Here in Our Math Class, We Learn, We Grow, and We Belong
Joan Garcia, LaGuardia Community College
Bio
I’ve been teaching math for over 20 years and computer science for 10 years in the NYC Public highschools and as an adjunct lecturer at LaGuardia Community College (CUNY) for a decade at one of the NYCPS sites. Right now, I teach Algebra 2, Trigonometry, and introductory computer science. I love helping students build confidence, think critically, and see how they can leverage math and technology skills outside of the classroom.
Course Setting
College Now- MAT 115 College Algebra 2 and Trigonometry: This course starts with a review of basic algebra skills such as factoring, solving linear equations and inequalities and proceeds to a study of polynomial, exponential, logarithmic, and trigonometric functions. These functions are used in applications involving simple mathematical modeling where students engage in inquiry activities aimed at improving critical-thinking skills. Students develop the ability to explore and solve real-world application problems, demonstrate the appropriate use of graphing calculators, and communicate mathematical ideas clearly. Students learn and apply the principles of Algebra while employing 21st Century Skills, including creativity/innovation, communication, collaboration, critical thinking, problem solving, and decision-making. Students experience hands-on activities and participate in class discussions with open-ended problem solving. This course lays the foundation for mathematical literacy that will help students be successful in every subsequent course in mathematics.
Problem of Practice
The question, “How can I effectively increase meaningful student engagement and participation during synchronous online math class when explaining mathematical thinking/reasoning?,” focuses on increasing meaningful student engagement and participation during synchronous online math instruction, particularly when students are expected to explain their mathematical reasoning. Although many students demonstrate understanding during independent work, they do not consistently share their thinking during live virtual discussions. This is especially true for multilingual learners, who may need additional scaffolds to express their ideas confidently in English. However, these students are capable of participating actively when given structured opportunities and support. This Problem of Practice explores how intentional strategies—such as discussion routines, language supports, and multiple modes of participation, can create a more inclusive environment where all students engage in explaining, justifying, and building on mathematical ideas during online learning.Strategy
I implemented intentional, language-focused strategies to support both participation and understanding. An SEL check-in at the start of class creates a safe, low-risk environment where students feel comfortable speaking, which is especially important for multilingual learners. Think-Pair-Share activities, with and without timing, provide structured opportunities for students to rehearse ideas before sharing publicly. Warm-up or entry tickets give students time to process concepts independently or collaboratively, promoting deeper thinking. Exit tickets serve as quick formative assessments, requiring students to explain their reasoning and strengthening both conceptual understanding and language use. Additionally, math talk starters (sentence frames) support students in expressing their thinking clearly while lowering language barriers. Together, these strategies offer consistent, scaffolded opportunities for students to think, speak, and justify their ideas, leading to increased engagement, confidence, and stronger mathematical discourse.
Documentation
Entry Ticket/Warm Up: Review Simplifying Fractions
This rubric evaluates students’ ability to select and correctly apply a quadratic solving strategy, demonstrate mathematical accuracy, clearly explain their reasoning, and justify their preferred method. Higher scores reflect strong understanding, precise work, and thoughtful reflection on why a strategy is effective based on efficiency, clarity, or personal learning preference.
Assessment: Quadratic Equations
This activity has students solve quadratic equations using graphing, factoring, completing the square, and the quadratic formula. Students then select, compare, and justify the strategy they find most effective. Through reflection, they evaluate which methods best match their understanding, considering efficiency, accuracy, and ease of use when explaining their preference.
Measuring Impact
3 Assessments Scores v.1 - multi line graphs showing “How do students’ scores improve over time”
This line graph data demonstrates a clear upward trend in student performance across the three assessments, with most students showing improvement by the third assessment. This growth indicates that students were increasingly able to engage meaningfully and demonstrate understanding over time. Students demontsrated greater consistency and higher levels of performance in later assessments, indicating that they were better able to articulate their thinking and apply concepts. Despite overall gains, challenges remain for a small group of students who did not demonstrate consistent improvement across all assessments. These students may require more individualized support, such as differentiated instruction, additional practice opportunities, or targeted interventions.
3 Assessments Scores v.2 bar graph that shows “How are students’ scores now “ based on students’ growth, drops or consistency
Most of the students show improvements from Assessment 1 (assessment before introducing the strategies), Assessment 2 (after Cycle 1 of PDSA) and Assessment 3, which have the greatest improvement (after Cycle 2 and structured implementation of the strategies in online classes for the past 4 meetings). Most students bounce back strongly in Assessment 3 (many reaching near 100) Students with large gaps between bars quickly stand out for intervention.
CN Algebra 2 Class Participation Cycle
Analysis
The strategies I implemented: SEL Check-in, Think-Pair Share Activities, Warm-Up/Entry Tickets, Math Talk Starters & Exit Tickets were intentionally used for the purpose of showing meaningful improvements in student online participation such as using math content vocabulary to understand and make connections on previous-current-next lesson/skills expected of the students. I can say that based on the data I have collected, using most of these strategies is successful as I have noticed not only an increase of participation but deepening of understanding of math concepts in Algebra 2.
Based on their self-assessment and my assessment of their participation in these cycles, significant improvements were noted: many students can use math vocab, manage/leverage use of technology as part of the process, collaborate with peers and apply concepts learned in their assessments. Most students who actively participated in these cycles also saw improvement in their Quizzes and Long Tests (last Assessment) after completing the cycles. Most of the ENL students are now able to use most high mathematical thinking skills and reading comprehension with the task at hand that resulted in not only a high score but a perfect score (whether the item questions are multiple choice or FRQ’s).
I will definitely continue using most of these strategies in class and devote more meaningful time to making sense of learning rather than rushing through the maximum quantity of topics. I will definitely catch up anyway before finals but in the future, once students have learning routines to help them make connections and make sense of the concepts and skills they are learning, I believe that it will help us learn and use these strategies with more complex topics in Algebra 2 and Trigonometry.
Recommendation
SEL Check In - must be everyday to set the tone and develop a sense of belonging to activate students’ feelings that they have a place in my class.
Entry and Exit Tickets - consistently use for prior knowledge and quick checks for understanding to drive your next lessons (tells you whether to reinforce the skill or level up for a new skill in your lesson).
Clear, Transparent and Targeted Rubrics/Scoring - I believe that students get more motivated when we recognize what they do and what they can do as part of their performance improvement over time. With this PDSA cycle I learned that it is also important for students to check the temperature of their understanding or evaluate their own skill understanding. More than the score that we give, at the end of the day, it's students who measure their own understanding. Ours is just a confirmation that they are doing well/better.