Math Empowers 2
Middletown Township Public Schools
SECOND GRADE - 2nd QUARTER 2016-2017
The 100th Day of School: February 16, 2017
- Starting at 100, encourage students to find different ways to make/build 100 using base ten blocks, coins or ten frames.
- Extend the task by having the students draw representational models of their findings
REMEMBER: The POWER of NUMBER TALKS
The video below showcases Jo Boaler, a British education author, and Professor of Mathematics Education at the Stanford Graduate School of Education. She explains, "Having kids solve problems in different ways teaches them a very, very important building block in number sense and mathematics. It teaches them the ability and willingness to break numbers apart or decompose the numbers and regroup them. This is an important foundational base from which all other mathematics builds." Furthermore, "Number Talks are the only quick pedagogical practice that teaches number fluency or automaticity at the same time as conceptual understanding of number."
Consider watching the video below. See Number Talks in action and GET INSPIRED to implement this Best Practice in your classroom.
These are two powerful images that educators must keep in mind when teaching students key concepts, especially regrouping. Donna Boucher, author of Math Coach's Corner, writes about the importance of following the concrete, representational, abstract (CRA) sequence for math instruction. Please know, CRA is for all grades levels and should overlap. "It’s not all concrete, then all representational, and finally all abstract. [Teachers] ... have to connect the abstract to the concrete or representational or the symbols remain abstract." Furthermore, moving too quickly toward the traditional algorithm is a major cause of why students lack understanding with regrouping.
Bottom line, "Students must experience and interact with a concept to develop a true understanding." Donna challenges teachers to reflect on their current teaching practices and to asks themselves, "Are the students getting enough concrete and pictorial experiences with base ten blocks or ten frames? How well do teachers understand the standards, and how to incorporate CRA into their mathematics instruction. These are two of the most important ways [one] ... can improve student understanding and achievement."
Click to learn more about CRA. Also consider checking out this follow-up post which includes a video (embeded below) showing how to connect concrete learning with the abstract algorithm for subtraction with regrouping.
The IDEAL MATH LESSON vs. The Reading Workshop Model
- Engage/Explore, where the teacher guides the students through a discovery of the lesson,
- Explain/Elaborate, where students complete their formative assessment,
- Differentiation based on the assessment, which can consist of centers or stations, and
- Evaluate, where the lesson is summed up and reflected upon.
The Workshop Model, as used in Reading and Writing, differs from this model. For more about the comparison between the two different models, please see this document.
IMPORTANT UPDATE !!!! NEW.... Progress Monitoring Capability in DreamBox
What Math Lies Between Direct Modelling and Fact Memorization?
The answer.... The opportunity to achieve deep mathematical understanding lies here. The time in between modeling and memorization is a foundational building block for higher mathematics and for mental fluency. Students who construct personal strategies, over time, for solving calculations often learn mathematics that serves them for the rest of their lives. This is achieved, "... not through direct instruction, but rather as a result of teachers posing well-constructed problems that elicit and work with these evolving strategies, augmented by extensive practice in different contexts."
Want some Tips for Teaching Math Facts ? A concise list is provided in this research monograph What Works? Research into Practice: The Mathematical Territory Between Direct Modelling and Proficiency by Dr. Alex Lawson. Simply click the link to learn more.
Got Rekenreks?!?!?
"Numbers are abstract, which is why many students have difficulty making sense of them. Incorporating a Rekenrek allows students to discover number and number relationships in a way that makes sense." ~Graham Fletcher
Watching this eye opening video and learning why using this popular DreamBox tool is such vital asset for teachers and students is strongly encouraged.
Thank You for Reading!
Valerie DeMatteo
Elementary Mathematics Specialist
Harmony Elementary School
Math Empowers - Grade 2 Representative
Email: dematteov@middletownk12.org
Twitter: @val_dematteo