ACE Mathematics Newsletter
3 - 8 Mathematics | OCT 2017 YEAR 3: VOL. 1
In this Edition:
Mathematics Instructional Block: General Overview featuring Teacher and Student Moves
Instructional Resources: 3rd Six Weeks Instructional Calendars & Exemplars
Instructional Trends in Mathematics: Embracing the Power of Productive Struggle in Mathematics
Upcoming PD: Monthly Math PD Opportunities
Announcements: ACE Website's New Layout
Mathematics Instructional Block
General Overview featuring Teacher and Student Moves
Readiness or Review Routine
An academic routine is a short teaching and learning segment that focuses on skills either previously taught or skills soon to be introduced. The routine is a form of spaced or distributive practice that reactivates neurological pathways to strengthen connections within the brain.
· A routine is a means of spiraling multiple student expectations.
· A routine develops skills that have been previously taught or is used to preview skills before the skills are formally taught.
· Routines are deliberately repetitive to promote long-term retention.
· Convey a sense of urgency with a use of a timer. Set the timer; adhere to the time frame.
· Depending on the students’ familiarity with the routine, modeling of the skill or aggressive monitoring is appropriate.
· Work toward students facilitating the routine—from recording responses to providing explanation of the thinking process.
· Do Nows can be facilitated in partnerships to promote discussion and collaboration.
· If classroom management is a concern, partnership is not a viable format to begin class.
The problem posed to students during this segment is used to introduce the day’s lesson. The challenge is not the lesson. The concept the challenge addresses is the topic of the lesson. The problem may or may not be solved during the allotted time and may be used the next day. Teachers monitor students to ascertain the students’ initial performance level with the concept. This information is used to highlight specific aspects of the concept during instruction with which students particularly struggled. A decision must be made regarding whether the Preview Challenge is addressed at the close of the lesson or used the next day. Once students have the required skills to solve the problem, students are redirected to the challenge question. The intent is to make the learning transparent to students; they now possess the knowledge and skills to answer the question successfully.
The Preview Challenge can:
· heighten students curiosity
· prime students for learning
· provide a reason for students to pay attention
· motivate students to learning
- Establish time frame; use timer; share 1 minute mark; establish expectation that it is okay if the challenge is not completed.
- Aggressively monitor as students work on this problem.
- Note individual student performance to determine how the Challenge is used to introduce the lesson and whether the Preview Challenge is or is not revisited later in the lesson.
Students may work in any configuration deemed appropriate: alone, partnered, or small group.
Demonstration (I Do)
· Connect instruction to Preview Challenge. Acknowledge the Challenge may not have been solved and will be revisited the next day. State how the day’s instruction connects to the Challenge and the LO.
· Mark critical vocabulary; add to word wall or concept display if not already displayed.
· State specifically how knowledge and skill links to the day’s DOL.
· Ask questions to check for understanding to determine if students are ready to move to Guided Practice.
Students are engaged in some way other than passively listening.
· Taking notes
· Answering questions
· Engaging in a Turn and Talk.
Check for Understanding #1
· A Turn and Talk and the Think-Pair-Share is a brain break that promotes students personally processing the learning through discussion.
· The question generates discussion—not a one word answer. If the answer is one word, a Think Pair Share/Turn and Talk is not appropriate.
· Assign roles for ease in facilitation.
· Aggressively monitor
· Listen to discussion to know who to call on when time has lapsed.
· Determine if students’ responses indicate understanding and are ready to move to
· Engage in conversation with partners that need support.
· Determine if the lesson will progress to Guided Practice or Additional Demonstration is warranted.
Students practice and apply the knowledge and skill during these segments. These segments provide additional opportunities for the teacher to aggressively monitor and make instructional decisions that meet students’ needs. The intent is to scaffold the learning through structured interactions with classmates to ensure the student is successful on the Demonstration of Learning.
- Continue to model and ask questions.
- Convey a sense of urgency.
- Aggressively monitor to determine if students’ level of performance indicates they are ready for Peer Practice.
Check for Understanding #2
· A multiple-response strategy may also be used to determine the understanding of all students.
· Determine if the lesson will progress to Peer Practice or additional Guided Practice is warranted.
The point of peer practice is
· to generate conversation
· to facilitate construction.
· Establish clear expectations.
