The three current projects detailed below provide examples on engaging with all learners, particularly those looking for a fresh start in their STEM education. We can’t derail youth from STEM careers due to a class they failed, a concept they don’t grasp, or a learning challenge they face with memorization.
Advanced CTE Mathematics. Too many students do not complete a 3rd-year math course. Shirley Malcom, a senior adviser to the American Association for the Advancement of Science, states she views the issues “as less about calculus and more about equity.” (Jaschik, 2022). LWJ/2DS and DUSD developed an Advanced CTE Mathematics curriculum to promote mathematical achievement. Designed with artisans and small business operations needs in mind, each unit of the class contains three components.
- A work-based problem.
- Experimenting/navigating/ manipulating that problem using technology.
- Solving the work-based problem with hands-on technology utilizing mathematics aligns primarily with a course outline like an expanded Algebra 2.
Our solution allows student collaboration on a work-based problem using comfort-zone skills and communication to develop a mental model. We present work-based problem scenarios and encourage students to practice. We use technology to adapt, discuss, and create solutions to leverage critical thinking. By the time the math undergirding a unit emerges, it is clear to the student what the problem is and how to address it. Students learn and apply math while building robots, machining parts, installing plumbing, mastering culinary techniques, and welding joints.
Emphasis includes problem-solving, reasoning and proof, communication, representation, and connections. Inspired by mathematical proficiency detailed by the National Research Council, our solution uses approaches such as adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition toward mathematics.
The class integrates processes and proficiencies of the Common Core Standards for Mathematical Practice and the National Council of Teachers of Mathematics process standards. Emphasis includes problem-solving, reasoning and proof, communication, representation and connections, and strands of mathematical proficiency detailed by the National Research Council, such as adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition toward mathematics. DUSD supports the intersection between mathematical practice and the Standards for Mathematical Content, which highlight student understanding and support long-term engagement (California Department of Education, 2021).
The premise is that while students collaborate on a work-based problem, they use comfort-zone skills and communication to develop a mental model. Technology practice includes various freely available web apps, such as Wolfram Alpha, Autodesk, and more. Using technology to adapt, discuss, and create options for a work-based problem contributes to students seeing and thinking about the workforce problem from multiple perspectives. By the time the math undergirding a unit emerges, it is apparent in the student’s mind what the problem is and how to address it. This comfort level with the work problem and using hands with tools and technology to explore the activity in depth increases understanding the intended solution.
Advanced CTE Mathematics intends to represent the workplace in the classroom; students apply math in real-life work-based scenarios. This three-phase approach to learning mathematics has been anecdotally observed by teachers and administrators watching students build robots, frame walls and install plumbing, master culinary techniques, assess blood pressure, and weld joints. CTE careers require STEM skills and students demonstrate their affinity with math as makers at the same time they avoid their third-year math requirement.
One example is a spiral staircase in a 2-story, 42,000 square-foot building where the architect and the engineer did not collaborate on the staircase, and the structure has accessibility problems. As the staircase turns, the treads and risers become too narrow on one end and too wide on the other. Students review numerous photos and videos of the staircase, blueprints, examples of staircase design, and the United Nations guidelines for accessible staircases. Based on a typical experience accessing a staircase, this work problem explores several concepts in Algebra 2. The technology piece of the stairs will include students working with their hands, using paper, cardboard, and tape, and then inputting data into an Autodesk application. Within Autodesk, and with a handmade cardboard prototype, students will adjust the staircase and improve the design. Students rework the center landing, step and riser configuration, and the top landing to meet United Nations accessibility. Through this challenge, students gain confidence in utilizing technology and exploring mathematics to solve industry-informed problems. All content is in progress or available at the DUSD Math4CTE.org website, meets accessibility standards, and is Creative Commons (CC by 4.0) licensed. This proposal targets student success in Advanced Mathematics for CTE, an increase in student completion of third year mathematics coursework, and relevance of the study design and content to serve Hispanic students.
Computer Science Work-based-learning (WBL) offers current and relevant Science, Technology, Engineering, and Mathematics (STEM) content to benefit high-need high school students by developing industry-informed prototypes and portfolio-quality projects. We designed and built a 2-year pathway in Game Development, launched in Fall 2021, emphasizing higher-level programming languages C# with Unity (year one) and C++ with Unreal Engine (year two). Students explore gaming as a career and develop foundational programming skills.
LWJ/2DS developed supplemental WBL content and an online community of practice to expand teachers’ capacity and confidence in supporting students. 2DS contracted with Akupara Games, a Los Angeles indie gaming publisher, to design and code a series of games that, if included in a student portfolio, qualify the student to be hired by a Game Developer company. This reverse engineering from hire to high school transitions students across the WBL games, led to LWJ authored and DUSD published Open Education Resources (OER) Downey Platformer workbook and a supplemental text, and Mathematics for Game Developers (available in English and Spanish).
CS-WBL ties to the U.S. Dept. of Education’s WBL toolkit, which outlines how comprehensive programs enhance classroom learning and create paths to a stronger and more diverse STEM workforce. As a strategy to advance equity in STEM, WBL involves a project-based assignment and team development strategy that aligns with sector employer expectations (Cahill, 2016). With projects, students in high-quality WBL gain technical skills and academic credentials that lead to high-demand, well-paying careers in STEM and promote equity through social mobility.
Embedding advanced mathematics in students’ schedules within CTE pathways underpins DUSD’s conceptual framework for this promising new strategy. In this Algebra 2 level class, mathematical processes and standards are expressed through student understanding, engagement, and a hands-on maker-focus that encourages students’ strengths in experimenting with a problem using technology within current comfort levels. Studies have reviewed the ways teacher partnerships across academic departments introduce Common Core State Standards (CCSS) into CTE classes, connecting learning to math standards. In these models, teachers assess students’ math awareness related to a CTE lesson and embed a math example in a CTE lesson leading to a formal assessment (Richner, 2014). Advanced CTE Mathematics develops deeper math connections through contextualized learning.
Advanced Placement for CTE (AP4CTE). Parents and schools often view Advanced Placement as a demonstration of student excellence and a provider of competitive advantage for university admittance. This approach limits high-need student participation. 2DS determined CTE capstone portfolio projects offer a unique demonstration of problem-solving, critical thinking, and complex learning.
AP4CTE consists of two interdisciplinary courses, AP Seminar, and AP Research, that promote college-level critical thinking. The project component leverages early research findings following one year of college outcome data showing that skills learned through cross-curricular exploration in taking AP Seminar provides a foundation for positive college and career outcomes (Jagesic et al., 2020). The CTE/STEM year two capstone project component has the potential to embed valuable research knowledge transferable to ongoing learning and the need to dovetail into CTE coursework in a relevant academic context.
This year, The AP Seminar topic is Building a Dynamic Workforce. Students follow AP Seminar requirements, and their research explores, for example, DUSD pathways in Computer Science/Game Development or Advanced Manufacturing. In AP Research, students develop Game Development digital and Advanced Manufacturing physical portfolios that receive AP Research credit and DUSD capstone course credit and serve as skill set demonstration to employers, colleges, and universities. Students receive AP credit for both AP Seminar and AP Research.