SF APEX trigger and test fails

trigger GoogleScholarResults on Lead (before insert, before update) {

    for(Lead lead_record: Trigger.new){
        if(lead_record.FirstName == 'Matthew' && lead_record.LastName == 'Poer'){
            lead_record.FirstName = 'Matt';
        }
    }

}

// and the corresponding test, which fails

@isTest
private class TestGoogleScholarResults {

    static testMethod void testMattPoer(){
        // setup the leads
        Lead lead_record_matthew_poer = new Lead(FirstName = 'Matthew',LastName = 'Poer',Company = 'PSI');
        Lead lead_record_ron_fisher = new Lead(FirstName = 'Ron',LastName = 'Fisher',Company = 'PSI');

        // start test, insert leads, stop test
        Test.startTest();
        insert lead_record_matthew_poer;
        insert lead_record_ron_fisher;
        Test.stopTest();

        // assert that Ron is still Ron
        List<Lead> rons = [select FirstName,LastName from Lead where LastName = 'Fisher' and Company = 'PSI'];
        for(Lead ron: rons){
            system.assertEquals('Ron', ron.FirstName, 'The name should have been Ron');
        }

        // assert that Matthew became Matt
        List<Lead> matthews = [select FirstName,LastName from Lead where LastName = 'Poer' and Company = 'PSI'];
        for(Lead matthew: matthews){
            system.assertEquals('Matt', matthew.FirstName, 'The name should have been adjusted to Matt, not Matthew');
        }

    }
}