Many of the 6th graders at Athena Middle School are experiencing a new twist on mathematics: Math in Focus – A Singapore Math Approach. The math curriculum in Singapore has been recognized worldwide for its excellence in producing students high skilled in mathematics. Students in Singapore have ranked at the top of the world in mathematics on the Trends in International Mathematics and Science Study (TIMSS) over multiple years. Because of this, Singapore Math has gained interest and popularity in the United States.
“Mathematics is an excellent vehicle for the development and improvement of a persons intellectual competence.” -Singapore Math
Students have been working with unifix cubes and the “bar model” to solve complex ratio and proportion problems. This strategy was particularly successful with 12:1:1 math classes and students with special needs. The idea is to go from concrete tasks to pictorial to abstract. Many math teachers tend to start with abstract, while Singapore suggests to start with concrete tasks. This is also a key concept of the Common Core Standards.
Well done 6th grade teachers, Mrs. Mayer, Mrs. Schreiber, Mr. Titus, and Mr. Smith for undertaking this challenge and engaging your students in different ways. These teachers have devoted many hours in planning and professional development to help their students to be successful and truly understand mathematics. Well done!
On January 5, 2012, Andy Brown and Julie Mayer taught a 6th grade interactive lesson on volume using manipulatives, an iPhone, and a web based service called Evernote (www.evernote.com). Mr. Brown built a box out of cubes while asking students reflective questions to get them to understand the concept of volume. After the the box was built, a picture was taken using an iPhone and uploaded to an Evernote notebook.
Students were very engaged in this lesson because the picture they saw Mr. Brown take was instantly shown on the SmartBoard in their classroom. Individual students were then assigned dimensions and built boxes of their own out of cubes (see photos below). The iPhone was used again to take photos of their individual boxes and post them to the Evernote notebook. Then, the class had a discussion about the concept of volume and had to calculate how many cubes made the box. Every student was able to discover how to find the volume of a rectangular prism. They are now ready to dig deeper and learn how to show more sophisticated work in the coming days.
Great work students and teachers!
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!
Teachers at Athena Middle and High School are using SMART response clickers! Mr. Titus, Mrs. Schrieber, Miss Northrup (University of Rochester student teacher), and Mrs. Derleth have been utilizing this interactive technology in their classrooms. The SMART Response system gives teachers the ability to instantly track quiz results and lesson comprehension to gain immediate insight into student learning and help increase overall retention and engagement.
- Warm-ups/Ticket out the Door: All students will have a clicker in their hand and be expected to answer questions on a warm-up and/or ticket out the door. These questions could be multiple choice, short response, true/false, etc. As each student answers the question, the teacher will receive immediate feedback on topic areas of strength and opportunities for improvement based on their answers. The teacher can use this information to modify and adjust his or her instruction based on the demonstrated student knowledge.
- Instant Questions: During a lesson, a teacher may want to assess if all students understand the content being taught. Often times a teacher will ask, “Does anyone have any questions?” and no one raises their hands. It is unlikely that all students understand what was being taught, but did not raise their hands or demonstrate knowledge of the topic. With SMART response, a teacher can have the students answer an instant and spontaneous question to gage whether all students can answer the question. If students need additional instruction or time on task, the teacher will instantly have the data to make that decision.
- Common Formative Assessments (CFAs): The CFA process has been embraced by many in the Greece Central School District. The CFA process means that teachers from the same grade or course ask the same questions to a similar group of students to collect data. This data is analyzed and discussed by this common group of teachers to improve their instruction. This collaboration will likely increase student and teacher learning. One of the struggles for teachers in this process is that compiling data into a meaningful form can be difficult and time consuming. The SMART response technology organized this data in seconds and can display it in graphs and charts.
Great job Athena! Students are more engaged and instruction is continuing to improve. You rock!
Mrs. Stowell was searching for a way to engage her students in a 6th grade proportions lesson, while at the same time showing them real world applications. She came up with a great idea: a cooking lesson. These students would be given a Marshmallow Ghosts recipe that serves 12, and use proportions to determine the necessary ingredients to serve the 30 students in the class. After determining the ingredients, students cooked with Mrs. Stowell to make delicious Halloween treats. As all students couldn’t cook at the same time, there were four stations set up in the class that students rotated through. In addition to the cooking and recipe stations, there was a decimals station, and a poster station. All students were engaged and left with smiles on their faces. This is certainly an experience that Mrs. Stowell’s students will never forget.
If you would like a copy of the recipe worksheet, click Popcorn Ghost Worksheet.