http://traffic.libsyn.com/remarkablechatter/BTN_15.mp3 “It’s not complicated, faster is better!”  If you believe the AT&T commercials faster is always better and for years we have taught math using that same theory!  We taught procedures and gave daily timed math facts tests to ensure students would become faster and faster at “doing” math.   We celebrated two things; the correct answer and arriving at it quickly or automatically.  Through our efforts a small segment of our population was congratulated and made to believe they were our best and brightest.  They were true mathematicians!  But for a much larger group of people we proved just the opposite. The message was sent; you either were a mathematician or you weren’t. The Common Core State Standards want to change that perception for our teachers, our students, and our population as a whole.  Mathematics can be learned by all.  Speed is not the end-all, be-all. The standards for mathematics stress two components:  conceptual understanding and fluency. The standards emphasize the need for fluency, which is not to be misinterpreted as speed, a great deal.  Fluency, in the standards, is described as an understanding of the meaning of operations and their relationships to each other, the knowledge of number relationships, and a thorough understanding of the base ten number system.  There are standards that call specifically for fluency with addition and multiplication facts and with standard algorithms, but this fluency is to come after adequate groundwork involving work with strategies and algorithms based on place value and the properties of operations has occurred. According to William McCallum, author of the common core for math,  “…being fluent in math refers to knowing how to do a calculation, whereas to know from memory means being able to produce the answer when prompted without having to do the calculation” (blog 9/4/12).  On the topic of timed tests for basic facts, Marilyn Burns writes in About Teaching Mathematics, “…timed tests do not measure children’s understanding…It doesn’t ensure that students will be able to use the facts in problem-solving situations.  Furthermore, it conveys to children that memorizing is the way to mathematical power, rather than learning to think and reason to figure out answers” (2000, p. 157).  Accordingly, John A. Van de Walle states (2006), speed (using timed tests) “is effective only for students who are goal oriented and who can perform in pressure situations. The pressure of speed can be debilitating and provides no positive benefits.”  He continues with the comment, “these timed tests should generally be avoided as they do not promote reasoned approaches to fact mastery. If there is any defensible purpose for a timed test of basic facts it may be for diagnosis – to determine which combinations are mastered and which remain to be learned. Even for diagnostic purposes there is little reason for a timed test more than once every couple of months” (pp. 95-96). For this reason, the common core recommends that students master strategies for efficient fact retrieval prior to practicing the facts for fluency (accuracy and speed).  In the end, fluency and automaticity are important.  As students explore the conceptual understandings of more rigorous concepts, they need efficient methods for determining basic facts.  However, fluency and speed should not be “the goal”,  but one ingredient that leads to students’ success in meeting their year end math goals. Bill McCallum:  http://commoncoretools.me/author/wgmccallum/  Marilyn Burns:  Math Solutions Van de Walle Series:  Elementary and Middle School Mathe...

http://traffic.libsyn.com/remarkablechatter/BTN_14.mp3   Most of you know me as the math girl and that is absolutely true, but….before I was the math girl, I was the word girl.  I like to joke that I am a word”smith” but it isn’t a joke. I really am.  I often introduce myself to new teachers by telling them that my plans for life included becoming a noted children’s book author but (as I point upward) someone up there had a sense of humor and made me a math teacher instead.  I usually do that to let them know that even if we don’t start out believing math is our favorite subject, we can  get better at it and, in my case, come to find it is our favorite thing to teach.So, a funny thing happened on the way to the Common Core; math and writing collided.  One of those darn Standards for Mathematical Practice insists I help children learn to construct viable arguments, to justify their thinking, and critique the reasoning of others.  Suddenly, I find myself cast in the role of the communications teacher as well as math  teacher. So how can this be accomplished?First and foremost, students have to be immersed in rich problem solving activities (M.P. 1) and we, the adults, have to back off and let them think on their own instead of telling them how to solve.  If problems are rigorous enough, children begin to pay attention to the structure of the problem (M.P. 7) and use strategies to solve that might include tools (M.P. 5), or representations that were not part of our math experiences.  A student may use a different method to solve than his neighbor which provides him something to justify or construct argument about (M.P. 3).  It also gives them the opportunity for higher level thinking as we compare and contrast strategies together in the whole group setting.After orally communicating their thinking, students should transfer that thinking to writing.  A math journal can serve as a portfolio of a student’s thinking about problem solving.  Students of every age should be encouraged to capture this thinking in print.  For our earliest learners this might mean transferring what they did with a tool into a pictorial representation.  It might include the algorithm for solving as soon as they are ready for this more abstract concept.  Eventually, students start writing about their thinking.  At first teachers may suggest a format for this.  They might provide sentence starters to help students with sequencing their thinking but eventually students should be able to do this on their own.  In classrooms where this is being done regularly, students are able to communicate their thinking very proficiently by the middle of second grade.Students need regular feedback during this process which is why teachers I have been working with are using a rubric we aligned to the Common Core Standards for Mathematical Practice to assess student thinking in problem solving.  They are able to capture notes about areas in which students excel and areas in which students need additional help.  The rubric can be found under math resources on this site.So for all the sceptics out there that say, “Writing in a math classroom?”,  my response would be,  “Right, or should I say, ‘Write’ on!” You can contact Renee’ Smith, Curriculum & Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee’s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts.

