the year. A teacher can, however, observe a child within the context of play with materials and areas the child has chosen.
Creative Curriculum’s assessment system is entirely performance-based, uses the “developmental continuum” to assess all four areas of development, and is both the most comprehensive and least biased assessment I have seen. While it can be quite helpful in providing information about your students, it is not necessarily the most accessible data for kindergarten teachers to use the following year, so I do think the more traditional assessments (e.g., letter identification, book handling checklist) have a role to play.
“Your students’ growth will be your growth”: wise words from one of my three greatest role models as a teacher, an older Teach For America teacher who taught in my district.
Each year, as we begin to discuss signs of spring in the sprouting flowers and leaves outside, I can also notice my students’ academic growth, particularly in basic literacy skills. As I observe them throughout the day, I see how the individual action plans I created and implemented facilitated their achievement. The anecdotal notes and work samples in their portfolios provided insights into my students’ strengths and weaknesses. I then used that data to develop teaching plans for both me and the students’ families to follow. While I started using these plans last year, more practice with anecdotal note taking and familiarity with analyzing skill deficits using our performance based assessments strengthened my ability to target and address student needs this year. The success of this valuable teaching tool makes me feel like I have really improved as an instructional leader.
Here are just a few examples of their growth:
• David’s anecdotes and work samples from the fall revealed the need to work on listening skills (e.g., incorporating ideas from discussions into play). Consequently, I linked my questions before and during choice time to ideas we had discussed during circle time. I also brought in more topics that seemed to appeal to him, such as transportation and animals. David recently approached me with a toy airplane and his name card and said, “Look Ms. Pappas, the airplane ‘bout to take off on the runway. It can’t just go straight up, it has to go like this,” as he rolled to airplane on the flat surface and then had it take off. • Tyrone’s target areas in the fall included relating stories to his own life. So, I worked on this skill with Tyrone in whole-group and small-group instruction, modeling how to connect stories to our own experiences. For example, during a read aloud of Cat in the Hat, I might relate to the experience of the children sitting at home on a rainy day by saying, “I remember when it was pouring rain and I couldn’t go outside to play tag with my friends. I felt sad.” I also designed activities around comparing and contrasting characters’ lives with our own. Tyrone’s recent literary insights include: “I took a long train like the one in the book to New York.” and “I went to the zoo too. We saw an elephant.” • In the fall, Fuquan was strong in letter identification and was starting to identify beginning sounds in words. From that foundation, he needed to work on making letter-sound connections and using that skill to write words. My plan for him included playing letter-sound sorting games in small group, discussing sounds in words one on one during activities like journal time, and singing songs about letter sounds during transition times. Fuquan is now labeling his drawings with the letters that match the pictures and can write short sentences with some guidance from me.
I look forward to using my improved planning skills to make the most of the precious few months left with my students this school year.
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Blocks Area – Quite logically, the blocks area contains different types of blocks - wooden and plastic, large and small. In addition, we have worker hats, transportation toys, animal toys, and people figurines. We put illustrated labels on all toys to help make children aware of letters and words and how we use print in a functional way. When this photo was taken David and Samar were trying to construct a tunnel through which the car could pass. I asked them to recall what the tunnel looked like in the book we read. They found the book and discovered they were missing the top part of the tunnel. They also learned about cause and effect when they pushed a car through their construction project too fast and the tall sides fell in.
Dramatic Play – This area includes everything from plastic fruit to a medical kit. The children take on pretend roles ranging from mommies and daddies to doctors and waiters. We expose them to different functions of print by including real maps, menus, recipe books, and bus schedules to support their play. I often engage students with open ended questions that build their vocabulary and target their individual needs. In the "doctor's office," I asked Doctor Tyrique whether he was going to fill out a prescription for my medicine. He responded by grabbing a notepad and writing my name. We worked on listening for the sounds in Pappas and connecting those sound to letters. In the photo, Tyrone is writing a grocery list for his family.
Art Area – This area includes a wide range of materials intended to spark the children's creativity and invite constructive and open-ended dialogue between the teacher and student. Rather than tell children exactly what to make, we give them tools such as water color paint, paint markers, hard and soft clay, and collage materials. We provide an example, and then encourage them to express themselves with their tools. The symmetrical paintings shown on the back wall in the photo exemplify this process. I showed students how to paint on one side and make a mirror image on the other side by folding their paper. They then made their own paintings and, in the process, learned about symmetry.
