The Magic of Patterns: How Young Children Express Repeating Patterns with Objects, Pictures, Sounds, and Movements

The Virginia Standards of Learning curriculum Framework outlines various methods of expressing repeating patterns, encompassing objects, pictures, sounds, and movements. However, making thoughtful choices is crucial to ensure inclusive and practical learning experiences. This post will discuss attributes that express repeating patterns and highlight some important considerations. Let's dive into the attributes and address some challenges regarding a few of them.

1. Colors: While colors can be visually appealing, it's important to consider individuals with color vision deficiencies. Approximately 1 out of 12 males of Northern European ancestry have a color vision deficiency gene. (Females can also have color vision deficiency although not nearly as common as observed in males.) To accommodate all learners, avoid relying solely on color distinctions. Instead, use visually distinct objects with different colors, such as red cubes and green bear counters to represent the pattern.

2. Sizes: When using proportions to express patterns, ensure the differences are easily discernible. Unless there is a significant difference, avoid using small/medium or large/medium, as children may miscalculate these sizes and will create a mismatched pattern. Instead, opt for noticeable differences like small and large. 

Use attributes such as width or thickness. One engaging activity is to use paintbrushes with varying bristle widths. During circle time, line up a row of paintbrushes, alternating between wide and thin bristle brushes while reciting the pattern.

Then provide each child with a thick and a thin bristle paintbrush, allowing them to create an ABABAB painted pattern with alternating strokes of different widths on paper. Display the work on a bulletin board for children to observe.

3. Geometric Figures: Use geometric figures for expressing patterns, but be mindful of potential confusion, especially among young children. Squares and rectangles, for instance, can be easily mixed up. To avoid this, consider using shapes like squares and circles that are less likely to be confused.

4. Orientation in Space: Orientation arrangements offer a hands-on approach to patterns without requiring additional materials. Select six student volunteers to line up against a wall. Have every other child face the wall while the others face the front of the class. Recite the pattern as "Front, back, front, back, front, back". Then invite two more students to join the volunteers and extend the pattern. This activity allows students to perceive the pattern based on orientation. Develop the orientation in space feature with objects on desks or tables, having students position objects as right side up and upside down.

Create repeating patterns using orientation cards and objects.

5. Movements: Using movements is a convenient approach to introducing repeating patterns. The "stand/sit" ABABAB pattern, requiring only chairs, is particularly engaging. Students can vocalize the actions as they perform them, reinforcing the pattern through verbalization.

6. Sounds: Engaging students with sounds adds an auditory dimension to pattern recognition. However, it's crucial to consider the abilities and limitations of young children. For example, snapping fingers may be challenging for many kindergartners. To an ensure inclusive learning situation, substitute the "snap" with a "pat". Model hands on a table or desk, followed by a clap. this modification allows for a clear sound pattern within the ABABAB sequence.

7. Numerical Sequences: It's important to distinguish between numerical sequences and growing patterns. Growing patterns increase predictably. Let's explore an example of a numerical sequence demonstrating a repeating pattern. The example below uses real numbers to create the pattern instead of symbols.

8. Pictures: It is essential to remember that the Virginia Standards of Learning Curriculum Framework encourages the use of objects, pictures, sounds, and movements to express repeating patterns. You can develop diverse and engaging classroom activities by incorporating the attributes suggested to represent patterns. Using photographic picture cards is a fantastic way to enhance your repeating patterns activities. Manipulate photographic picture cards to provide visual representations that create patterns. They are effective in teaching patterning concepts, and they integrate with other subjects. For example, if you are studying animal groups in a science unit, you can use picture cards representing an ABABAB repeating pattern with mammals and birds. You can create an ABCABCABC pattern with mammals, birds, and fish. This cross-curricular approach adds depth and relevance to your lessons while reinforcing the concept of repeating patterns.

A well-rounded approach to expressing repeating patterns ensures inclusiveness, engagement, and stimulating learning experiences. By expanding their repertoire of patterns, students will develop a deeper understanding of this mathematical concept.

Lastly, it's important to note that while the ABABAB pattern is the first one to teach in kindergarten, it is not the only one to learn. In my upcoming post I will introduce five types of repeating patterns aligned with kindergarten standards. Additionally, I will provide a helpful rubric to evaluate student progress and success in working with repeating patterns. Stay tuned for the next installment, where we'll explore more exciting patterns and assessment strategies!  

