# Blog Archives

## Graphing Linear Equations–Common Core Style

Mrs. Marsh and Mrs. Vernon’s Pre-Algebra classes participated in many Common Core Math activities that focused on the following standard:

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Their students worked on investigations (see below to download), discussed their findings verbally and on the SMART board, and applied their knowledge on the Buzz Math computer website. Well done students!

## Niagara University Professor Engages Teachers at Athena

Niagara University Education Professor Dr. Paul Vermette presented to the Athena High School math department on Monday, Dec. 12 on the “ENGAGING Framework in Secondary Mathematics.” He began his workshop acknowledging that we are in “an age of standards, technology, 21st century skills, social distancing, recession, Common Core Curriculum, teacher accountability, standardized tests, brain research, adolescent boredom, research availability and lack of social-emotional skill, increased innumeracy, change in parental supervision, and attacks on public schools…whew…” Dr. Vermette presented with NU graduate student Kristin Manguso.

In a workshop filled with collaboration, reflection, activity, and discussion, Vermette embedded the many aspects of his “ENGAGING Framework.” This framework highlights eight factors that teachers should keep in mind as they plan and carry out there daily work. These factors are:

- ENTICE EFFORT and BUILD COMMUNITY: Every opportunity to motivate, encourage and support students is taken.
- NEGOTIATE MEANING: Students must develop their own understanding of important ideas; they are never expected to memorize without meaning nor are they to claim understanding without their own examination.
- GROUP COLLABORATIVELY: Students work in and out of partnerships; consequently, they must be respectful of everyone else and accept the responsibility of honoring a community of diverse individuals.
- ACTIVE LEARNING and AUTHENTIC ASSESSMENT: Learning is seen as the result of thinking and is demonstrated by a performance of understanding. Learning is doing and is always visible and audible; “tests” mean providing evidence of understanding by skilled use of ideas in a new and realistic situation.
- GRAPHIC ORGANIZERS: A simplistic but powerful tool, these are used regularly to examine information, record thinking, and to document relationships. Students think visually on a regular basis and keep these as other people keep computer files.
- INTELLIGENCE INTERVENTIONS: Diversity is the norm, so differentiated intervention (many based on Multiple Intelligence Theory) has also become the norm. Teachers and students utilize a myriad set of strategies, ideas, and practices to find ones that work for specific individuals.
- NOTE MAKING: Unlike most secondary classrooms in which every student is expected to develop a set of “notes” that are identical to the teacher’s, note making expects each student to record his or her own ideas as they happen and as questions are being answered. Like a “captain’s log,” those notes explicate the musings, the analogies, the partial answers, and the insights gathered as students navigate the realities of their investigations.
- GRADE WISELY: The least-well-examined phenomena in education, grading practices stand as the real belief system of a teacher. In every case, the teacher should give the benefit of the doubt to the thinker-learner and uses the grades as motivators for continued work. The approach to grading a project, an assignment, a homework or an interaction becomes the vehicle by which a teacher defines his or her philosophy and sends messages to teens about their own expectations for success in that class.

The Athena math department purchased a copy of Dr. Vermette’s (2009) “ENGAGING Teens in Their Own Learning” book and will begin a book study next month. In addition, Dr. Vermette will be doing follow up workshops to dig deeper into what makes math instruction engaging for all students. See photos of the workshop including Vermette’s famous GRONK activity.

## Geometer’s Sketchpad in Action

Mrs. Mayer engaged her students using the dynamic software program Geometer’s Sketchpad. In both of Mrs. Mayer’s 12:1:1 classes, she asked high level questions that challenged her students to think. Her students responded with great answers using appropriate mathematical language and did an amazing job with the program! Mrs. Mayer’s students used Sketchpad to measure the three angles of a triangle. Even though all students in the class had different size triangles, they all came up with the same angle sum–180 degrees! This was a great constructivist lesson that allowed the students to discover mathematics, rather than be told mathematics. Teaching assistants Mrs. Arsenault and Mrs. Hale also did a great job working with students and facilitating conversations.

Students were also challenged to answer the following questions that pushed mathematical thought:

- What is the sum of the angles in a triangle?
- Could we have 2 right angles in a triangle?
- How can you prove that this is an obtuse triangle?

Students commented on how fun Geometer’s Sketchpad was and asked if they could download it on their computers at home. Mrs. Mayer and her students clearly met the learning objectives of the lesson and will likely remember them for a long time. Well done!