http://traffic.libsyn.com/remarkablechatter/BTN_13.mp3 Recently, I spent a day with K-6 teachers exploring the why and how of using math tools in their classrooms. The “why” is easy!  Years of research indicate students gain deeper conceptual understanding when they have teachers who engage in specific instructional practices.  The recommendations form NCTM’s Principles and Standards for School Mathematics suggest that teachers employ 8 specific instructional practices. They include: * A Problem Solving approach * Children are Active Learners  in the classroom * The use of Concrete materials * Cooperative Work in small groups * Discussion of ideas * Justification of thinking * Writing in class lessons * On-going assessment The common core state standards were born out of this type of  research and the 8 mathematical practices were framed around these ideas and the Strands of Mathematical Proficiency from the National Research Council. The “How” of using math takes more time. During our day together we explored the use of concrete, pictorial, and web based tools in the classroom.   It is essential that teachers immerse themselves in the use of manipulatives to solve problems in order to understand their value.  Typically,  the teachers I work with did not have much experience with manipulatives as students or in their pre-service methods classes.  This should be an element of preparation for any manipulative – based lesson.  Teacher need to be sure students will use the manipulative to deepen understanding rather than merely mimicking a rote procedure they have learned previously.  Teachers also need to be organized with their objectives for the lesson, have materials prepared, and questions ready to guide the learning experience. We also discussed helping students move from the concrete tool, through the pictorial representation, to the abstract form of mathematics using numbers and symbols, that is what the 4th CC Mathematical Practice, modeling with mathematics, requires. Suggestions we discussed included: Encouraging the use of a variety of strategies at all times.  Children should share thinking with the teacher, with a partner, in small  and whole group allows these strategies to Set aside time to do mental math activities and have students share their strategies.  Let children know that working “in their heads” is valued.  Start with simple problems without access to manipulatives, or paper and pencil.  Encourage “individual think time” to allow everyone to process at their own pace, before sharing answers and strategies. Choosing prompts and questions carefully.  When children struggle, instead of prompting them to use a manipulative, ask them what they know about the problem, what is important in the problem, and what the numbers in the problem represent.   When students have trouble explaining how they have solved a problem ask questions like, “What number did you start with?” or “What did you do next”.  When students solve with manipulatives, ask them to explain what they did mentally without recreating the actions with the manipulatives. Create a safe environment and a spirit of risk taking in your math classroom.  Help students understand that mistakes are not fatal but opportunities to learn.  Examine student work where students have made mistakes (remember to remove names or even rewrite the work) to show that mistakes can teach us. Encourage students to challenge themselves by using another method to solve the same problem. This encourages flexible thinking and gives them something else to try if a favored strategy doesn’t work in a particular situation.

http://traffic.libsyn.com/remarkablechatter/tsgt_6.mp3 Renee was a guest on The Short Giraffe Teacher where the podcast centered around Kansas Early Learning Standards. Kansas Early Learning Standards are aligned with the K-12 College and Career Ready Standards.  The purpose of the Kansas Early Learning Standards: *   To create a continuum that links early development to school readiness and later learning in school and life; *   To provide a clear statement of what young children should know and be able to do as a result of experiencing quality early learning opportunities . *   To provide guidance for early learning professionals that enhance and support their abilities to create experiences that promote early learning opportunities and sup- port families; and *   To show that during the early years, children acquire skills, knowledge and abilities in all developmental areas (e .g ., social-emotional, physical, early literacy, mathematics, music) critical to future learning Join Carianne and Renee’ as they discuss what are some of the math expectations in early childhood. This podcast was first published on The Short Giraffe Teacher.   You can contact Renee’ Smith, Curriculum & Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee’s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts.     target="_blank" title="Share On Facebook" >

http://traffic.libsyn.com/remarkablechatter/btn_t__r_small_groups.mp3 Renee’ and Tammy Fellers discuss the importance of teaching fractions conceptually in the Common Core.  They stress the need for students to conceptually understand “unit” fractions in various representations.  This understanding is imperative for students to understand larger fractions, fractions greater than one, and operations of fractions. This podcast was recorded while Renee’ and Tammy were out in the field. You can contact Renee’ Smith, Curriculum & Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee’s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts. target="_blank" title="Share On Facebook" >

http://traffic.libsyn.com/remarkablechatter/BTN_10.mp3 In a previous podcast, Tammy and I talked about untimed small group station. Today we are  talking about the teacher table and some key things to consider when intervening with students.  We will talk about the answers to these questions and more:  “Why do we have teacher stations during small group time?”;  “Do we need to see all students at the teacher table?”;  “How do we decide who to bring to the table?”;  “How many students should we see at a time?”. You can contact Renee’ Smith, Curriculum & Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee’s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts. target="_blank" title="Share On Facebook" >

