Click here for a Quick Guide for Observing Classroom Content and Practice Content (Math Advanced CCRSAE Levels D and E)

The examples below feature several Indicators from the ABE Professional Standards. These Indicators are just a sampling from the full set of the ABE Professional Standards and were chosen because they create a sequence: the teacher plans a lesson that sets clear and high expectations, the teacher then delivers high quality instruction, and finally the teacher uses a variety of assessments to see if students understand the material or if re-teaching is necessary. These examples highlight teacher and student behaviors aligned to these Indicators that you can expect to see in a rigorous ABE advanced level Math class.


(Indicators P1.1, P1.2, C1.1)

The teacher plans and implements CCRSAE aligned, academically rigorous, differentiated lessons that include clear content and language objectives, set high expectations for all learners, cultivate a safe classroom environment, encourage productive struggle, and motivate all students to succeed.
Virtual/Hands-On Tools: a problem to engage with at arrival; thinking tools (graphing calculator, Desmos, GeoGebra) and materials (graph paper, rulers, spaghetti-lines) accessible to students; non-routine math problems and experiences.
What is the teacher doing?What are adult learners doing?
Demonstrating sophisticated mathematical models (flow charts, formulas, spreadsheets)Using mathematical models (computer generated Desmos or GeoGebra), equations, graphs (hand drawn or spreadsheet).
Creating or selecting culturally responsive lessons that engage and sustain student attentionEngaging in challenging learning tasks regardless of learning needs (linguistic and cultural background)
Establishing classroom routines that require students to defend their thinking using a logical progressionJustifying a solution method using a logical progression of arguments and critiquing the reasoning of others
Focusing attention on mathematical languageUsing mathematical language precisely to convey meaning


(Indicators P1.3, P1.4)

The teacher delivers high quality, culturally responsive instruction that meets the diverse needs of all students and engages them with meaningful topics and tasks that develop students’ critical thinking and problem-solving skills.
Virtual/Hands-On Tools:
balance scale, algebra tiles, spreadsheets, grid paper, bar models, Desmos calculator, 3-dimensional solid objects.
What is the teacher doing?What are adult learners doing?
Creating a culture of being careful and precise when communicating mathematical ideasNegotiating with others in response to new ideas, preferences, or contributions
Highlighting commonalities, differences, and patterns in students’ ideasReferencing mathematical elements in context while logically providing claims and counterclaims
Providing opportunities to evaluate different approaches to a problemActively incorporating others into discussions about mathematical ideas, incorporating a variety of approaches


(Indicators P2.1, P2.2, P2.3) 

The teacher uses a variety of formative and summative assessments to measure student learning and understanding, evaluate the effectiveness of instruction, develop differentiated and advanced learning experiences, and inform future instruction.
Virtual/Hands-On Tools: exit tickets, math journals or logs, My Favorite No, checklists for teacher observation of objectives being demonstrated or evidence of learning, or completion of a project.
What is the teacher doing?What are adult learners doing?
Prompting students’ reasoning; listening to responses to gauge their understandingDemonstrating their thinking by drawing, modeling with graphs or equations, and discussing and sharing their work
Conducting frequent checks for understanding and adjusting instruction accordinglyIncorporating feedback from the teacher and their peers to adjust their thinking
Using multiple formative approaches to assess students (journals, analyzing group work, student explanation)Using drawings, diagrams, graphs, equations, and computer-generated models to show understanding and explain mathematical concepts