· Assign roles for ease in facilitating, especially when students are becoming comfortable with the format and there is a danger of one student overshadowing another.
· Aggressively monitor to determine if students are ready for Independent Practice.
· Differentiated Instruction is flexible grouping of identified struggling students to provide reinforcement of concepts and skills based on teacher observations, MRS data collected during daily lesson, common assessment and/or ACP data.
· Form a small group of students who will continue to receive scaffolded support provided by the teacher.
Students work alone, in pairs, triads, or small groups applying concepts skills to differentiated tasks to reach concept mastery.
Demonstration of Learning (DOL)
Establish a time frame. Cue students when to begin; keep students abreast of time.
· The formation of small groups is based on DOL data.
· All students must be engaged while select students are working with the teacher.
Hot off the press: 3rd Six Weeks curriculum calendars
When reviewing these calendars, pay close attention to the proposed unpacking of the targeted standards in order to facilitate conceptual understanding.
Exemplars: We have developed both 2nd Six Weeks Common Assessments and Grades 3-8 Assessment of Course Performance Exemplars for your reference. These tools are available on the ACE website under Coaching Tools/Preview Assessments, and are recommended as a framework for specific strategies to be incorporated during instruction as you address those targeted SEs.
Assessment of Course Performance Exemplars are based on the 2016 STAAR Mathematics released tests, and will allow you to spiral back to those critical SEs, while providing students with additional exposure and practice before the December 11 test administration. Your middle school instructional calendars provide a daily alignment to the ACP Exemplars, including practice sample questions to be used as daily routines during the 3rd Six Weeks.
Instructional Trends in Mathematics
Embracing the Power of Productive Struggle in Mathematics
Productive struggle is a highly effective methodology when it comes to teaching math and other STEM related subjects. Used mostly in the primary level, it involves letting students deal with problems and puzzles on their own, even when they are a bit too advanced for them, and letting them figure out to how to solve them. This, which may seem counterintuitive, is actually intended to let students resort to their own creativity to find possible solutions to problems that do not necessarily have a single way to approach them.
Different studies have led to the conclusion that struggling to make sense of mathematics is an essential part of the learning process, and is the most efficient way to get students to really understand the topics at hand. Unfortunately, struggle is not often perceived as a positive and constructive part of the learning process and, rather, it is treated as failure both by the learner and the teacher. And with curriculums that are designed to move from one topic to the other, regardless of the students’ capacity to master a particular knowledge before moving on, are creating major problems in the study of this field.
Many math courses are taking a dubious approach in which the correct answer is valued more than reasoning and understanding, and where strict formulas are provided in a lecture-like manner, without giving students the possibility to discuss them or to fully understand why they work the way they do. According to some specialists, this leads to students who lack confidence in their abilities, and who – because of this insecurity – are reluctant to put the effort to understand. A problem which is worsened by popular beliefs like that you are either good in mathematics, or that you are not.
Productive Struggle is a methodology that was proposed to end this, and to foster true understanding of math related topics in students of all levels and ages, but especially among younger ones. The goal of this technique is to help students make sense of problems and persevere in solving them, no matter how difficult they find them to be. In order to apply this methodology, teachers present a problem to the class, and give individual students time to think it in on their own. These problems can be framed in any way, but according to recent research studies, problems that have a real-life feel to them are often more meaningful, as students can apply their personal experience, and feel more secure when working out the answer.
After giving students enough time to develop a strategy to resolve the problem and to try it out, fail, and start over, until they figure out an effective way to reach a solution, teachers gather students in small groups, where different solutions are meant to be compared, and used to come up with a better solution based on what the group learnt. Finally, the whole class is meant to discuss the problem, and all the proposed solutions. During the course of the exercises, teachers are not supposed to help students out other than encouraging them, or helping them identify the source of their struggle (are they having trouble identifying how to get started, or how to lay down a strategy? Or are they having a problem applying their line of thought?), or just by pointing out that difficulties are an essential part of learning, and that failing is an option as long as they try.
Only after the whole class has discussed the possible solutions and the different answers, teachers are allowed to draw a map to the solution, and to provide students with tools and tasks that may help them in the future. But, according to experts, it is important that they address that math is hard, and that it is supposed to feel complicated in order for it to be understood, as a means to downsize frustration and encourage students to keep trying.