Helping Struggling Learners

IF we want to impact achievement for ALL students… IF we want to impact achievement for ALL students…. Geri Lorway Thinking101.ca

It’s the teaching! Geri Lorway Thinking101.ca

EVOLVE or go EXTINCT

I can help you grow, I cannot let you go? Geri Lorway Thinking101.ca

Feel the force. IF it is to be, it is up to me!

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READY?

Students come up and describe the parts.

Students come up and describe the parts.

Students come up and describe the parts.

Did you see 6 + 3 5 + 4 7 + 2 8 + 1 3 + 3 + 3 4 + 3 + 2 This collection is 9 Students come up and describe the parts.

How are they related? 6 + 3 = 5 + 4 (4 + 3) + 2 = 7 + 2 7 + 2 = 8 + 1 4 + (3 + 2) = 4 + 5 How are they related? 6 + 3 = 5 + 4 (4 + 3) + 2 = 7 + 2 7 + 2 = 8 + 1 (3 + 3) + 3 = 6 + 3 Students come up and describe the parts.

READY?

These expressions describe 10. 6 + 4 8 +2 3 + 2 + 3 + 2 7 + 3 4 + 2 + 4 5 + 5

Are any related? 6 + 4 8 +2 3 + 2 + 3 + 2 7 + 3 4 + 2 + 4 5 + 5

The ability to subitize and its impact on counting undergoes a long lasting development until the age of 17 years. A great percentage of students struggling with acquiring basic arithmetic skills exhibit developmental deficits in the correctness and speed of this special visual capacity. Research demonstrates that subitizing and visual counting can be improved by daily practice AND THAT a significant improvement in basic arithmetic skills when students were given daily practice for 21 days. Burkhart Fischer, Dipl. Phys., Andrea Köngeter, Dipl. Biol., and Klaus Hartnegg, Dipl. Phys. 2008

Number Sense: Case, Griffin, and Siegler (1994) found that children who have a well-developed Number Sense are able to succeed in early math (and beyond), while children who don’t are at much greater risk of falling increasingly further behind.  They also demonstrated that virtually any child could develop Number Sense (Griffin, 2004). The good news is that researchers have identified a specific, well-defined set of concepts and skills that can make the difference between children’s success and failure in mathematics in the early years (Griffin, Case, & Siegler, 1996). 

Ready?

Ready?

Nearly a century of research confirms the close connection between spatial thinking and mathematics performance. The relation between spatial ability and mathematics is so well established that it no longer makes sense to ask whether they are related. (Mix & Cheng, 2012). The connection does not appear to be limited to any one strand of mathematics. It plays a role in arithmetic, word problems, measurement, geometry, algebra and calculus. Research mathematics education, psychology and even neuroscience is attempting to map these relationships.

In a longitudinal study involving 400,000 students, Wai and colleagues (2009) found that spatial skills assessed in high school predicted which students would later enter and succeed in disciplines related to science, technology, engineering and mathematics. Moreover, spatial thinking was a better predictor of mathematics success than either verbal or mathematical skills.

http://www.mathematicslearning.org

Overwhelming agreement: We must attend to reasoning and arithmetic. Attention to one cannot outweigh attention to the other.

No!!! www.Mathematicslearning.org or glorway@thinking101.ca

No!!! www.Mathematicslearning.org or glorway@thinking101.ca

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Which Set Does Not Belong?

Interventions that benefit all students : Use visual spatial models to engage students in reasoning about number space and shape Focus on students describing, modeling, explaining, representing, reasoning Teachers immerse students in vocabulary and encourage guide expect demand it be used. Engage students for 10 minutes a day for 6 weeks, then ……

Improve all students: 10 minutes a day everyday devoted to practice with imagery. If you are interested in accepting the challenge……. I will share 6 weeks of tasks… Every day See the difference. Good Grouws Wheatley

Finding Similarities and Differences Are we teaching to reach all students? Finding Similarities and Differences The brain seeks patterns, connections, and relationships between and among prior and new learning The ability to break a concept into its similar and dissimilar characteristics allows students to understand and often solve complex problems by analyzing them in a more simple way

Graphic Organizers for Similarities and Differences Finding similarities and differences can increase student achievement by 45% Graphic Organizers for Similarities and Differences Compare Classify Create metaphors and analogies

Finding similarities and differences can increase student achievement by 45% Guidance in identifying similarities and differences enhances students' understanding of and ability to use knowledge. Independently identifying similarities and differences enhances students' understanding of and the ability to use knowledge. Representing similarities and differences in graphic or symbolic form enhances students' understanding of and ability to use knowledge.

Summarizing and Note Taking increases student achievement by 34% These skills promote greater comprehension by asking students to analyze a subject to expose what’s essential and then put it into their own words. verbatim note taking is ineffective because it does not allow time for processing the information.

Summarizing and Note Taking increases student achievement by 34% To effectively summarize, students must delete some information, substitute some information, and keep some information. To effectively delete, substitute, and keep information, students must analyze the information thoroughly. Being aware of the explicit structure of information is an aid to summarizing information.

Summarizing and Note Taking increases student achievement by 34% Teach students how to process information for their own note taking. Use a variety of organizers Graphic Organizers for Similarities and Differences

10-2 Strategy For every ten minutes of new learning provide students two minutes to process the new learning. You can either pay attention or make meaning. So time to process is essential to transfer learning to long term memory.

Generating Nonlinguistic Representations Increases student achievement by 27% Research says that knowledge is stored in two forms: linguistic (in ways associated with words) and nonlinguistic (mental pictures or even physical sensations like smell, touch, kinesthetic association or sound) The more we can use nonlinguistic representations while learning, the better we can think about and recall our knowledge

Generating Nonlinguistic Representations Increases student achievement by 27% Research says that knowledge is stored in two forms: linguistic (in ways associated with words) and nonlinguistic (mental pictures or even physical sensations like smell, touch, kinesthetic association or sound) The more we can use nonlinguistic representations while learning, the better we can think about and recall our knowledge

Reinforcing Effort and Providing Recognition increases student achievement by 29% Feedback should be timely. The larger the delay in giving feedback, the less improvement one will see. Feedback should be specific to a criterion, telling students where they stand relative to a specific target of knowledge or skill.

Students can effectively provide some of their own feedback. In fact, non-authoritative feedback produces the most gain. Feedback should be corrective in nature. The best feedback shows students what is accurate and what is not. Asking students to keep working on a task until they succeed appears to enhance student achievement.

Effective Praise Specifies the particulars of the accomplishment Provides information to students about their competence or the value of their accomplishments Is given in recognition of noteworthy effort or success at difficult tasks Attributes success to effort and ability

Problem Solving Problem solving is about finding the best solution, not just any solution. Problem solving of unstructured problems - those that do not have clearly defined goals and usually have more than one solution- are the kinds of problems we find in everyday life. Example: Ask students to build something using limited resources. This will generate questions and hypotheses about what may work or not work.

Teachers need specific support in understanding how to develop number sense in students, to guide their learning as they plan for and provide instruction (Ball & Cohen, 1996) and, ultimately, to ensure that they are spending time encouraging students to do the thinking that will improve number sense.

This model represents discussions and connections that are to be made in virtually every math lesson. This is not a progressive model wherein once one wedge is taught it is then seen as review material. Rather, each wedge is to be connected to each lesson throughout the curriculum