If you missed the previous post, view it here: Kindergarten Repeating Patterns Objective: Unveiling the Five Components

 

© 2023 Molly McMahon, Lessons by Molly

(References: 1.  Virginia Department of Education, Standards of Learning, 2016. 2. National Institute of Health, National Eye Institute, Color Blindness 2019)

  

 

 

Kindergarten Repeating Patterns Objective: Unveiling the Five Components

Introduction: This blog post delves into a kindergarten math standard focusing on repeating patterns. This standard is from the state of Virginia. I break down the objective into five distinct components and provide examples. Let's explore each piece and its practical application in the classroom.

Breaking Down the Objective: The kindergarten math standard reads: "The student will identify, describe, extend, create, and transfer repeating patterns." To simplify and clarify, I reframe the objective as follows:

1.  Identify repeating patterns.
2.  Describe repeating patterns.
3.  Extend repeating patterns.
4.  Create repeating patterns.
5.  Transfer repeating patterns.

Component Examplars: To better understand each component, I provide concrete examples for clarity:

1. Identify: Presenting two rows of objects, such as bear counters and shapes; the student correctly identifies the row with the ABABAB pattern. 

 

 

2. Describe: The student describes the ABABAB pattern of bear counters and distinguishes it from the ABCABC pattern of shapes.

 

3. Extend: Extending the existing pattern, the student adds more bears or shapes in the appropriate sequence to continue the repeating pattern.  

 

4. Create: Using paint daubers, the student creates the ABABAB pattern by alternating between green and pink colors. 

 

5. Transfer: The student replicates an existing pattern with different objects or mediums, such as recreating the ABABAB pattern shown with the squares and triangles and then using large and small circles.

 

Conclusion: Teaching repeating patterns in kindergarten allows educators to engage students at the highest level of cognitive processes, as aligned with Bloom's Revised Taxonomy (2001):  Remember, Understand, Apply, Analyze, Evaluate, and Create. The five components of the math standard (identify, describe, extend, create, and transfer) encompass five of these six cognitive levels, enabling educators to deliver instruction that encourages critical thinking and creativity. This approach empowers students to reach the pinnacle of Bloom's Taxonomy by creating original patterns.

Stay tuned for my next blog post. I will delve into the five types of repeating patterns introduced in kindergarten, emphasize the key attributes to prioritize when teaching repeating patterns and shed light on things to avoid. Read it here: The Magic of Patterns: How Young Children Express Repeating Patterns with Objects, Pictures, Sounds, and Movements

 

 © 2023 Molly McMahon, Lessons by Molly

 

(References: 1.  Virginia Department of Education, Standards of Learning, 2016. 2. A Taxonomy for Learning, Teaching and Assessing; A Revision of Bloom's Taxonomy of Educational Objectives, Lorin Anderson, David Krathwohl, Peter Airasian, Kathleen Cruikshan, Richard Mayer, Paul Pintrich, James Raths, Merlin Wittrock.)
                                  

Ensuring Fidelity: The Key to an Effective Assessment in Kindergarten Mathematics

This blog post will examine three fictitious examples of teachers checking students' understanding of a math standard highlighting the importance of adhering to the standard's guidelines. Can you identify the teacher who accurately administered the assessment to align fully with the intended standard shown below?

"The student, given no more than three sets, each set containing 10 or fewer concrete objects, will compare and describe one set as having more, fewer, or the same number of objects as the other set or sets."

The three educators mentioned below plan to assess the concepts of "more" with their students. They know that conducting multiple problems with different number combinations is essential to verify the students' understanding of "more."  For this blog post, each scenario offers one problem. Fewer and same are omitted in these scenarios, but the underlying principles remain relevant in each case.

Mrs. Seegar's Approach

Mrs. Seegar evaluated her students' comprehension of comparing two sets by employing images of butterfly groups in her assessment. She presented two picture cards, one with six butterflies and the other with two butterflies. Some students correctly identified the group with six butterflies as having more. How did Mrs. Seegar perform with her assessment? Mrs. Seegar stayed within the number range, but her assessment fails to meet the standard's requirements since it utilizes images on picture cards instead of concrete objects.

Mr. Bishop's Approach

Similarly, Mr. Bishop evaluated his students' understanding of comparing two sets of numbers and their proficiency in describing the larger quantity as "more". He used cubes as concrete objects. He presents two groups of cubes, one with five and the other with seventeen cubes. Some students correctly identified the group with seventeen cubes as having more. How did Mr. Bishop perform with his assessment? This assessment falls short of the standard's expectation by exceeding the specified range of ten or fewer objects. Mr. Bishop employed concrete objects, but he failed to align his assessment with the specific requirements of the standard. Although the assessment appears to exceed the goal, the objective does not explicitly require counting the exact number of objects. Comparing the quantities of five and seventeen cubes visually may offer an advantage compared to closely aligned numbers, such as five and seven. Consequently, Mr. Bishop's testing method is insufficient for the standard's requirements within the given field of numbers.

