Ashley Gutierrez: Mathematical Mindset Teaching and Learning Plan
ELM-465: Elementary and Middle School Mathematics
Information
Hello! My name is Ashley Gutierrez, and I am pursuing my degree in Elementary Education at Grand Canyon University. I am passionate about helping students build confidence in mathematics through a growth mindset and hands-on learning experiences. My goal is to create a positive, inclusive classroom where students see this as a tool for problem-solving and creativity.
Learning Experiences
One of my favorite math memories was in 4th grade when my teacher introduced patterns using colored tiles. We explored how patterns repeated and how they connected to multiplication and skip counting. I remember feeling proud when I realized that patterns could help me solve problems faster. This experience helped me understand that math isn't just about numbers. It is about discovering relationships and making sense of how things connect. Another memory was in middle school. Fractions were a challenge for me. I often got frustrated because I couldn't visualize what the numbers represented. One day, my teacher used pizza slices to explain equivalent fractions, and everything finally clicked. This is now something I use when my own kids bring home fraction homework and are struggling to understand it. That moment taught me the importance of using visuals and real-life examples to understand abstract ideas. It also showed me that struggle is part of learning, and mistakes can lead to a deeper understanding.
Glows
1. One of my strengths as a math learner has always been finding creative ways to solve problems. I enjoy looking for patterns and exploring multiple strategies rather than sticking to just one method. This helps me better understand how math concepts connect and apply to real life.
2. Another glow was my persistence. Even when a problem seemed difficult, I was determined to figure it out. I learned to slow down, recheck my steps, and keep trying until I found a solution that made sense.
3. I think I shine when working with others to solve math problems. Explaining my thinking out loud and listening to how others approach a problem often helps me see new perspectives. I have found that collaboration builds confidence, strengthens understanding, and makes learning math more enjoyable.
Grows
1. One area I struggled with in the past was my math anxiety. I used to worry too much about getting the "right" answer instead of focusing on the process. Over time, I've learned that mistakes are an important part of learning.
2. A current grow for me is continuing to build my confidence when teaching math concepts to others. I want to keep improving my ability to explain math in clear and engaging ways that make sense to every student.
Mathematics Instruction
Current research in mathematics education emphasizes the importance of helping students develop a mathematical mindset. This is the belief that everyone can learn and grow in math through effort, practice, and perseverance. According to Boaler (2016), students thrive when teachers focus on reasoning, collaboration, and problem-solving rather than memorization or speed. When math instruction encourages exploration and productive struggle, students become more confident and engaged learners. Equity also plays a vital role in effective math instruction. Every student, regardless of background or ability, deserves access to meaningful math experiences that build understanding and self-efficacy. Teachers can promote equity by using multiple representations, connecting math to real-world contexts, and valuing diverse ways of thinking. The National Council of Teachers of Mathematics (2014) talks about equitable teaching practices supporting deep mathematical understanding and how it helps to close learning gaps. By fostering a mathematical mindset, teachers can help students view mistakes as learning opportunities and build lasting confidence in their mathematical abilities.
My Mathematics Teaching Philosophy
My mathematics teaching philosophy is grounded in the belief that all students are capable of learning and succeeding mathematics when they are provided with equitable access, supportive instruction, and meaningful learning experiences. I believe that math should not be about speed, memorization, or simply getting the ”right” answer. Instead, it should focus on developing reasoning, problem-solving skills, and confidence. One bias I have become more aware of is the long-standing idea that some students are naturally good at math while others are not. This belief can create barriers and negatively affect students who need more time, encouragement, or different ways to access the content. I want my classroom to be a safe space where students feel comfortable taking risks and making mistakes. I believe mistakes are a necessary part of learning, and when students are encouraged to learn from them, they begin to see themselves as capable mathematicians. I will design lessons that promote curiosity and exploration by using real-world examples, visual models, hands-on activities, and collaborative problem-solving. Open-ended questions will allow students to share their thinking in different ways and learn from one another. Equity is central to my approach to teaching math. Every student, regardless of background, learning style, or ability level, deserves access to engaging and meaningful math experiences. I plan to use differentiated instruction, flexible grouping, and multiple representations to meet the diverse needs of my students. I also understand the importance of culturally responsive teaching and will work to connect math learning to students’ experiences while maintaining high expectations for all learners. From a Christian perspective, I see mathematics as a reflection of God’s order and design for the world. Teaching math with patiences, compassion, and love allows me to honor each students as made in the image of God. Through opening reflection, student feedback, and assessment data, I will continue to grow as an educator. My ultimate goal is to help students build confidence, appreciate the beauty of math, and develop a lifelong love for learning.
Strategies
Resources and Technology Tools
https://www.prodigygame.com/main-en
Family Math Book Resource
How Many Seeds in a Pumpkin?
•This children's book introduces counting, estimation, comparison, and number sense through a relatable classroom pumpkin activity. It encourages curiosity, discussion, and problem-solving, making math accessible and engaging for young learners.
Family Math Connections
•Families can estimate and count every day items at home to build number sense and estimation skills.
•Parents can ask open-ended questions ("How did you decide?" or "What strategy did you use?") to promote math thinking and growth mindset.
•Caregivers can connect math to cultural traditions, such as counting ingredients during family cooking or estimating portions during shared meals.
Community Resources
1. El Paso Public Library
•The EP Public Library provides free access to math-related books, digital learning tools, tutoring programs, and family learning events for children. Some branches offer bilingual services.
2. La Nube STEAM Discovery Center
•This hands-on center offers inquiry-based learning experiences focused on science, tech, engineering, arts and math. Through interactive exhibits and problem-solving activities, students can explore different math concepts. La Nube emphasizes accessibility, curiosity, and experiential learning.
3. UTEP Centennial Museum
•The UTEP museum provides educational programs, exhibits, and field trip opportunities that integrate math with science, history, and culture. Students engage with math concepts through exploration of fossils, artifacts, and visual data, supporting interdisciplinary learning. It promotes equity by valuing students' cultural backgrounds and offering authentic contexts where math is used to understand the world.
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