Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks

This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the arithmetic average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of “equal‐sharing” or “per‐unit‐quantity,” and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced.     

Synthesis of β-phenyl-δ,ε-unsaturated amino acids and stereoselective introduction of side chain groups into [4,3,0]-bicyclic β-turn dipeptides

(2S,3S)- and (2R,3R)-2-amino-3-phenyl-5-hexenoic acids have been synthesized in large scale by using Ni(II)-complexes as a template. The amino acids were used in the synthesis of [4,3,0]-bicyclic β-turn mimetics by a convergent methodology. The unique advantage of this strategy is the convenience of introducing side chain groups with predetermined chiralities on both the five- and six-membered heterocyclic rings.     

Chinese (Mainland) teachers’ views of effective mathematics teaching and learning

This study investigates Chinese teachers’ cultural beliefs concerning effective mathematics teaching through semi-structured interview with nine experienced teachers. For the Chinese teachers, an effective teacher should always be passionate and committed to the teaching profession. She should not only understand the knowledge in the textbook thoroughly but also be able to carefully craft the knowledge from the textbook for teaching by predicting possible students’ difficulties. Although Chinese teachers emphasize student participation and flexible teaching, they tend to see the teacher’s ability to design and lead coherent lessons as the key for facilitating students’ understanding. The result of this study helps researchers and educators understand the teacher-designed and content-oriented teaching model in Chinese classrooms.     

Stereoselective synthesis of individual isomers of Leu-enkephalin analogues containing substituted beta-turn bicyclic dipeptide mimetics

Novel constrained beta-turn dipeptide mimetics, 8-phenyl thiaindolizidinone amino acids 3, have been synthesized stereoselectively and incorporated into Leu-enkephalin peptides as a replacement of dipeptide Gly3-Phe4 to afford four individual isomers of Leu-enkephalin analogues 6.     

合成多肽的电喷雾质谱研究

利用电喷雾多极串联质谱对3种合成多肽进行了系统的鉴定和分析研究。首先通过全扫描模式测定了其分子量，然后选择[M H]^ 或[M 2H]^2 离子通过串联质谱(MS／MS)得到碎片离子，采用y离子和b离子互补的方法测定了多肽序列。利用文献数据对这种方法进行了验证，实验结果表明，该方法简便、快速、实用。     

An Effective Pd–Ni2P/C Anode Catalyst for Direct Formic Acid Fuel Cells

The direct formic acid fuel cell is an emerging energy conversion device for which palladium is considered as the state‐of‐the‐art anode catalyst. In this communication, we show that the activity and stability of palladium for formic acid oxidation can be significantly enhanced using nickel phosphide (Ni₂P) nanoparticles as a cocatalyst. X‐ray photoelectron spectroscopy (XPS) reveals a strong electronic interaction between Ni₂P and Pd. A direct formic acid fuel cell incorporating the best Pd–Ni₂P anode catalyst exhibits a power density of 550 mW cm^?2, which is 3.5 times of that of an analogous device using a commercial Pd anode catalyst.     

Characterizing Methyl‐Bearing Side Chain Contacts and Dynamics Mediating Amyloid β Protofibril Interactions Using 13Cmethyl‐DEST and Lifetime Line Broadening

Many details pertaining to the formation and interactions of protein aggregates associated with neurodegenerative diseases are invisible to conventional biophysical techniques. We recently introduced ¹⁵N dark‐state exchange saturation transfer (DEST) and ¹⁵N lifetime line‐broadening to study solution backbone dynamics and position‐specific binding probabilities for amyloid β (Aβ) monomers in exchange with large (2–80 MDa) protofibrillar Aβ aggregates. Here we use ¹³C_methyl DEST and lifetime line‐broadening to probe the interactions and dynamics of methyl‐bearing side chains in the Aβ‐protofibril‐bound state. We show that all methyl groups of Aβ40 populate direct‐contact bound states with a very fast effective transverse relaxation rate, indicative of side‐chain‐mediated direct binding to the protofibril surface. The data are consistent with position‐specific enhancements of ¹³C_methyl‐${R{{{\rm tethered}\hfill \atop 2\hfill}}}$ values in tethered states, providing further insights into the structural ensemble of the protofibril‐bound state.     

Stereoselective bromination-suzuki cross-coupling of dehydroamino acids to form novel reverse-turn peptidomimetics: substituted unsaturated and saturated indolizidinone amino acids

A general and efficient methodology has been developed to prepare the C4-substituted dipeptide reverse-turn mimetics unsaturated (9a, 10a) and saturated (11a) azabicyclo[4.3.0] alkane amino acid derivatives. The side chain was introduced by bromination of dehydroamino acid intermediates followed by Suzuki coupling. Hydrogenation of the bicyclic dehydroamino acid 9a afforded saturated bicyclic lactam 11a. This approach can be further explored for the synthesis of a variety of such beta-turn mimetics with aryl and alkyl side chain functionalities. [reaction: see text]