Mrs. Riley's Approach

In contrast, Mrs. Riley conducted an assessment that targeted the desired learning objective. She placed eight small seashells on one paper plate and two larger seashells on another. Students correctly identified the group of eight seashells as having more. How did Mrs. Riley perform with her assessment? Mrs. Riley's assessment adhered to the standard by utilizing concrete objects and keeping the numbers within the specified range. Moreover, she effectively staged a potential cognitive conflict in the children's minds using the large seashells in the group with fewer objects. This strategy ensured that the students' responses were founded solely on the quantity rather than being influenced by the size of the objects.

Conclusion

Educators must ensure that their screening methods align fully with the intended standards they aim to measure. When assessing this standard, which focuses on comparing quantities, aligning assessments directly with the standard's guidelines is vital. The examples discussed above demonstrate the importance of using concrete objects, staying within the specified range, and ensuring that the assessments solely test the concept at hand. Mrs. Riley's approach is an accurate assessment that effectively measures the desired learning objective. By adhering closely to the standard, teachers can ensure that screenings provide a reliable measure of students' understanding. This data guides instructional decisions effectively and enables teachers to plan appropriate independent math centers, as discussed in the previous two posts. If you would like, view them here:

The Value of Independent Math Centers for Young Children

Common Misconceptions About Independent Math Centers and How to Overcome Them

 

 © 2023 Molly McMahon, Lessons by Molly

 

Common Misconceptions About Independent Math Centers and How to Overcome Them

Independent math centers are an excellent way for educators to provide students with learning experiences tailored to individual needs. However, many teachers neglect to provide their students with these centers for various reasons. This blog post will explore why educators struggle with independent math centers and offer ideas to overcome these issues.

1. "I teach kindergarten, there are no activities that are on my students' independent level."

It is important to remember that every student is unique, and each student has an independent level, even in kindergarten. Teachers must assess their students' abilities and provide appropriate centers for their students. Teachers can start with one-to-one correspondence, sorting, and number approximation. These concepts do not require rote counting, counting objects, or number-symbol identification. Activities that are open-ended or self-correcting are also great for independent math centers. These might include a book center with topic books such as colors, patterns, numerals, and comparisons, numeral-art, and self-correcting puzzles.

2. "My students will find activities they have already mastered boring. They need to be challenged."

Independent math centers do not have to be boring. Teachers can incorporate fun and engaging activities that align with students' interest into their centers. For example, teachers can use pretend play, artwork, or games to make the activities exciting and engaging.

3. "I teach the whole year and I do not have a sufficient supply of centers or materials to create enough independent math centers."

Teachers can create independent math centers using dice, dominoes, playing cards, math cubes, and counters. They can also collaborate with other teachers to share and rotate materials. They can use online resources to find ideas for their centers. 

4. "The school day should be spent on learning new content and not reviewing."

Independent math centers can foster learning in a variety of ways. They can provide students with the opportunity to explore mathematical concepts on their own and develop problem-solving skills. Independent math centers can be designed to align with subjects other than math and provide opportunities for students to apply their knowledge in new ways. 

5. "My first graders have mastered the kindergarten math standards. I use kindergarten standards centers; therefore, they are already at their independent level."

It is not a good idea to assume that a class full of first graders has mastered all their kindergarten math standards. Some students may have forgotten over the summer break.  Other students may be coming from another state with different kindergarten standards. Teachers must assess their students regularly to determine their independent and instructional levels. This information will help teachers provide appropriate activities for each student's level. Teachers can use various assessment methods such as observations, informal assessments, or standardized tests.

6. "I use heterogeneous grouping to build a class community where we support others. The children who have mastered the concepts can help the children that are at instructional level."

View the photo above. How will grouping Ethel and Bethany in a heterogeneous number symbols center be helpful to either child? While it is beneficial for students to work in small groups and collaborate with their peers, it is crucial to ensure that all students are receiving activities that are appropriate for their level. Students do not carry the burden of teaching other children. That is up to the adults! Think back to Ethel and Bethany. Placing the two girls in separate homogeneous groups allows Ethel to work independently with the numerals she knows (0 to 10). Ethel's teacher can structure small group instructional activities for numerals 11 to 20, and with the support of an adult, Ethel can learn to identify numerals beyond ten. Bethany can work independently with numerals 0 to 20, and she will quickly learn to determine the number symbol she missed.

INDEPENDENT MATH CENTERS provide students with an opportunity to explore mathematical concepts on their own and develop problem-solving skills. By using appropriate materials, providing engaging activities, and assessing students regularly, teachers can overcome  challenges and provide students with meaningful learning experiences.