Renee’ talks to Carianne Short, an early childhood specialist at ESSDACK, about  math activities you can do with your preschooler to ensure they are ready to begin school.   Carianne shares that your kitchen is a great place to work on early childhood math skills.  Examples include ideas like: sorting different everyday objects into muffin tins and counting the objects, rolling a can and measuring how far it goes, or discussing how the top and bottom of the can is round and its shape is a cylinder.   Carianne also shares the expectation for preschoolers is to be able to count to thirty. Join Renee’ and Carianne as they share many more early childhood math tips. http://traffic.libsyn.com/remarkablechatter/btn_9_carianne.mp3 You can contact Renee’ Smith, Curriculum & Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee’s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts. target="_blank" title="Share On Facebook" >

http://traffic.libsyn.com/remarkablechatter/btn_8.mp3 Join Renee’ as she talks to Ashley Weeast, a kindergarten teacher in Liberal, Kansas, about small group math time and workstations.   Ashley shares how during her limited time for math, with half-day kindergarten, she has taught her students to work independently in workstations while she works in small groups to support student learning.   You can contact Renee’ Smith, Curriculum & Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee’s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts. target="_blank" title="Share On Facebook" >

http://traffic.libsyn.com/remarkablechatter/btn_7.mp3 While out in the field, Renee&#8217; and Tammy Fellers discuss their on-going work with small group math time and workstations.   They share ideas about the structure, organization and expectations for small group time. Their discussion also includes information on student accountability during small group time. Listen in as Tammy and Renee’ discuss: The Need: Why have small group time in math?…in a perfect world it might not be necessary but in reality classrooms consist of individual children with individual needs.  Some students need to spend more time on a concept, some need remediation on a concept, and some need to be pushed to explore more difficult concepts.  Because all these children exist in  one room, usually with one teacher, there has to be a structured time to best serve the needs of the students. The Structure:  Students need to know the expectations and routines. Teaching these expectations takes time.   Tammy and Renee’ suggest not rotating stations on a timer. Not every student learns or processes at the same rate. They believe in creating a system where students rotate individually when they have met the learning goal for that station. No student is too young for this; it is being used successfully in kindergarten classrooms. One key to success in this area, is to teach and practice the routines. Student Accountability: At each station, expect students to be accountable and record their learning.  This will look different depending on the activity at the station. The recording does not need to be lengthy. It should not impede the learning but should solidify and explain the students’ learning. Expect students to keep a folder that tracks their accountability sheets. Engaging Activities:  Each station should have a purpose, learning goal and or objective. Students can tell the difference between when they are “filling time” and when the activity is meaningful. Variety:  Vary the  concepts in each of the stations. Also, vary the learning styles students use. Small group learning time is a great opportunity for differentiated instruction. Teachers do not have to require every student go to every station. Teachers can assign students which stations to complete based on individual learning needs. During this time, teachers are also able to work with specific students who need additional instructional on a concept. You can contact Renee’ Smith, Curriculum &amp; Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee&#8217;s blog:  By The Numbers Facebook @By The Numbers Be sure to subscribe to receive an email of future podcasts. target="_blank" title="Share On Facebook" ><a href="javascript:" onclick="javascript:window.open('//www.linkedin.com/shareArticle?mini=true&url=https://remarkablechatter.com/category/podcasts/by-the-numbers/feed/','', 'menubar=no,toolbar=no,resizable=yes,scrollbars=yes,height=600,

http://traffic.libsyn.com/remarkablechatter/btn_6.mp3 Renee&#8217; talks with 4th grade teacher, Kris Styes, who shares the power of professional learning for teachers of math.  Kris shares how learning and teaching through Cognitively Guided Instruction and the Dan Meyer &#8220;real-world&#8221; method have positively impacted her students. You can contact Renee’ Smith, Curriculum &amp; Instructional Specialist at: [email protected] 620-931-2528 Work 620-200-0763 Cell twitter @reneesmith1 Renee&#8217;s blog:  By The Numbers . Go down deep enough into anything and you will find mathematics.  ~Dean Schlicter . Be sure to subscribe to receive an email of future podcasts. target="_blank" title="Share On Facebook" >